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![Symmetry resolved static susceptibilities. a Temperature dependences of the static susceptibility in 3 different symmetries, B1g,B2g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{1g},{B}_{2g}$$\end{document}, and A1g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{1g}$$\end{document}, as a function of doping. The form factors for each symmetry are depicted in reciprocal space in insets. They are given in terms of the lowest order Brillouin zone harmonics: cos(kx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{x}$$\end{document}) − cos(ky\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{y}$$\end{document}) for B1g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{1g}$$\end{document}, sin(kx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{x}$$\end{document})sin(ky\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{y}$$\end{document}) for B2g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{2g}$$\end{document}, cos(kx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{x}$$\end{document}) + cos(ky\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{y}$$\end{document}) and cos(kx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{x}$$\end{document})cos(ky\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{y}$$\end{document}) for A1g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{1g}$$\end{document}. The error bars correspond to the standard error of the low energy fits used for the low energy extrapolation (see supplementary note 1). b Curie-Weiss fits of the inverse B1g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{1g}$$\end{document} nematic susceptibility for temperatures above max(TcT*\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{c}\,{T}^{*}$$\end{document}). The inset shows the full temperature dependence of the inverse susceptibility of OD74 and UD85 where deviation from Curie-Weiss law are observed at T*\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}^{* }$$\end{document}, and an additional upturn is observed at Tc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{c}$$\end{document}. Full and open symbol correspond to data above and below T*\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}^{*}$$\end{document}, respectively](publication/337281935/figure/fig3/AS:958973272391712@1605648453707/Symmetry-resolved-static-susceptibilities-a-Temperature-dependences-of-the-static.png)
Symmetry resolved static susceptibilities. a Temperature dependences of the static susceptibility in 3 different symmetries, B1g,B2g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{1g},{B}_{2g}$$\end{document}, and A1g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{1g}$$\end{document}, as a function of doping. The form factors for each symmetry are depicted in reciprocal space in insets. They are given in terms of the lowest order Brillouin zone harmonics: cos(kx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{x}$$\end{document}) − cos(ky\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{y}$$\end{document}) for B1g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{1g}$$\end{document}, sin(kx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{x}$$\end{document})sin(ky\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{y}$$\end{document}) for B2g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{2g}$$\end{document}, cos(kx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{x}$$\end{document}) + cos(ky\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{y}$$\end{document}) and cos(kx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{x}$$\end{document})cos(ky\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{y}$$\end{document}) for A1g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{1g}$$\end{document}. The error bars correspond to the standard error of the low energy fits used for the low energy extrapolation (see supplementary note 1). b Curie-Weiss fits of the inverse B1g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{1g}$$\end{document} nematic susceptibility for temperatures above max(TcT*\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{c}\,{T}^{*}$$\end{document}). The inset shows the full temperature dependence of the inverse susceptibility of OD74 and UD85 where deviation from Curie-Weiss law are observed at T*\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}^{* }$$\end{document}, and an additional upturn is observed at Tc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{c}$$\end{document}. Full and open symbol correspond to data above and below T*\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}^{*}$$\end{document}, respectively
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Establishing the presence and the nature of a quantum critical point in their phase diagram is a central enigma of the high-temperature superconducting cuprates. It could explain their pseudogap and strange metal phases, and ultimately their high superconducting temperatures. Yet, while solid evidences exist in several unconventional superconductor...
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Citations
... Notably, the obtained scaling law near T c ∼ 0 is incompatible with the mean-field theory such as the dwave Bardeen-Cooper-Schrieffer theory even with the dirty limit, pointing to the local pairing and massive phase fluctuation in the real space [10]. Note that nematic fluctuation in Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212) [11] and reentrant charge order in Pb-Bi2201 [12] have been reported in the overdoped region. ...
The real and imaginary parts of the self-energy in the wide energy range have been evaluated from high-resolution angle-resolved photoemission spectroscopy (ARPES) spectra of a heavily overdoped single-layer cuprate superconductor ( Bi , Pb ) 2 Sr 2 CuO 6 + δ in the normal state. The real part of the self-energy has the zero-point crossing at − 0.6 eV, where the lifetime broadening takes maximum and the ARPES spectral intensity is significantly suppressed forming a high-energy anomaly (HEA). The self-energy part responsible for the HEA is almost temperature independent and the coupling parameter is λ HEA ∼ 1 at 300 K, indicating strongly correlated nature of the strange metal state. Meanwhile, the self-energy part responsible for the low-energy kink (LEK) near the Fermi level shows significant temperature dependence: it is λ LEK ∼ 0.1 at 300 K but enhances steeply below ∼ 150 K up to λ LEK ∼ 0.8 , leading to the total coupling strength of λ tot = λ HEA + λ LEK = 1.8 at 20 K. The temperature-dependent enhancement cannot be explained by the electron-phonon interaction with a fixed magnitude of the Eliashberg function, which suggests an unexplored mechanism that enhances the coupling parameter at lower temperatures. Our results clearly indicate distinct energy scales in the self-energy, providing insight into the strange metal state as well as the temperature-dependent interplay of many-body interactions.
Published by the American Physical Society 2025
... The study of critical fluctuations near the transition temperature in high-temperature cuprate superconductors, HTSC, has attracted much interest since the discovery of these materials [1][2][3][4][5][6][7][8]. In HTSC, these critical effects are especially significant due, mainly, to the short coherence lengths and corresponding reduced-dimensionality enhancements when competing with the size of the intrinsic layered nanostructure formed by the CuO 2 superconducting planes [1][2][3][4][9][10][11]. ...
... In HTSC, these critical effects are especially significant due, mainly, to the short coherence lengths and corresponding reduced-dimensionality enhancements when competing with the size of the intrinsic layered nanostructure formed by the CuO 2 superconducting planes [1][2][3][4][9][10][11]. It was quite early noted that the temperature behavior of the critical fluctuations (including both critical exponents and amplitudes) could provide information about HTSC such as, e.g., the locus where superconductivity occurs, the symmetry of the pairing wave function, or the possible influence of phase fluctuations on the high value of transition temperature itself [1][2][3][4][5][6][7][8][9][10][11][12][13]. ...
We study the critical fluctuations near the resistive transition of very thin films of high-temperature cuprate superconductors composed of a number N of only a few unit cells of superconducting bilayers. For that, we solve the fluctuation spectrum of a Gaussian-Ginzburg-Landau model for few-bilayers superconductors considering two alternating Josephson interlayer interaction strengths, and we obtain the corresponding paraconductivity above the transition. Then, we extend these calculations to temperatures below the transition through expressions for the Ginzburg number and Kosterlitz--Thouless-like critical region. When compared with previously available data in YBaCuO few-bilayers systems, with N=1 to 4, our results seem to provide a plausible scenario for their critical regime.
... In this device, breaking C 4 symmetry is essential to generate the JDE. Besides the C 4 symmetry breaking in the s-d interlayer couplings due to the lattice deviates from standard square shape, it can also arise from the C 4 symmetry breaking in the d-wave pairing function, which is indicated in relative experimentally works [36,41,[66][67][68][69]. The JDE can also exist for the C 4 symmetry breaking in d-wave pairing function, ∆ d k = ∆ d (cos k x − cos k y ) + ∆ ds , with ∆ ds /∆ d represent the C 4 symmetry breaking [43]. ...
Motivated by recent progress in both the Josephson diode effect (JDE) and the high-temperature Josephson junction, we propose to realize the JDE in an s-wave/d-wave/s-wave (s-d-s) superconductor junction and investigate the high-temperature superconducting order parameters. The interlayer coupling between s-wave and d-wave superconductors can induce an effective d+is superconducting state, spontaneously breaking time-reversal symmetry. The asymmetric s-d interlayer couplings break the inversion symmetry. Remarkably, the breaking of these two symmetries leads to a -junction but does not generate JDE. We find that the emergence of the JDE in this junction depends on the rotational symmetry of the system. Although breaking rotational symmetry does not affect time-reversal and inversion symmetries, it can control the magnitude and polarity of diode efficiency. Furthermore, we propose observing C symmetry breaking controlled JDE through asymmetric Shapiro steps. Our work suggests a JDE mechanism that relies on high-temperature d-wave pairing, which could inversely contribute to a potential experimental method for detecting the unconventional pairing symmetry in superconductors.
... One of the most enigmatic phases of hole-doped cuprates is charge nematicity [1]. This long-ranged charge order has been investigated quite frequently in the past two decades [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. It manifests itself as the spontaneous breaking, by the electronic structure, of the four-fold rotational symmetry of the CuO 2 unit cell [11] common to all cuprates. ...
Recent scanning-tunneling microscopy on hole-doped BiSrCaCuO, one of the materials of the cuprate family, finds a long-range ordered spontaneous splitting of the energy levels of oxygen orbitals inside the CuO unit cells [S. Wang et al., Nat. Mat. 23, 492-498 (2024)]. This spontaneous intra-unit-cell orbital ordering, also known as electronic nematicity, breaks symmetry and is thought to arise from the Coulomb interaction (denoted by ) between oxygen and electrons. In this work, we study the spontaneous emergence of electronic nematicity within the three-band Hubbard (aka the Emery-VSA model), using cluster dynamical mean field theory. This method incorporates short-range electronic correlations and gives us access to the density of states, a quantity that is directly probed in experiments. We argue that there is a delicate competition between and (the latter being the Coulomb interaction between copper and oxygen electrons) that must be taken into account in order to find a Zhang-Rice singlet band well-resolved from the upper Hubbard band, and a splitting of the charge-transfer band (one of the signatures of charge nematicity) by roughly 50 meV, as observed recently.
... These fluctuations might give rise to non-Fermi liquid behaviors [27,28] and they might provide a pairing glue between electrons leading to superconductivity, and this becomes particularly relevant in the proximity of a nematic QCP [29][30][31][32]. The poorly-understood relation between nematicity and unconventional superconductivity explains the huge interest about the former phase: It might explain the origins of the latter [33][34][35][36]. Coming to a more concrete example, in several of the iron-based superconductors [37], one observes the follow-ing phenomenology: Below a critical temperature T nem , an Ising Z 2 symmetry is broken and the nematic character seems to have electronic origin [33]. ...
Starting from a low-energy model for the band dispersion of the charge-ordered phase of the kagome metals AVSb (A= K, Rb, Cs), we show that nematicity can develop in this state driven either by charge fluctuations preemptive of a charge order (CO), or by an actual zero momentum d-wave charge Pomeranchuk instability (PI). We perform an analysis that starts from a Kohn-Luttinger theory in the particle-hole sector, which allows us to establish a criterion for the development of an attractive nematic channel near the onset of the CO and near the d-wave charge PI, respectively. We derive an effective charge-fermion model for the d-wave PI with a nematic susceptibility given via a random phase approximation (RPA) summation. By contrast, for the finite momentum CO, the RPA scheme breaks down and needs to be improved upon by including Aslamazov-Larkin contributions to the nematic pairing vertex. We then move to the derivation of the Ginzburg-Landau potentials for the CO and for the d-wave PI, and we obtain the corresponding expression for the nematic susceptibility at the nematic transition temperature T in both cases. Our work establishes a relation between the nematicity observed in some of the iron-based superconductors, where the nematic phase might be driven by spin fluctuations, and the vanadium-based kagome metals, where charge fluctuations likely induce nematicity. The two microscopic mechanisms we propose for the stabilization of the nematic state in AVSb are distinguishable by diffusive scattering experiments, meaning that it is possible to gauge which of the two theories, if any, is the most likely to describe this phase. Both mechanisms might also be relevant for the recently discovered titanium-based family ATiSb.
... This competition has been observed as a function of temperature, hole-doping, applied magnetic fields, uniaxial strain, and optical pumping (5)(6)(7)(8)(9)(10)(11)(12)(13)(14). In addition to CDW order, cuprates also exhibit nematic order (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27), a breaking of the rotational symmetry of the electronic structure within the CuO 2 planes from four-to two-fold symmetric (C 4 rotational symmetry breaking). ...
Understanding the interplay between charge, nematic, and structural ordering tendencies in cuprate superconductors is critical to unraveling their complex phase diagram. Using pump–probe time-resolved resonant X-ray scattering on the (0 0 1) Bragg peak at the Cu L 3 and O K resonances, we investigate nonequilibrium dynamics of Q a = Q b = 0 nematic order and its association with both charge density wave (CDW) order and lattice dynamics in La 1.65 Eu 0.2 Sr 0.15 CuO 4 . The orbital selectivity of the resonant X-ray scattering cross-section allows nematicity dynamics associated with the planar O 2 p and Cu 3 d states to be distinguished from the response of anisotropic lattice distortions. A direct time-domain comparison of CDW translational-symmetry breaking and nematic rotational-symmetry breaking reveals that these broken symmetries remain closely linked in the photoexcited state, consistent with the stability of CDW topological defects in the investigated pump fluence regime.
... This could be explained if bulk inversion symmetry was broken; alongside this, nematicity is also seen. In polarization-resolved Raman scattering 50 , the suppression of susceptibility near T* is observed. Elastoresistance measurements 51 of in-plane anisotropy that onsets near T* also indicate a nematic state. ...
The primordial ingredient of cuprate superconductivity is the CuO2 unit cell. Theories usually concentrate on the intra-atom Coulombic interactions dominating the 3d⁹ and 3d¹⁰ configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p⁶ orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long-predicted intra-unit-cell symmetry breaking should generate an orbitally ordered phase, for which the charge transfer energy ε separating the 2p⁶ and 3d¹⁰ orbitals is distinct for the two oxygen atoms. Here we introduce sublattice-resolved ε(r) imaging to CuO2 studies and discover intra-unit-cell rotational symmetry breaking of ε(r). Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order bounded by dopant ions, and within whose domain walls low-energy electronic quadrupolar two-level systems occur. Overall, these data reveal a Q = 0 orbitally ordered state that splits the oxygen energy levels by ~50 meV, in underdoped CuO2.
... Theoretical investigations indicate that the nematic interaction has a strong impact on the short-time dynamics of unconventional superconductors (51). Moreover, recent terahertz Kerr measurements have also identified a clear nematic order contribution in iron-based superconductors (52), while Raman spectroscopy has observed nematic fluctuations in various hole-doped cuprates up to T * (53). On the basis of these observations, it is possible that nematic order may contribute THG signals up to T * . ...
We report on nonlinear terahertz third-harmonic generation (THG) measurements on YBa 2 Cu 3 O 6+ x thin films. Different from conventional superconductors, the THG signal starts to appear in the normal state, which is consistent with the crossover temperature T * of pseudogap over broad doping levels. Upon lowering the temperature, the THG signal shows an anomaly just below T c in the optimally doped sample. Notably, we observe a beat pattern directly in the measured real-time waveform of the THG signal. We elaborate that the Higgs mode, which develops below T c , couples to the mode already developed below T * , resulting in an energy level splitting. However, this coupling effect is not evident in underdoped samples. We explore different potential explanations for the observed phenomena. Our research offers valuable insight into the interplay between superconductivity and pseudogap.
... Besides, it has been conjectured that NSC can be stabilized by density-wave uctuations [34], addressing its potential role in twisted bilayer Graphene. From an experimental point of view, nematic uctuations have been veried by using Raman spectroscopy in the cuprate superconductor Bi 2 Sr 2 CaCu 2 O 8+δ [35], where the Pair-Density Wave state (PDW) has also been measured [36]. ...
In this article, we investigate the existence of nematic-superconducting states in the Ginzburg–Landau regime, both analytically and numerically. From the configurations considered, a slab and a cylinder with a circular cross-section, we demonstrate the existence of geometrical thresholds for the obtention of non-zero nematic order parameters. Within the frame of this constraint, the numerical calculations on the slab reveal that the competition or collaboration between nematicity and superconductivity is a complex energy minimization problem, requiring the accommodation of the Ginzburg–Landau parameters of the decoupled individual systems, the sign of the bi-quadratic potential energy relating both order parameters and the magnitude of the applied magnetic field. Specifically, the numerical results show the existence of a parameter regime for which it is possible to find mixed nematic-superconducting states. These regimes depend strongly on both the applied magnetic field and the potential coupling parameter. Since the proposed model corresponds to the weak coupling regime, and since it is a condition on these parameters, we design a test to decide whether this condition is fulfilled.
... 95.32, 95.03, 91.73, and 94.50 K, respectively. The data hints that the T c of the thin film is superior than that of the bulk (89 K) [35], and is also higher than that of single crystal film (90 K) [36,37], this may be related to the stress on the film [38,39]. These values signify the homogenous crystalline integrity of the Bi2212 grains in the HTSFs. ...
