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# Influence of the moiré potential on the intrinsic properties of TMD heterobilayers a) False color map of the σ-PL emission from IX of S2 measured with a resolution of 10 mT in the vicinity of the two identified resonant magnetic fields. The magnetic field for every sharp peak is different and the resonance has a diagonal profile. The white line indicates the energy dependence of the excitonic g factor, whose slope is ∂g/∂E ≈ 7.5 eV −1 (at B ≈ 24.2 T) and 8.5 eV −1 (at B ≈ 24.9 T) for the two resonant magnetic fields. b) PL Emission spectrum (left axis) of the IX at B= 0 T of S2 with energy dependent g-factor value (right axis) extracted from the data of panel a.

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Optical selection rules in monolayers of transition metal dichalcogenides and of their heterostructures are determined by the conservation of the z-component of the total angular momentum - J Z = L Z +S Z - associated with the C3 rotational lattice symmetry which assumes half integer values corresponding, modulo 3, to distinct states. Here we show,...

## Contexts in source publication

**Context 1**

... high magnetic fields required to reach this resonance prevent any direct application of this effect but this very efficient scattering mechanism can play a crucial role enabling energy level lifetime engineering in optical devices. The same phenomenon is observed in sample S2 as shown in Figure 4a. Due to the slightly smaller g factor for S2, the resonant magnetic fields for this sample are B = 24.25 T and B = 24.9 ...

**Context 2**

... to the slightly smaller g factor for S2, the resonant magnetic fields for this sample are B = 24.25 T and B = 24.9 T (see Figure 4a). In contrast to S1, the resonance occurs over a broader range of magnetic fields due to different emission components composing the IX emission feature [14,49], but appears in the form of the specific diagonal feature seen in Fig- ure 4a. ...

**Context 3**

... (see Figure 4a). In contrast to S1, the resonance occurs over a broader range of magnetic fields due to different emission components composing the IX emission feature [14,49], but appears in the form of the specific diagonal feature seen in Fig- ure 4a. The exciton-phonon resonance remains nevertheless extremely sharp for each emission peak composing the broad IX emission, still occurring over a variation of magnetic field as small as 100 mT. ...

**Context 4**

... for S2 the same phonon energies as in sample S1, the finesse of this exciton-phonon coupling enables to resolve the energy dependence of the excitonic g-factor, whose slope is ∂g/∂E ≈ 7.5 and 8.5 eV −1 for the two resonant magnetic fields, respectively. We also present in Figure 4b the values of g-factor extracted close to B ∼ 24.2 T together with the zero field IX spectrum (an alternative analysis can be found in the Supplementary Information Section S9-10). The magnitude of the slope as well as the fact that the exciton g-factor is determined by the excitation energy are consistent with the standard band theory expression for the orbital contribution g orb i to the g-factor of a single-electron band i due to virtual transitions to other bands j [50]: ...

**Context 5**

... ||i|ˆp||i|ˆp ± |j| 2 /m 0 is several eV, a few times larger than nearest band energy differences. If different components of the luminescence spectrum are due to random band energy variations across the sample, Eq. (1) gives ∂g/∂E of the order of a few eV −1 , in agreement with the experimental observation in Figure 4a. ...

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The absorption, reflection and photoluminescence spectra of GaSe crystals with different thicknesses (100 nm–1 mm) were investigated in a wide temperature interval (300 K–10 K). Features due to excitonic states in the spectra were recognized. The contours of the excitonic reflection spectra measured at 10 K were calculated by dispersion equations....

## Citations

... Chiral phonons were studied in many two dimensional (2D) lattices, e.g., honeycomb lattice [1,2], kagome lattice [3], or moiré superlattices [4]. Recently, chiral phonons were also reported in many three dimensional (3D) materials, e.g.: transition metal dichalcogenides [5][6][7][8] and their heterostructures [9][10][11], pervoskites [12][13][14][15], graphene/hexagonal boron nitride heterostructure [16], 2D magnets (CrBr 3 [17] or Fe 3 GeTe 2 [18]), cuprates [19], CoSn-like systems [20], ternary YAlSi compound [21], chiral systems (ABi-like compounds [22], α-HgS [23] or SiO 4 [24]), and magnetic topological insulators T Bi 2 Te 4 [25]. Due to their extraordinary properties (e.g., realization of the phonon Hall effect [26][27][28][29][30][31][32][33]), it has attracted a lot of theoretical and experimental attentions. ...

A$B$_{2}$ ($A=$K, Rb, Cs) compounds crystallize in the cubic Laves phase (symmetry Fd$\bar{3}$m). The geometry of the crystal structure allows the realization of chiral phonons, which are associated with the circulation of atoms around their equilibrium positions. Due to the inversion symmetry and time reversal symmetry, total pseudo-angular momentum (PAM) of the system vanishes. We show that the doping of these system can lead to a new phase with symmetry F$\bar{4}3$m. New systems (KRbBi$_{4}$ and RbCsBi$_{4}$) do not exhibit soft modes (are stable dynamically). Due to the inversion symmetry breaking, realized chiral phonon modes posses a non-zero total PAM. In both type of systems the chiral phonons are realized for the wavectors at the edge of the Brillouine zone. This study explores the possibility of chiral phonon engineering via doping, and predicts two new materials. Discussing the problem opens a new way to study the phonon Hall effect.

... Recently, chiral phonons, in which atomic motions have rotational components with chirality, have been predicted theoretically [1] and observed experimentally [2]. In addition, chiral phonons are expected to have a variety of applications and have been studied extensively [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Furthermore, the concept of chiral phonons has been studied in crystals with screw symmetry, and interactions with other particles with chirality and experimental methods have been proposed [21][22][23][24][25][26][27][28][29][30][31][32]. ...

Properties of systems with exact n-fold screw symmetry (n=2, 3, 4, 6) have been well studied because they can be understood in terms of space groups. On the other hand, existence of materials with approximate screw symmetries, such as 7-fold and 10-fold screw symmetries, has been predicted. In this paper, we study properties of phonons in crystals with approximate screw symmetries, which will lead to unique and new physical phenomena. In a crystal with an approximate screw symmetry, we propose a method to extract information of pseudoangular momentum of phonons, which is a quantum number characterizing the properties of phonon modes under screw symmetry, based on the fact that the information of the quantum numbers defined under exact screw symmetry partially remains in the eigenvectors of approximate screw symmetric systems. As a preparation, we study a one-dimensional crystal with partially broken translation symmetry to have an enlarged unit cell, and we show how to extract information of a quantum number corresponding to the pseudoangular momentum, by studying a relative phase between neighboring atoms. We also extend this method to systems with an approximate screw symmetry, and discuss properties of the pseudoangular momentum. We apply this method to results of our first-principle calculations on candidate materials with an approximate translational symmetry or with an approximate screw symmetry, and show how this approximate symmetry is reflected in the phonon wavefunctions.

... The chiral phonons can be realized in a large class of the two-dimensional (2D) systems with hexagonal symmetry [2], like the honeycomb lattice [3,4] or the kagome lattice [5]. Indeed, recently the observation of the chiral phonons in layered structures was reported in, e.g., B-decorated graphene [6], dichalcogenide monolayers [7][8][9][10][11] and bilayers [12,13], moiré twisted bilayer [14,15], or CrBr 3 [16]. However, the threedimensional (3D) systems can also exhibit the chiral phonons, e.g., cuprates [17], perovskites [18][19][20][21] and their superlattices [22], Fe 3 GeTe 2 [23], or CoSn-like compounds [24]. ...

Binary compounds $A$Bi ($A$ = K, Rb, Cs) crystallize in P2$_1$/c structure containing both clockwise and anticlockwise chiral chains of Bi atoms. Electronic band structure exhibits the insulating nature of these systems, with the band gap about 0.25 eV. The presented study of dynamical properties confirm a stability of the system with P2$_1$/c symmetry. Independently of the absence of the three-fold (or higher) rotational symmetry axes, the chiral modes propagate along the Bi atom chains in these systems. We discuss basic properties of these modes in monoatomic chiral chains.

... The important role the moiré potential plays in the confinement of IXs is further supported by the twist-dependent IX diffusion in TMD heterobilayers, in which the diffusion length of the IX ensemble depends on the moiré periodicity [27,28]. However, the narrow emission linewidths observed for single trapped IXs contrast with the broad photoluminescence (PL) spectra observed in similar MoSe 2 =WSe 2 heterostructures [4][5][6][7]16,[29][30][31], which show IX emission bands with linewidths of 4-6 meV in the cleanest samples [6,16,30,32], 2 orders of magnitude broader than single trapped IXs. Such contrasting observations have opened a debate regarding a unified picture of the nature of IX emission in TMD heterobilayers, and in particular, in the prototypical heterostructure: MoSe 2 =WSe 2 heterobilayers [33]. ...

Transition-metal dichalcogenide heterobilayers offer attractive opportunities to realize lattices of interacting bosons with several degrees of freedom. Such heterobilayers can feature moiré patterns that modulate their electronic band structure, leading to spatial confinement of single interlayer excitons (IXs) that act as quantum emitters with C3 symmetry. However, the narrow emission linewidths of the quantum emitters contrast with a broad ensemble IX emission observed in nominally identical heterobilayers, opening a debate regarding the origin of IX emission. Here we report the continuous evolution from a few trapped IXs to an ensemble of IXs with both triplet- and singlet-spin configurations in a gate-tunable 2H−MoSe2/WSe2 heterobilayer. We observe signatures of dipolar interactions in the IX ensemble regime which, when combined with magneto-optical spectroscopy, reveal that the narrow quantum-dot-like and broad ensemble emission originate from IXs trapped in moiré potentials with the same atomic registry. Finally, electron doping leads to the formation of three different species of localized negative trions with contrasting spin-valley configurations, among which we observe both intervalley and intravalley IX trions with spin-triplet optical transitions. Our results identify the origin of IX emission in MoSe2/WSe2 heterobilayers and highlight the important role of exciton-exciton interactions and Fermi-level control in these highly tunable quantum materials.

... For example, Zhang and Niu [5] predicted the existence of chiral phonons at the K and K valleys of monolayer WSe 2 , which was subsequently verified by experiments that measured the circular dichroism of phonon-assisted intervalley transitions of holes [6]. The interaction of such chiral valley phonons with other quasiparticles is relevant for understanding and controlling many electronic and optical phenomena [7][8][9][10][11][12][13]. For instance, Li et al. demonstrated that the coupling between a chiral valley phonon and an intervalley exciton in monolayer WSe 2 can lead to a long exciton lifetime maintaining the valley polarization, which is important for valley-excitonics [12]. ...

We investigate the chirality of phonon modes in twisted bilayer WSe2. We demonstrate distinct chiral behavior of the K/K' valley phonon modes for twist angles close to 0 degrees and close to 60 degrees. Moreover, we discover two sets of well-separated chiral valley modes in moire lattices for angles close to 60 degrees. These emergent moire chiral valley phonons originate from inversion symmetry breaking at the moire scale. We also find similar emergent chiral modes in moire patterns of strain-engineered bilayer WSe2 and MoSe2/WSe2 heterostructure. Furthermore, we observe the flattening of bands near the phononic band-gap edges for a broad range of twist angles in twisted bilayer WSe2. Our findings, which are expected to be generic for moire systems composed of two-dimensional materials that break inversion symmetry, are relevant for understanding electron-phonon and exciton-phonon scattering, and for designing phononic crystals to mimic behaviors of electrons in moire materials.

... , the interlayer exciton g-factors of heterostructures in the H registry are substantially higher, 15-16 for the energetically lowest contribution 50,51 . Based on theoretical results from density functional theory calculations, the interlayer excitons have thus been interpreted to be zero-momentum singlet and triplet excitations at the K and K points. . ...

The optical spectra of vertically stacked MoSe2/WSe2 heterostructures contain additional ’interlayer’ excitonic peaks that are absent in the individual monolayer materials and exhibit a significant spatial charge separation in out‐of‐plane direction. Extending on a previous study, we used a many‐body perturbation theory approach to simulate and analyse the excitonic spectra of MoSe2/WSe2 heterobilayers with three stacking orders, considering both momentum‐direct and momentum‐indirect excitons. We find that the small oscillator strengths and corresponding optical responses of the interlayer excitons are significantly stacking‐dependent and give rise to high radiative lifetimes in the range of 5‐200 ns (at T=4 K) for the ’bright’ interlayer excitons. Solving the finite‐momentum Bethe‐Salpeter Equation, we predict that the lowest‐energy excitation should be an indirect exciton over the fundamental indirect band gap (K→Q), with a binding energy of 220 meV. However, in agreement with recent magneto‐optics experiments and previous theoretical studies, our simulations of the effective excitonic Landé g‐factors suggest that the low‐energy momentum‐indirect excitons are not experimentally observed for MoSe2/WSe2 heterostructures. We further reveal the existence of ’interlayer’ C excitons with significant exciton binding energies and optical oscillator strengths, which are analogous to the prominent band nesting excitons in mono‐ and few‐layer transition‐metal dichalcogenides.
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... Despite numerous experimental and theoretical studies of MoSe 2 -WSe 2 HBLs, the origin of the lowest energy PL remains a subject of debate [22]. While the majority of experimental studies interpret the HBL emission in terms of zero-momentum interlayer excitons with K or K valley electrons and holes in MoSe 2 and WSe 2 [15, 16,19,21,[23][24][25][26][27][28][29], others invoke excitons built from hybridized HBL conduction band states at Q [30-32]. Band structure calculations indeed suggest that hybridization of Q conduction and Γ valence bands of MoSe 2 and WSe 2 gives rise to strong energy renormalization upon HBL formation [2, 33, 34] which might turn either QK or QΓ interlayer excitons into the lowest energy states. ...

... Despite numerous experimental and theoretical studies of MoSe 2 -WSe 2 HBLs, the origin of the lowest energy PL remains a subject of debate [22]. While the majority of experimental studies interpret the HBL emission in terms of zero-momentum interlayer excitons with K or K valley electrons and holes in MoSe 2 and WSe 2 [15,16,19,21,[23][24][25][26][27][28][29], others invoke excitons built from hybridized HBL conduction band states at Q [30][31][32]. Band structure calculations indeed suggest that hybridization of Q conduction and Γ valence bands of MoSe 2 and WSe 2 gives rise to strong energy renormalization upon HBL formation [2,33,34] which might turn either QK or QΓ interlayer excitons into the lowest energy states. ...

... Another striking difference in the PL from HBL and HTL is evident for interlayer excitons with emission around 1.35 and 1.30 eV in the spectra of Fig. 1a and b, respectively. Consistent with finite twist angle, the multi-peak PL of the HBL around 1.35 eV is reminiscent of rich MoSe 2 -WSe 2 moiré spectral features [16] rather than of simple spectra from aligned HBLs [24][25][26][27][28][29]. The PL of the HTL shows a red-shift of ∼ 80 meV upon the addition of an extra MoSe 2 layer and exhibits a different spectral structure that is strikingly similar to the cryogenic PL from bilayer WSe 2 [42] (see the Supplementary Information for direct comparison). ...

We report experimental and theoretical studies of excitons in twisted stacks of MoSe$_2$-WSe$_2$ heterobilayers and heterotrilayers. We observe distinct optical signatures for the heterobilayer and heterotrilayer regions of a MoSe$_2$-WSe$_2$ heterostack, and interpret our experimental findings in the framework of moir\'e modulated momentum direct and indirect interlayer excitons. Our results highlight the role of interlayer hybridization for exciton relaxation and formation in multi-layered semiconductor van der Waals heterostructures.

Heterobilayers consisting of MoSe 2 and WSe 2 monolayers can host optically bright interlayer excitons with intriguing properties such as ultralong lifetimes and pronounced circular polarization of their photoluminescence due to valley polarization, which can be induced by circularly polarized excitation or applied magnetic fields. Here, we report on the observation of an intrinsic valley-magnetophonon resonance for localized interlayer excitons promoted by invervalley hole scattering. It leads to a resonant increase of the photoluminescence polarization degree at the same field of 24.2 Tesla for H-type and R-type stacking configurations despite their vastly different excitonic energy splittings. As a microscopic mechanism of the hole intervalley scattering we identify the scattering with chiral TA phonons of MoSe 2 between excitonic states mixed by the long-range electron hole exchange interaction.