Article

Unique Gap Structure and Symmetry of the Charge Density Wave in Single-Layer VSe 2

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Abstract

Single layers of transition metal dichalcogenides (TMDCs) are excellent candidates for electronic applications beyond the graphene platform; many of them exhibit novel properties including charge density waves (CDWs) and magnetic ordering. CDWs in these single layers are generally a planar projection of the corresponding bulk CDWs because of the quasi-two-dimensional nature of TMDCs; a different CDW symmetry is unexpected. We report herein the successful creation of pristine single-layer VSe2, which shows a (7×3) CDW in contrast to the (4×4) CDW for the layers in bulk VSe2. Angle-resolved photoemission spectroscopy from the single layer shows a sizable (7×3) CDW gap of ∼100 meV at the zone boundary, a 220 K CDW transition temperature twice the bulk value, and no ferromagnetic exchange splitting as predicted by theory. This robust CDW with an exotic broken symmetry as the ground state is explained via a first-principles analysis. The results illustrate a unique CDW phenomenon in the two-dimensional limit.

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... 1T -VSe 2 is a group-5 TMD that has gathered significant attention because of the dramatic change in its electronic properties and emergent phenomena in the monolayer limit, including; strongly enhanced CDW order [8,9], a metal-to-insulator transition at high temperature [10], and possible room-temperature ferromagnetism [11,12] which remains controversial [9,13]. A zoo of charge-ordered phases with various symmetries have been found [8,14,15], and linked to substrate interactions, opening the possibility of strain engineering [16]. ...
... 1T -VSe 2 is a group-5 TMD that has gathered significant attention because of the dramatic change in its electronic properties and emergent phenomena in the monolayer limit, including; strongly enhanced CDW order [8,9], a metal-to-insulator transition at high temperature [10], and possible room-temperature ferromagnetism [11,12] which remains controversial [9,13]. A zoo of charge-ordered phases with various symmetries have been found [8,14,15], and linked to substrate interactions, opening the possibility of strain engineering [16]. ...
... Bulk 1T -VSe 2 undergoes a CDW transition at T CDW ≈ 110 K, resulting in a rearrangement of the electronic structure and a small bandgap of ∼ 10 meV [40] opening on portions of the V-3d electron pockets centered around theM points of the two-dimensional Brillouin zone (BZ) [8,45], although significant k z dispersion should also be considered [46,47]. As shown in Fig. 1a, this manifests as a slight increase in the electrical resistance near T CDW due to the partially gapped Fermi surface, before exhibiting overall metallic behaviour as the temperature is reduced further [48]. ...
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A charge-density-wave (CDW) is characterized by a dynamical order parameter consisting of a time-dependent amplitude and phase, which manifest as optically-active collective modes of the CDW phase. Studying the behaviour of such collective modes in the time-domain, and their coupling with electronic and lattice order, provides important insight into the underlying mechanisms behind CDW formation. In this work, we report on femtosecond broadband transient reflectivity experiments on bulk 1T-VSe2 using near-infrared excitation. At low temperature, we observe coherent oscillations associated with the CDW amplitude mode and phonons of the distorted lattice. Across the expected transition temperature at 110 K, we confirm signatures of a rearrangement of the electronic structure evident in the quasiparticle dynamics. However, we find that the amplitude mode instead softens to zero frequency at 80 K, possibly indicating an additional phase transition at this temperature. In addition, we demonstrate photoinduced CDW melting, associated with a collapse of the electronic and lattice order, which occurs at moderate excitation densities, consistent with a dominant electron-phonon CDW mechanism.
... Among TMDCs, considerable attention has been given to 1T-VSe 2 due to the claims of a 3D-CDW phase in bulk specimens below 110 K 7 , and a related multi-CDW phase appearing in monolayers over a wide range of temperatures [8][9][10] as well as various anomalies in transport and magnetic measurements [11][12][13] . In particular, the surface electronic structure of 1T-VSe 2 has been the subject of many studies reporting an overall good agreement between experimental data and ab initio calculations [7][8][9][10] . ...
... Among TMDCs, considerable attention has been given to 1T-VSe 2 due to the claims of a 3D-CDW phase in bulk specimens below 110 K 7 , and a related multi-CDW phase appearing in monolayers over a wide range of temperatures [8][9][10] as well as various anomalies in transport and magnetic measurements [11][12][13] . In particular, the surface electronic structure of 1T-VSe 2 has been the subject of many studies reporting an overall good agreement between experimental data and ab initio calculations [7][8][9][10] . The main features of the electronic structure are a flower-like, V-3d derived Fermi surface and highly dispersive Se-4p derived bands that nearly touch the Fermi level at the Brillouin zone center. ...
... The corresponding 3D hexagonal Brillouin zone is shown in Fig. 1b. The band structure of stoichiometric 1T-VSe 2 is known to be topologically trivial [7][8][9][10] . Keeping this in mind, DFT calculations are used to identify the atomic and orbital characters of the electronic states and explore possible band inversion experimentally. ...
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Transition metal dichalcogenides exhibit many fascinating properties including superconductivity, magnetic orders, and charge density wave. The combination of these features with a non-trivial band topology opens the possibility of additional exotic states such as Majorana fermions and quantum anomalous Hall effect. Here, we report on photon-energy and polarization dependent spin-resolved angle-resolved photoemission spectroscopy experiments on single crystal 1T-VSe2, revealing an unexpected band inversion and emergent Dirac nodal arc with spin-momentum locking. Density functional theory calculations suggest a surface lattice strain could be the driving mechanism for the topologically nontrivial electronic structure of 1T-VSe2.
... ‡ Contact author: liaozm@pku.edu.cn this context, 1T-vanadium diselenide (VSe 2 ) stands out as an intriguing candidate. 1T-VSe 2 , a member of the TMD family, undergoes a CDW transition with decreasing temperature [25][26][27][28][29][30], which significantly alters its electronic structure and symmetry properties [31][32][33][34][35][36][37][38]. This CDW phase transition provides an excellent platform to explore the interplay between symmetry breaking, band geometric properties, and nonlinear transport phenomena. ...
... This is expected by considering that the emerging CDW in 1T-VSe 2 is not identical along three wave vector directions. The anisotropic CDW modulation would break the original rotational invariance of the crystal lattice and result in lowersymmetry structure of the charge distribution [31,32,46,47]. The material might conduct electricity more easily along the direction of the CDW than perpendicular to it. ...
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We report the observation of a pronounced third-order nonlinear Hall effect (NLHE) in 1T-phase VSe2_2 nanosheets, synthesized using chemical vapor deposition (CVD). The nanosheets exhibit a charge density wave (CDW) transition at \sim77 K. Detailed angle-resolved and temperature-dependent measurements reveal a strong cubic relationship between the third-harmonic Hall voltage V3ωV_{3\omega}^\perp and the bias current IωI_\omega, persisting up to room temperature. Notably, the third-order NLHE demonstrates a twofold angular dependence and significant enhancement below the CDW transition temperature, indicative of threefold symmetry breaking in the CDW phase. Scaling analysis suggests that the intrinsic contribution from the Berry connection polarizability tensor is substantially increased in the CDW phase, while extrinsic effects dominate at higher temperatures. Our findings highlight the critical role of CDW-induced symmetry breaking in modulating quantum geometric properties and nonlinear transport phenomena in VSe2_2, paving the way for future explorations in low-dimensional quantum materials.
... In this approximation, the gap size was estimated to be between 20 meV to 50 meV. More recently, high-resolution angle-resolved photoemission spectroscopy (ARPES) experiments, however, did not report an energy gap around the M(L) point of the Brillouin zone [10][11][12], where spectral distortions are expected to be stronger due to coincidence with the CDW wave vector. On the other hand, a small gap of 12 meV was detected by scanning tunneling spectroscopy (STM) [13]. ...
... The LH Fermi surface exhibits ellipsoidal pockets centered at the M(M ′ ) points and an intense spectral feature in the zone center due to Se 4p-atomic orbitals (Figure 2a). The electronic structure along the M-Γ-M ′ direction looks identical to the previous reports [8][9][10][11][12][13][14][15][16][17][18]. However, the Fermi level momentum distribution curve (MDC) given above the spectrum shows weak shoulders, indicating the presence of two distinct bands close to the Fermi level (see dashed pink and yellow lines in Figure 2b). ...
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Periodic lattice distortion, known as the charge density wave, is generally attributed to electron–phonon coupling. This correlation is expected to induce a pseudogap at the Fermi level in order to gain the required energy for stable lattice distortion. The transition metal dichalcogenide 1T-VSe2 also undergoes such a transition at 110 K. Here, we present detailed angle-resolved photoemission spectroscopy experiments to investigate the electronic structure in 1T-VSe2 across the structural transition. Previously reported warping of the electronic structure and the energy shift of a secondary peak near the Fermi level as the origin of the charge density wave phase are shown to be temperature independent and hence cannot be attributed to the structural transition. Our work reveals new states that were not resolved in previous studies. Earlier results can be explained by the different dispersion natures of these states and temperature-induced broadening. Only the overall size of the Fermi surface is found to change across the structural transition. These observations, quite different from the charge density wave scenario commonly considered for 1T-VSe2 and other transition metal dichalcogenides, bring fresh perspectives toward correctly describing structural transitions. Therefore, these new results can be applied to material families in which the origin of the structural transition has not been resolved.
... In this approximation, the gap size was estimated between 20 meV to 50 meV. More recently, high-resolution angle-resolved photoemission spectroscopy (ARPES) experiments, however, did not report an energy gap around the M(L)-point of the Brillouin zone [10][11][12], where spectral distortions are expected to be stronger due to coincidence with the CDW wave vector. On the other hand, a small gap of 12 meV was detected by scanning tunneling spectroscopy (STM) [13]. ...
... The LH Fermi surface exhibits ellipsoidal pockets centered at the M(M ′ )-points and an intense spectral feature in the zone center due to Se 4p-atomic orbitals (Figure 2(a)). The electronic structure along the M -Γ -M ′ direction looks identical to the previous reports [8][9][10][11][12][13][14][15][16][17][18]. But the Fermi level energy distribution curve (EDC) given above the spectrum shows weak shoulders indicating the presence of two distinct bands close to the Fermi level (see dashed pink and yellow lines in Figure 2(b)). ...
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The electronic origin of the structural transition in 1T-VSe2_2 is re-evaluated through an extensive angle-resolved photoemission spectroscopy experiment. The components of the band structure, missing in previous reports, are revealed. Earlier observations, shown to be temperature independent and therefore not correlated with the phase transition, are explained in terms of the increased complexity of the band structure close to the Fermi level. Only the overall size of the Fermi surface is found to be positively correlated with the phase transition at 110 K. These observations, quite distant from the charge density wave scenario commonly considered for 1T-VSe2_2, bring fresh perspectives toward the correct description of structural transitions in dichalcogenides materials.
... In addition, the CDW gap opening (electron instabilities) is less studied. The location of the CDW gap in the Brillouin zone (BZ) can be identified by band unfolding [13][14][15], which, however, requires prior knowledge of the CDW structure and cannot reveal the underlying mechanism. Thus, the driving force of the CDW gap is still elusive. ...
... where f (ε) is the Fermi-Dirac function at energy ε and δ is the delta function. The peak in χ q indicates the instability of the electronic system, while χ q is a direct measurement of the Fermi surface topology [4,15,40]. Generally, χ q and χ q produce similar fluctuations, but one should note that although we use a small value to broaden the δ function due to the finite k points, only χ q can really capture electronic information above and below the Fermi surface (hidden nesting) [4,33,41]. As discussed in the main text, there are two theoretical methods to obtain the EPC matrix elements. ...
Article
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The origin of the charge density wave (CDW) in transition metal dichalcogenides has been hotly debated, and no conclusive agreement has been reached. Here, we propose an ab initio framework for an accurate description of both Fermi surface nesting and electron-phonon coupling (EPC) and systematically investigate their roles in the formation of the CDW. Using monolayer 1H−NbSe2 and 1T−VTe2 as representative examples, we show that it is the momentum-dependent EPC that softens the phonon frequencies, which become imaginary (phonon instabilities) at CDW vectors (indicating CDW formation). In addition, the distribution of the CDW gap opening (electron instabilities) can be correctly predicted only if EPC is included in the mean-field model. These results emphasize the decisive role of EPC in the CDW formation. Our analytical process is general and can be applied to other CDW systems.
... The purple circle located at the bottom of the map marked with coordinates (0, 0) encompasses materials in which the bandgap remains zero both before and after the CDW transition. Although, usually a k-dependent non-zero CDW gap can be defined in these systems [47][48][49][50][51][52][53][54] . The purple dots on the gray oval background represent the material in which the bandgap really opens after the CDW transition, but the bandgap opening is quite small and in a range of 0.04-0.6 ...
Article
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Charge density wave (CDW) is the phenomenon of a material that undergoes a spontaneous lattice distortion and modulation of the electron density. Typically, the formation of CDW is attributed to Fermi surface nesting or electron-phonon coupling, where the CDW vector (QCDW) corresponds to localized extreme points of electronic susceptibility or imaginary phonon frequencies. Here, we propose a new family of multiple CDW orders, including chiral Star-of-David configuration in nine 2D III2–VI3 van der Waals materials, backed by first-principles calculations. The distinct feature of this system is the presence of large and flat imaginary frequencies in the optical phonon branch across the Brillouin zone, which facilitates the formation of the diverse CDW phases. The electronic structures of 2D III2–VI3 materials are relatively simple, with only III-s,p and VI-p orbitals contributing to the formation of the CDW order. Despite that, the CDW transitions involve both metal-to-insulator and insulator-to-insulator transitions, accompanied by a significant increase in the bandgap caused by an enhanced electronic localization. Our study not only reveals a new dimension in the family of 2D CDWs, but is also expected to offer deeper insights into the origins of the CDWs.
... The CDW can also manifest in systems with higher dimensions, wherein the CDW formation mechanisms tend to be more intricate and typically specific to the materials involved [12][13][14]. These materials include two-dimensional (2D) layered transition-metal dichalcogenides such as NbSe 2 , TiSe 2 , TaS 2 , VSe 2 , and VTe 2 [15][16][17][18][19][20][21], quasi-2D kagome materials AV 3 Sb 5 (A=K, Rb, Cs) [22][23][24][25][26], kagome magnet FeGe [27,28], quasi-2D rare-earth tritelluride family [2], and 5 f -electron uranium [29][30][31] as well as kagome intermetallic ScV 6 Sn 6 [32][33][34] with three-dimensional (3D) character. ...
... The CDW can also manifest in systems with higher dimensions, wherein the CDW formation mechanisms tend to be more intricate and typically specific to the materials involved [12][13][14]. These materials include two-dimensional (2D) layered transition-metal dichalcogenides such as NbSe 2 , TiSe 2 , TaS 2 , VSe 2 , and VTe 2 [15][16][17][18][19][20][21], quasi-2D kagome materials AV 3 Sb 5 (A=K, Rb, Cs) [22][23][24][25][26], kagome magnet FeGe [27,28], quasi-2D rare-earth tritelluride family [2], and 5 f -electron uranium [29][30][31] as well as kagome intermetallic ScV 6 Sn 6 [32][33][34] with three-dimensional (3D) character. ...
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Recently, a first-order phase transition associated with charge density wave (CDW) has been observed at low temperatures in intermetallic compound BaFe2_2Al9_9. However, this transition is absent in its isostructural sister compound BaCo2_2Al9_9. Consequently, an intriguing question arises as to the underlying factors that differentiate BaFe2_2Al9_9 from BaCo2_2Al9_9 and drive the CDW transition in BaFe2_2Al9_9. Here, we set out to address this question by conducting a comparative \emph{ab initio} study of the electronic structures, lattice dynamics, \textcolor{black}{and electron-phonon interactions} of their high-temperature phases. We find that both compounds are dynamically stable with similar phonon dispersions. The electronic structure calculations reveal that both compounds are nonmagnetic metals; however, they exhibit distinct band structures around the Fermi level. In particular, BaFe2_2Al9_9 exhibits a higher density of states at the Fermi level with dominant partially filled Fe-3d states and a more intricate Fermi surface. This leads to an electronic instability of BaFe2_2Al9_9 toward the CDW transition, which is manifested by the diverged electronic susceptibility at the CDW wave vector qCDW\mathbf{q}_{\rm CDW}=(0.5, 0, 0.3), observable in both the real and imaginary parts. Conversely, BaCo2_2Al9_9 does not display such behavior, aligning well with experimental observations. Although the electron-phonon interactions in BaFe2_2Al9_9 surpass those in BaCo2_2Al9_9 by two orders of magnitude, the strength is relatively weak at the CDW wave vector, suggesting that the CDW in BaFe2_2Al9_9 is primarily driven by electronic factors.
... First-principles methods based on the density-functional theory (DFT) have made great successes in calculating electronic structures of solid states. Within this framework, supercells are widely used to model doping and interface [1][2][3][4][5][6][7][8][9][10][11]. Unfortunately, the use of supercells leads to band folding, which hides the nature of the band structure. ...
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We introduce a program named KPROJ that unfolds the electronic and phononic band structure of materials modeled by supercells. The program is based on the k\textit{k}-projection method, which projects the wavefunction of the supercell onto the k{\textbf{k}}-points in the Brillouin zone of the artificial primitive cell. It allows for obtaining an effective "local" band structure by performing partial integration over the wavefunctions, e.g., the unfolded band structure with layer-projection for interfaces and the weighted band structure in the vacuum for slabs. The layer projection is accelerated by a scheme that combines the Fast Fourier Transform (FFT) and the inverse FFT algorithms. It is now interfaced with a few first-principles codes based on plane waves such as VASP, Quantum Espresso, and ABINIT. In addition, it also has interfaces with ABACUS, a first-principles simulation package based on numerical atomic basis sets, and PHONOPY, a program for phonon calculations.
... This was the first study to demonstrate that the CDW of single layer 1T-VSe 2 is coupled with its magnetic properties 9 . Despite room temperature ferromagnetism being reproduced in some cases, such as for a chemically exfoliated monolayer 10 , there have been several conflicting reports of the magnetic properties and the interplay between the CDW state and magnetism [9][10][11][12][13][14][15][16][17][18][19][20][21][22] . For example, some studies have found the nonmagnetic CDW phase to be experimentally favorable, with an inherent absence of ferromagnetism [13][14][15][16] . ...
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Two-dimensional (2D) 1T-VSe2_2 has prompted significant interest due to the discrepancies regarding alleged ferromagnetism (FM) at room temperature, charge density wave (CDW) states and the interplay between the two. We employed a combined Diffusion Monte Carlo (DMC) and density functional theory (DFT) approach to accurately investigate the magnetic properties and response of strain of monolayer 1T-VSe2_2. Our calculations show the delicate competition between various phases, revealing critical insights into the relationship between their energetic and structural properties. We went on to perform Classical Monte Carlo simulations informed by our DMC and DFT results, and found the magnetic transition temperature (TcT_c) of the undistorted (non-CDW) FM phase to be 228 K and the distorted (CDW) phase to be 68 K. Additionally, we studied the response of biaxial strain on the energetic stability and magnetic properties of various phases of 2D 1T-VSe2_2 and found that small amounts of strain can enhance the TcT_c, suggesting a promising route for engineering and enhancing magnetic behavior. Finally, we synthesized 1T-VSe2_2 and performed Raman spectroscopy measurements, which were in close agreement with our calculated results. Our work emphasizes the role of highly accurate DMC methods in advancing the understanding of monolayer 1T-VSe2_2 and provides a robust framework for future studies of 2D magnetic materials.
... Bulk 1T-TiSe 2 can also be superconducting with the CDW suppressed by either Cu intercalation 2 or pressure 4,12 . Although the intrinsic ferromagnetism is still under debate, the interplay between CDW and ferromagnetic order in 1T-VSe 2 provides a fertile ground for achieving a Curie temperature higher than 330 K 3,13,14 , which is prominently high among ferromagnetic transition temperatures in two-dimensional magnets. Given that CDWs often play a critical role in the formation of magnetic order or superconductivity, exploring the related ground and excited states becomes crucial. ...
... 14) or indium atom chains on Si (ref. 15), and kinks in the temperature-dependent conductivity of 2D materials in which only part of the Fermi surface becomes gapped in the CDW phase 4,16 . Whereas CDW pinning at individual defects was imaged locally by scanning tunnelling microscopy (STM) 5,17,18 , the defect-induced low-energy phase dynamics have thus far been observed with techniques that averaged over ensembles of defects: neutron scattering found dispersing phase excitations down to 0.25 THz (ref. ...
Article
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Charge density waves are wave-like modulations of a material’s electron density that display collective amplitude and phase dynamics. The interaction with atomic impurities induces strong spatial heterogeneity of the charge-ordered phase. Direct real-space observation of phase excitation dynamics of such defect-induced charge modulation is absent. Here, by utilizing terahertz pump–probe spectroscopy in a scanning tunnelling microscope, we measure the ultrafast collective dynamics of the charge density wave in the transition metal dichalcogenide 2H-NbSe2 with atomic spatial resolution. The tip-enhanced electric field of the terahertz pulses excites oscillations of the charge density wave that vary in magnitude and frequency on the scale of individual atomic impurities. Overlapping phase excitations originating from the randomly distributed atomic defects in the surface create this spatially structured response of the charge density wave. This ability to observe collective charge order dynamics with local probes makes it possible to study the dynamics of correlated materials at the intrinsic length scale of their underlying interactions.
... On the one hand, theoretical predictions have suggested that because of the strong EPC, a √ 7 × √ 3 2D CDW superstructures may be favored in the freestanding monolayer 1T-VSe 2 [73]. While depending on the substrate-induced strain as well as the preparation conditions [74][75][76][77][78][79], various CDW phases, including 2 × 2, 4 × 4, 2 × √ 3, 4 × √ 3, and √ 7 × √ 3 2D CDW superstructures have been observed experimentally in the monolayer 1T-VSe 2 [80][81][82][83][84][85][86][87]. On the other hand, because of the strong FS nesting and EPC effects, a 4 × 4 × 3 3D CDW superstructure is favored in the bulk 1T-VSe 2 [73,[88][89][90][91][92][93][94]. ...
Article
By employing the first-principles calculations, the influence mechanism of external pressure and charge doping on the electron-phonon coupling (EPC) and superconductivity (SC) of bulk VSe2 is investigated. Our calculations reveal that with increasing pressure the charge density wave (CDW) of 1T−VSe2 is gradually suppressed, and a SC state subsequently emerges which is accompanied by a structural phase transition from the trigonal phase to a monoclinic phase at 15.5GPa. Increasing pressure from 15.5 to 35GPa, the SC transition temperature Tc of VSe2 slightly increases from 4.2 to 5.2K and no SC dome is found, which are in good agreement with the previous experimental results [S. Sahoo et al., Phys. Rev. B 101, 014514 (2020)]. Through electron- or hole-doping (denoted by ne and nh), the CDW order of the trigonal phase can be suppressed and SC states with Tc greater than 10.5 and 9.0K, respectively, emerge. The highest Tc under charge doping can be up to about 12K, and a weak double-dome like dependence of Tc on ne and nh is found. Combining systematical analysis of effects of pressure and charge doping, we demonstrate that the Kohn anomalies of phonons at certain Q points associated with the in-plane vibrations of V atoms play key roles in strengthening the EPC, which brings about the intriguing SC in VSe2. However, due to the weak pressure-induced modifications of phonon spectrum as well as Fermi surface (FS), the changes of EPC and Tc caused by pressure are not significant. Interestingly, charge doping will produce a local flat band along ΓA direction near the FS, which is mainly contributed by V 3d-orbitals, and result in large values of electronic density of states at Fermi level. Therefore, the effects caused by charge doping to the electronic structures, phonon anomalies, EPC, and Tc are evident. Our findings may provide a promising understanding to the pressure and doping-dependent SC of VSe2, and may be valuable for designing new materials with enhanced SC through the strategic manipulation of electronic and phononic properties.
... They are expected to host plentiful structures with exotic properties, such as the in-plane anomalous Hall effect in the VS2-VS superlattice with symmetry breaking, as reported in our previous work (24). Associated with the debatable 2D magnetic properties, 2D VX2 systems show distinct layer-dependent CDW states with reducing dimensionality (25)(26)(27)(28)(29). Specifically, the monolayer VS2 and VSe2 show various CDW superlattices with rotational symmetry breaking, such as √7 × √3 (29,30), while the monolayer VTe2 owns a modulated 4 × 4 CDW order, following the symmetry of its Bragg lattice (31,32). These CDW states with different periods and symmetries imply that multiple driven forces may contribute to the formation of CDW, in addition to the conventional electronphonon coupling. ...
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As a fundamental structural feature, the symmetry of materials determines the exotic quantum properties in transition metal dichalcogenides (TMDs) with charge density wave (CDW). Breaking the inversion symmetry, the Janus structure, an artificially constructed lattice, provides an opportunity to tune the CDW states and the related properties. However, limited by the difficulties in atomic-level fabrication and material stability, the experimental visualization of the CDW states in 2D TMDs with Janus structure is still rare. Here, using surface selenization of VTe2, we fabricated monolayer Janus VTeSe. With scanning tunneling microscopy, an unusual root13-root13 CDW state with threefold rotational symmetry breaking was observed and characterized. Combined with theoretical calculations, we find this CDW state can be attributed to the charge modulation in the Janus VTeSe, beyond the conventional electron-phonon coupling. Our findings provide a promising platform for studying the CDW states and artificially tuning the electronic properties toward the applications.
... We would like to emphasize that such a nesting vector causes a partial nesting of the Fermi surface, which is distinct from the perfect-nesting cases when slices (and not just discrete points) of a Fermi surface are connected by the same nesting vector. The evidence of incommensurate CDW orderings has been reported in materials like NbSe 2 and TaS 2 [69,70], VSe 2 [71], SmTe 3 [72], and TbTe 3 [73]. In some of these compounds, the CDW transition temperature can be tuned close to zero Kelvin by applying high pressure, unravelling a putative quantum critical point at the onset of the CDW ordering [74]. ...
... In the monolayer (ML) limit, 1T-type TMDs involving Se such as 1T-NbSe 2 and 1T-TaSe 2 have been found to exhibit strongly enhanced CDW order, where the temperature at which it sets in, T CDW(ML) , is higher than T CDW(3D) in the respective bulk material [63,64]. For example, while in bulk 1T-NbSe 2 the CDW order sets in at T CDW(3D) = 33.5 K, the CDW transition in a 1T-NbSe 2 monolayer takes place at T CDW(ML) = 145 K. Single-layer 1T-VSe 2 has also been reported to exhibit strongly enhanced CDW order, where T CDW(ML) = 220 K is nearly twice the bulk value of T CDW(3D) = 110 K. Contrary to the case of 1T-NbSe 2 , however, the CDW periodicity in a 1T-VSe 2 monolayer appears different from that of the layers in bulk 1T-VSe 2 [65]. It has been reported that a supported 1T-TiSe 2 monolayer preserves the 2a 0 × 2a 0 CDW periodicity of the stacked layers in bulk 1T-TiSe 2 and, furthermore, exhibits CDW order below T CDW(ML) = 232(5) K [44,53,66], which is the same as T CDW(2D) for the stacked layers forming bulk 1T-TiSe 2 . ...
Article
Using variable temperature atomic pair distribution function analysis, we study the emergence of charge density wave (CDW) order in 1T−TiSe2 and find that it takes place via a two-step transition. First, upon decreasing temperature to about 235(3) K, CDW-related lattice distortions emerge in the individual TiSe2 layers alone. Then, upon further decreasing the temperature, the two-dimensional distortions in the layers couple and the widely recognized three-dimensional 2a0×2a0×2c0 superstructure emerges at about 205(3) K. Because two different band gaps are known to emerge at the same temperatures, the finding indicates the presence of strong electron-phonon coupling. The transient phase between the two steps lacks inversion symmetry and may serve as a precursor of the debated chiral 1T-TiSe2 phase. Our findings are important for the understanding of the enigmatic CDW transition in 1T-TiSe2 and CDW instabilities in van der Waals materials in general.
... It was reported that VSe 2 monolayers grown on vdW substrates exhibit strong ferromagnetism [35], while some studies have reported that VSe 2 monolayers grown via molecular-beam epitaxy lack intrinsic ferromagnetism [54]. It is claimed that there is a charge density wave (CDW) transition at~110 K, and the CDW order competes with the ferromagnetic order [55][56][57]. It is assumed that the standalone 1T-VSe 2 monolayer is ferromagnetic (suggested by DFT calculations), and all the NAMD simulations and discussions are based on that presumption. ...
Article
Using photoexcitation to manipulate the magnetic moment in two-dimensional (2D) materials paves the way for the design of opto-spintronic devices. In this work, using ab initio nonadiabatic molecular dynamics simulation, we studied how photoexcitation changed the magnetic moment in the 2D ferromagnetic metal VSe2. The spin-orbit coupling and phonon excitation lead to the loss of the original spin orientation in both the spin-up and spin-down orbitals, forming a spin-mixing region approximately 1.0 eV above the Fermi level. When spin-up or spin-down electrons pass through this region during relaxation, they lose their original spin orientation. However, spin-down electrons relax approximately an order of magnitude faster than spin-up electrons, as the relaxation for spin-down is primarily intraband, while spin-up electrons undergo interband relaxation. Such different dynamical behaviors for spin-up and spin-down electrons result in the magnetic moment of VSe2 initially rising within approximately 10 fs after optical excitation, corresponding to the loss of the original spin orientation for spin-down electrons. Subsequently, it decreases by approximately 100 fs, corresponding to the loss of spin orientation for spin-up electrons. Finally, the total magnetic moment of the system gradually recovers to the preexcitation level on the order of picoseconds. This work provides new insight into how photoexcitation controls the magnetic properties of 2D materials.
... Monolayers of TMDCs interact by weak out-of-plane vdWs forces only, allowing bulk single crystals to be easily isolated to the monolayer limit, considered two-dimensional (2D) materials, with reduced dimensions effects and minimal interlayer interactions. Specific TMDCs have shown thickness dependent bandgap tuning [3][4][5][6][7], superconductivity properties [8][9][10][11], charge density waves instability [12][13][14][15][16][17] and ferromagnetic ordering [18][19][20], to name a few exciting properties. Moreover, extended ability to tune electronic and magnetic properties of TMDCs by external processes, such as controlled layer-by-layer growth with different stoichiometries, external doping, and stacking of distinct vdW layers in heterostructures could expand application of these materials in electronic devices. ...
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Transition metal dichalcogenides (TMDCs) are materials with unique electronic properties due to their two-dimensional nature. Recently, there is a large and growing interest in synthesizing ferromagnetic TMDCs for applications in electronic devices and spintronics. Apart from intrinsically magnetic examples, modification via either intrinsic defects or external dopants may induce ferromagnetism in non-magnetic TMDCs and, hence expand the application of these materials. Here, we review recent experimental work on intrinsically non-magnetic TMDCs that present ferromagnetism as a consequence of either intrinsic defects or doping via self-flux approach, ion implantation or e-beam evaporation. The experimental work discussed here is organized by modification/doping mechanism. We also review current work on DFT calculations that predict ferromagnetism in doped systems, which also serve as preliminary data for the choice of new doped TMDCs to be explored experimentally. Implementing a controlled process to induce magnetism in 2D materials is key for technological development and this topical review discusses the fundamental procedures while presenting promising materials to be investigated in order to achieve this goal.
... [33] On the other hand, the imaginary part ′′ ( ) reflects the information of FS nesting. [34] From Fig. 6(d), it can be seen that the strongest peak in ′′ ( ) locates at the middle point of the -path, indicating that the nesting vector is around (0.25 * , 0.25 * ). In addition, weaker peaks of ′′ ( ) show up at the CDW wave vector CDW = 0.5 * . ...
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Magnetic CeTe 2 achieving superconductivity under external pressure has received considerable attention. The intermingling of 4 f and 5 d electrons from Ce raised the speculation of an unconventional pairing mechanism arising from magnetic fluctuations. Here, we address this speculation using a nonmagnetic 4 f -electron-free LaTe 2 as an example. No structural phase transition can be observed up to 35 GPa in the in situ synchrotron diffraction patterns. Subsequent high-pressure electrical measurements show that LaTe 2 exhibits superconductivity at 20 Gpa with its T c (4.5 K) being two times higher than its Ce-counterpart. Detailed theoretical calculations reveal that charge transfer from the 4 p orbitals of the planar square Te–Te network to the 5 d orbitals of La is responsible for the emergence of superconductivity in LaTe 2 , as confirmed by Hall experiments. Furthermore, we study the modulation of q CDW by Sb substitution and find a record high T c onset ∼ 6.5 K in LaTe 1.6 Sb 0.4 . Our work provides an informative clue to comprehend the role of 5 d –4 p hybridization in the relationship between charge density wave (CDW) and superconductivity in these RETe 2 (RE = rare-earth elements) compounds.
... 2D van der Waals (vdW) magnetic materials have attracted much attention recently because of their potential for the understanding of 2D ferromagnetism and spintronic applications. There are various types of 2D vdW magnetic materials including ferromagnetic (FM) semiconductors like MX2 (M = V, Mn, X = S, Se) [1][2][3] and Ce 2 GeTe 6 [4,5], FM insulators like CrI 3 [6], CrBr 3 [7], CrSBr [8], and FM metals like CrTe 2 [9] and Fe 3 GeTe 2 [10,11]. Among the 2D vdW FM metal family, Fe n GeTe 2 (n = 3, 4, 5) (F n GT) [12] is quite intensively studied due to its intriguing magnetic properties such as strong perpendicular magnetic anisotropy (PMA), large anomalous Hall effect (AHE) and anomalous Nernst effect (ANE), high Curie temperatures (T c ), and easy mechanical exfoliation down to monolayer. ...
... To address this problem, we select a nanohybrid of VSe 2 an emerging TMD in recent times [29][30][31] and a single-wall carbon nanotube (SWCNT) [32,33] as the donor-accepter pair. Our motivation to stem out for selecting these materials is (1) VSe 2 is a two-dimensional (2D) material with high carrier mobility [34], exceptional intercalation activity [35], unique charge-density wave [36] and other excellent characteristics to become a good candidate for donor material and (2) one-dimensional (1D) SWCNTs made of one-atom-thick graphene sheet showing van Hove singularities in their density of states is an excellent candidate for acceptor material [37]. ...
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An ideal third-order nonlinear optical material, which can efficiently absorb and refract light over a broad spectral range, is of both fundamental and technological significance as it enables many helpful functionalities in photonics. However, the optical nonlinearities are rather weak due to their perturbative nature and are limited to electronic resonances, thus restricting the response to a narrow spectral range. A charge-coupled donor-acceptor material pair can enhance the nonlinear optical response and circumvent the narrow spectral range limitation. However, such studies on potential material pairs remain largely unexplored. Here, we report the experimental observation of ultrafast third-order nonlinear optical response spanning the entire visible-to-near-infrared (400–900 nm) region in single-wall-carbon-nanotube (SWCNT)–VSe2 nanohybrid in the strong coupling regime, enabled by efficient charge transfer. Compared to control systems, the measured nonlinear absorption and refraction of the nanohybrid show unprecedented or many-fold enhancements. Further, our density-functional theory and Bader-charge analysis show the strong electronic coupling of the nanohybrid in which the electrons are transferred from VSe2 to SWCNT, verified by steady-state and time-resolved photoluminescence measurements. The physics of the ultrafast nonlinear optical response is well captured by our five-level rate-equation model both qualitatively and quantitatively. Using the nanohybrid, we design a liquid cell-based optical limiter with an order of magnitude better device performance parameters, such as the optical limiting onset (2.5–8.0mJcm−2) and the differential transmittance (0.42–0.62), compared to several other benchmark optical limiters in the femtosecond regime.
... Two-dimensional materials beyond graphene attract much attention in last decade. [1][2][3][4][5][6][7][8] These structures are usually constructed from several layers connected with non-covalent interlayer bonds. So-called van der Waals heterostructures constructed from various monolayer 9-12 are also considered as key materials with multiple prospective applications in electronics, [13][14][15] energy storage, [16][17][18] electro- [19][20][21] and photo-catalysis, 22 sensing, 23-25 magnetism 26 etc. ...
Preprint
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Van der Waals heterostructures have emerged as an ideal platform for creating engineered artificial electronic states. While vertical heterostructures have been extensively studied, realizing high-quality lateral heterostructures with atomically sharp interfaces remains a major experimental challenge. Here, we advance a one-pot two-step molecular beam lateral epitaxy approach and successfully synthesize atomically well-defined 1T-VSe2_2 -- 1H-NbSe2_2 lateral heterostructures. We demonstrate the formation of defect-free lateral heterostructures and characterize their electronic structure using scanning tunnelling microscopy and spectroscopy together with density functional theory calculations. We find additional electronic states at the one-dimensional interface as well as signatures of Kondo resonances in a side-coupled geometry. Our experiments explore the full potential of lateral heterostructures for realizing exotic electronic states in low-dimensional systems for further studies of artificial designer quantum materials.
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The advent of 2D materials has ushered in the exploration of their synthesis, characterization and application. While plenty of 2D materials have been synthesized on various metallic substrates, interfacial interaction significantly affects their intrinsic electronic properties. Additionally, the complex transfer process presents further challenges. In this context, experimental efforts are devoted to the direct growth on technologically important semiconductor/insulator substrates. This review aims to uncover the effects of substrate on the growth of 2D materials. The focus is on non‐metallic substrate used for epitaxial growth and how this highlights the necessity for phase engineering and advanced characterization at atomic scale. Special attention is paid to monoelemental 2D structures with topological properties. The conclusion is drawn through a discussion of the requirements for integrating 2D materials with current semiconductor‐based technology and the unique properties of heterostructures based on 2D materials. Overall, this review describes how 2D materials can be fabricated directly on non‐metallic substrates and the exploration of growth mechanism at atomic scale.
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The bulk electronic structure of AV3Sb5 (A=K, Cs) has been investigated by means of hard x-ray photoemission spectroscopy (HAXPES). The asymmetric shape of V and Sb core level peaks indicates that the V 3d and Sb 5p electrons are involved in the conduction band. The absence of a satellite structure in the V 2p HAXPES spectra shows a weak electronic correlation in the V 3d states. Splitting of the V 2p peak is not observed in the density wave phase indicating the charge disproportionation between the V sites is undetectably small, consistent with the weakness of the on-site electronic correlation and the possibility of bond order. The Sb 4d5/2 binding energy agrees with that of the Cs-terminated surface, indicating that the electronic structure of the V3Sb5 layer just below the Cs surface is close to the bulk.
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Charge density wave (CDW) is one of the most ubiquitous electronic orders in quantum materials. While the essential ingredients of CDW order have been extensively studied, a comprehensive microscopic understanding is yet to be reached. Recent research efforts on the CDW phenomena in two-dimensional (2D) materials provide a new pathway toward a deeper understanding of its complexity. This review provides an overview of the CDW orders in 2D with atomically thin transition metal dichalcogenides (TMDCs) as the materials platform. We mainly focus on the electronic structure investigations on the epitaxially grown TMDC samples with angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy as complementary experimental tools. We discuss the possible origins of the 2D CDW, novel quantum states co-existing with them, and exotic types of charge orders that can only be realized in the 2D limit.
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To characterize in detail the charge density wave (CDW) transition of 1T−VSe2, its electronic structure and lattice dynamics are comprehensively studied by means of x-ray diffraction, muon spectroscopy, angle resolved photoemission (ARPES), diffuse and inelastic x-ray scattering, and state-of-the-art first-principles density functional theory calculations. Resonant elastic x-ray scattering does not show any resonant enhancement at either V or Se, indicating that the CDW peak at the K edges describes a purely structural modulation of the electronic ordering. ARPES experiments identify (i) a pseudogap at T>TCDW, which leads to a depletion of the density of states in the ML-M'L' plane at T<TCDW, and (ii) anomalies in the electronic dispersion reflecting a sizable impact of phonons on it. A diffuse scattering precursor, characteristic of soft phonons, is observed at room temperature (RT) and leads to the full collapse of the low-energy phonon (ω1) with propagation vector (0.25 0 −0.3) r.l.u. We show that the frequency and linewidth of this mode are anisotropic in momentum space, reflecting the momentum dependence of the electron-phonon interaction (EPI), hence demonstrating that the origin of the CDW is, to a much larger extent, due to the momentum dependent EPI with a small contribution from nesting. The pressure dependence of the ω1 soft mode remains nearly constant up to 13 GPa at RT, with only a modest softening before the transition to the high-pressure monoclinic C2/m phase. The wide set of experimental data is well captured by our state-of-the art first-principles anharmonic calculations with the inclusion of van der Waals corrections in the exchange-correlation functional. The comprehensive description of the electronic and dynamical properties of VSe2 reported here adds important pieces of information to the understanding of the electronic modulations in the family of transition-metal dichalcogenides.
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Owning unique optical and electronic properties, two dimensional (2D) materials have made remarkable strides in the field of photodetection applications. However, achieving highly sensitive and ultra‐broadband detection from microwave to terahertz (THz) range (0.02–0.54 THz) remains a significant challenge for photodetectors. This study presents a self‐powered THz photodetector based on VSe 2 and its van der Waals heterostructure. The photoresponse of the photodetector is primarily attributed to the photothermoelectric effect. At room temperature, the device exhibits lower noise equivalent power values of 21 pW Hz −1/2 at 0.28 THz. This work has achieved ultra‐broadband detection and demonstrated the potential for large‐area imaging, providing a new avenue for the application of THz technology in nondestructive testing and biometric identification fields.
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A peculiar charge-density wave (CDW) phase, absent in the bulk, has been widely studied in monolayer 1T−TiTe2 and newly observed in monolayer 1T−ZrTe2, while its origin and physical properties remain unclear. Here, we study the distorted lattice and associated energy band renormalization for TiTe2 and ZrTe2 monolayers using first-principles calculations. Both systems are found to exhibit a soft phonon mode at the M point leading to a 2×2 CDW order with similar distortion pattern as in TiSe2 case. Electronic structure results with semilocal functional indicate that the CDW phases of monolayer TiTe2 and ZrTe2 maintain semimetallicity owing to their smaller lattice distortion than in the TiSe2 semiconducting CDW state. The unfolded band structure for monolayer TiTe2 reveals CDW-reconstructed features consistent with experiments, including backfolded bands from Γ to M and vice versa, as well as a stronger energy gapping of the outer valence band along Γ−M due to orbital-dependent p−d hybridization. We also explore the role of exchange interaction in the CDW formation. The nonlocal exchange effect enlarges the lattice distortion amplitude and causes an overcorrection of the electronic structure for monolayer TiTe2, while it barely affects the CDW distortion of monolayer ZrTe2, despite inducing a metal-semiconductor transition. Comparison of the CDW properties of monolayer TiSe2, TiTe2, and ZrTe2 suggests that the judgment of relative CDW strength in these systems should involve coupled electron-lattice modifications. Our work paves the way for elucidating the CDW order in two-dimensional group-IV transition-metal dichalcogenides.
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Strong electron correlation under two-dimensional limit is intensely studied in the transition metal dichalcogenides monolayers, mostly within their charge density wave (CDW) states that host a star of David period. Here, by using scanning tunneling microscopy and spectroscopy and density functional theory calculations with on-site Hubbard corrections, we study the VTe2 monolayer with a different 23×23 CDW period. We find that the dimerization of neighboring Te-Te and V-V atoms occurs during the CDW transition, and that the strong correlation effect opens a Mott-like full gap at Fermi energy (EF). We further demonstrate that such a Mott phenomenon is ascribed to the combination of the CDW transition and on-site Coulomb interactions. Our work provides a new platform for exploring Mott physics in 2D materials.
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Intrinsic room-temperature ferromagnetic ordering and inversion asymmetry of V-based transition metal dichalcogenide (TMD) monolayers with trigonal prismatic coordinates are highly desirable to develop spintronic devices. Motivated by facilitating the performance improvement of V-based TMDs in data-storage applications, we investigated the influence of the interface magnetic proximity effect, mediated by Zeeman-type spin-orbit interaction (SOI), on the magnetic exchange interaction and magnetic anisotropy of the 2H-VSe2 monolayer. It has already been observed that strain and interlayer coupling does not have a significant effect on the magnetic anisotropy of V-based TMDs. Here we demonstrate using density functional theory (DFT) that the proximity effect of the archetypal metallic material NbSe2 at the van der Waals interface induces strong out-of-plane magnetic anisotropy in 2H-VSe2. The transition of magnetization from in plane to out of plane in 2H-VSe2 holds great promise toward the realization of faster and smaller magnetic bits in lower power-consuming memory devices such as random access memories. The valley polarization of the VSe2 system is significantly reversed by applying Zeeman-type SOI of NbSe2 substrate. Also, by combining the two-band k·p model with high-throughput DFT calculations, the change of k·p parameters of 2H-VSe2 is examined due to Zeeman-type SOI induced by NbSe2.
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Reducing the Schottky barrier at the metal-semiconductor interface and achieving ohmic contacts are very important for developing high-performance Schottky field-effect devices. Base on the fact that GaN and 1T-VSe2 monolayers have been successfully prepared experimentally, we theoretically construct a GaN/1T-VSe2 heterojunction model and investigate its stability, Schottky barrier property and its modulation effects by using first-principle method. The calculated formation energy and the molecular dynamics simulations show that the constructed heterojunction is very stable, meaning that it can be realized experimentally. The intrinsic heterojunction holds a p-type Schottky contact and always remains an unchanged p-type Schottky contact when tensile or compressive strain is applied. But when the external electric field is applied, the situation is different, for example, a higher forward electric field can cause the heterojunction changed from a Schottky contact to an ohmic contact, and a higher reverse electric field can lead to a variation from a p-type Schottky contact to an n-type Schottky contact. In particular, by implementing chemical doping, the transition from Schottky contact to ohmic contact can be achieved more easily for the heterojunction, for example, the introduction of B atomic enables the GaN/1T-VSe2 heterojunction to realize a typical ohmic contact, while for C and F atom doping, it enables the GaN/1T-VSe2 heterojunction to obtain a quasi-ohmic contact. These studies provide a theoretical reference for the practical application of the suggested heterojunction, and are of very important for designing novel high-performance nano-scale electronic devices.
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The itinerant ferromagnetism can be induced by a van Hove singularity (VHS) with a divergent density of states at Fermi level. Utilizing the giant magnified dielectric constant of SrTiO3(111) substrate with cooling, here we successfully manipulated the VHS in the epitaxial monolayer (ML) 1T-VSe2 film approaching to Fermi level via the large interfacial charge transfer, and thus induced a two-dimensional (2D) itinerant ferromagnetic state below 3.3 K. Combining the direct characterization of the VHS structure via angle-resolved photoemission spectroscopy (ARPES), together with the theoretical analysis, we ascribe the manipulation of VHS to the physical origin of the itinerant ferromagnetic state in ML 1T-VSe2. Therefore, we further demonstrated that the ferromagnetic state in the 2D system can be controlled through manipulating the VHS by engineering the film thickness or replacing the substrate. Our findings clearly evidence that the VHS can serve as an effective manipulating degree of freedom for the itinerant ferromagnetic state, expanding the application potentials of 2D magnets for the next-generation information technology.
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Angle-resolved photoemission spectroscopy experiments reveal a surprisingly richer surface electronic structure in 1T−VSe2 than previously predicted or probed. Earlier claims supporting a charge density wave phase in this material are reexamined in terms of these findings and are found to be untenable. The Fermi surface is found to be gapless, while band warping effects, currently attributed to three-dimensional lattice distortion, result from the simultaneous dispersion of the closely lying multiple bands. Based on these findings, a charge density wave scenario in 1T−VSe2 is unlikely. On the other side, the presence of multiple states crossing the Fermi level should constitute relevant constraints for any viable microscopic model of the structural phase transition of VSe2.
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Previous works have controversially claimed near-room-temperature ferromagnetism in two-dimensional (2D) VSe2, with conflicting results throughout the literature. These discrepancies in magnetic properties between both phases (T and H) of 2D VSe2 are most likely due to the structural parameters being coupled to the magnetic properties. Specifically, both phases have a close lattice match and similar total energies, which makes it difficult to determine which phase is being observed experimentally. In this study, we used a combination of density functional theory, highly accurate diffusion Monte Carlo (DMC), and a surrogate Hessian line-search optimization technique to resolve the previously reported discrepancy in structural parameters and relative phase stability. With DMC accuracy, we determined the free-standing geometry of both phases and constructed a phase diagram. Our findings demonstrate the successes of the DMC method coupled with the surrogate Hessian structural optimization technique when applied to a 2D magnetic system.
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Reduced dimensionality and interlayer coupling in van der Waals materials gives rise to fundamentally different electronic1, optical2and many-body quantum3-5properties in monolayers compared with the bulk. This layer-dependence permits the discovery of novel material properties in the monolayer regime. Ferromagnetic order in two-dimensional materials is a coveted property that would allow fundamental studies of spin behaviour in low dimensions and enable new spintronics applications6-8. Recent studies have shown that for the bulk-ferromagnetic layered materials CrI3(ref.9) and Cr2Ge2Te6(ref.10), ferromagnetic order is maintained down to the ultrathin limit at low temperatures. Contrary to these observations, we report the emergence of strong ferromagnetic ordering for monolayer VSe2, a material that is paramagnetic in the bulk11,12. Importantly, the ferromagnetic ordering with a large magnetic moment persists to above room temperature, making VSe2an attractive material for van der Waals spintronics applications.
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We present the electronic characterization of single-layer 1H-TaSe2 grown by molecular beam epitaxy (MBE) using a combined angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy/spectroscopy (STM/STS), and density functional theory (DFT) calculations. We demonstrate that 3×3 CDW order persists despite distinct changes in the low energy electronic structure highlighted by the reduction in the number of bands crossing the Fermi energy (EF) and the corresponding modification of Fermi surface (FS) topology. Enhanced spin-orbit coupling and lattice distortion in the single-layer limit play a crucial role in the formation of CDW order. Our findings provide a deeper understanding of the nature of CDW order in the 2D limit.
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Isolating single unit-cell thin layers from the bulk matrix of layered compounds offers tremendous opportunities to design novel functional electronic materials. However, a comprehensive thickness dependence study is paramount to harness the electronic properties of such atomic foils and their stacking into synthetic heterostructures. Here we show that a dimensional crossover and quantum confinement with reducing thickness result in a striking non-monotonic evolution of the charge density wave transition temperature in VSe2. Our conclusion is drawn from a direct derivation of the local order parameter and transition temperature from the real space charge modulation amplitude imaged by scanning tunnelling microscopy. This study lifts the disagreement of previous independent transport measurements. We find that thickness can be a non-trivial tuning parameter and demonstrate the importance of considering a finite thickness range to accurately characterize its influence.
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Since the celebrated discovery of graphene, the family of two-dimensional (2D) materials has grown to encompass a broad range of electronic properties. Recent additions include spin-valley coupled semiconductors, Ising superconductors that can be tuned into a quantum metal, possible Mott insulators with tunable charge-density waves, and topological semi-metals with edge transport. Despite this progress, there is still no 2D crystal with intrinsic magnetism, which would be useful for many technologies such as sensing, information, and data storage. Theoretically, magnetic order is prohibited in the 2D isotropic Heisenberg model at finite temperatures by the Mermin-Wagner theorem. However, magnetic anisotropy removes this restriction and enables, for instance, the occurrence of 2D Ising ferromagnetism. Here, we use magneto-optical Kerr effect (MOKE) microscopy to demonstrate that monolayer chromium triiodide (CrI3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 K is only slightly lower than the 61 K of the bulk crystal, consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase transition, showcasing the hallmark thickness-dependent physical properties typical of van der Waals crystals. Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect, while in trilayer the interlayer ferromagnetism observed in the bulk crystal is restored. Our work creates opportunities for studying magnetism by harnessing the unique features of atomically-thin materials, such as electrical control for realizing magnetoelectronics, and van der Waals engineering for novel interface phenomena.
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A single molecular layer of titanium diselenide (TiSe2) is a promising material for advanced electronics beyond graphene-a strong focus of current research. Such molecular layers are at the quantum limit of device miniaturization and can show enhanced electronic effects not realizable in thick films. We show that single-layer TiSe2 exhibits a charge density wave (CDW) transition at critical temperature TC=232±5 K, which is higher than the bulk TC=200±5 K. Angle-resolved photoemission spectroscopy measurements reveal a small absolute bandgap at room temperature, which grows wider with decreasing temperature T below TC in conjunction with the emergence of (2 × 2) ordering. The results are rationalized in terms of first-principles calculations, symmetry breaking and phonon entropy effects. The observed Bardeen-Cooper-Schrieffer (BCS) behaviour of the gap implies a mean-field CDW order in the single layer and an anisotropic CDW order in the bulk.
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Two-dimensional materials possess very different properties from their bulk counterparts. While changes in single-particle electronic properties have been investigated extensively, modifications in the many-body collective phenomena in the exact two-dimensional limit remain relatively unexplored. Here, we report a combined optical and electrical transport study on the many-body collective-order phase diagram of NbSe2 down to a thickness of one monolayer. Both the charge density wave and the superconducting phase have been observed down to the monolayer limit. The superconducting transition temperature decreases on lowering the layer thickness, but the newly observed charge-density-wave transition temperature increases from 33 K in the bulk to 145 K in the monolayer. Such highly unusual enhancement of charge density waves in atomically thin samples can be understood to be a result of significantly enhanced electron-phonon interactions in two-dimensional NbSe2 (ref. 4) and is supported by the large blueshift of the collective amplitude vibration observed in our experiment. Our results open up a new window for search and control of collective phases of two-dimensional matter, as well as expanding the functionalities of these materials for electronic applications.
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Layered transition metal dichalcogenides (TMDs) are ideal systems for exploring the effects of dimensionality on correlated electronic phases such as charge density wave (CDW) order and superconductivity. In bulk NbSe2 a CDW sets in at TCDW = 33 K and superconductivity sets in at Tc = 7.2 K. Below Tc these electronic states coexist but their microscopic formation mechanisms remain controversial. Here we present an electronic characterization study of a single 2D layer of NbSe2 by means of low temperature scanning tunneling microscopy/spectroscopy (STM/STS), angle-resolved photoemission spectroscopy (ARPES), and electrical transport measurements. We demonstrate that 3x3 CDW order in NbSe2 remains intact in 2D. Superconductivity also still remains in the 2D limit, but its onset temperature is depressed to 1.9 K. Our STS measurements at 5 K reveal a CDW gap of {\Delta} = 4 meV at the Fermi energy, which is accessible via STS due to the removal of bands crossing the Fermi level for a single layer. Our observations are consistent with the simplified (compared to bulk) electronic structure of single-layer NbSe2, thus providing new insight into CDW formation and superconductivity in this model strongly-correlated system.
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Phonon plays essential roles in dynamical behaviors and thermal properties, which are central topics in fundamental issues of materials science. The importance of first principles phonon calculations cannot be overly emphasized. Phonopy is an open source code for such calculations launched by the present authors, which has been world-widely used. Here we demonstrate phonon properties with fundamental equations and show examples how the phonon calculations are applied in materials science.
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We show that the spectral weights WmK(k)W_{m\vec K}(\vec k) used for the unfolding of two-component spinor eigenstates ψmKSC=αψmKSC,α+βψmKSC,β\left| {\psi _{m\vec K}^\mathrm{SC}} \right\rangle = \left| \alpha \right\rangle \left| {\psi _{m\vec{K}}^\mathrm{SC, \alpha}} \right\rangle + \left| \beta \right\rangle \left| {\psi _{m\vec{K}}^\mathrm{SC, \beta}} \right\rangle can be decomposed as the sum of the partial spectral weights WmKμ(k)W_{m\vec{K}}^{\mu}(\vec k) calculated for each component μ=α,β\mu = \alpha, \beta independently, effortlessly turning a possibly complicated problem involving two coupled quantities into two independent problems of easy solution. Furthermore, we define the unfolding-density operator ρ^K(ki;ε)\hat{\rho}_{\vec{K}}(\vec{k}_{i}; \, \varepsilon), which unfolds the primitive cell expectation values φpc(k;ε)\varphi^{pc}(\vec{k}; \varepsilon) of any arbitrary operator φ^\mathbf{\hat\varphi} according to φpc(ki;ε)=Tr(ρ^K(ki;ε)φ^)\varphi^{pc}(\vec{k}_{i}; \varepsilon) = \mathit{Tr}\left(\hat{\rho}_{\vec{K}}(\vec{k}_{i}; \, \varepsilon)\,\,\hat{\varphi}\right). As a proof-of-concept, we apply the method to obtain the unfolded band structures, as well as the expectation values of the Pauli spin matrices, for prototypical physical systems described by two-component spinor eigenfunctions.
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