Evidence for a vestigial nematic state in the cuprate pseudogap phase

The CuO2 antiferromagnetic insulator is transformed by hole-doping into an exotic quantum fluid usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic density-of-states D(E) for energies |E| < Δ*, where Δ* is the PG energy. Unanticipated broken-symmetry phases have been detected by a wide variety of techniques in the PG regime, most significantly a finite-Q density-wave (DW) state and a Q = 0 nematic (NE) state. Sublattice-phase-resolved imaging of electronic structure allows the doping and energy dependence of these distinct broken-symmetry states to be visualized simultaneously. Using this approach, we show that even though their reported ordering temperatures TDW and TNE are unrelated to each other, both the DW and NE states always exhibit their maximum spectral intensity at the same energy, and using independent measurements that this is the PG energy Δ*. Moreover, no new energy-gap opening coincides with the appearance of the DW state (which should theoretically open an energy gap on the Fermi surface), while the observed PG opening coincides with the appearance of the NE state (which should theoretically be incapable of opening a Fermi-surface gap). We demonstrate how this perplexing phenomenology of thermal transitions and energy-gap opening at the breaking of two highly distinct symmetries may be understood as the natural consequence of a vestigial nematic state within the pseudogap phase of Bi2Sr2CaCu2O8.

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Electronic nature of charge density wave and electron-phonon coupling in kagome superconductor KV3Sb5

Nature Communications ◽

10.1038/s41467-021-27946-6 ◽

2022 ◽

Vol 13 (1) ◽

Author(s):

Hailan Luo ◽

Qiang Gao ◽

Hongxiong Liu ◽

Yuhao Gu ◽

Dingsong Wu ◽

...

Keyword(s):

Electronic Structure ◽

Fermi Surface ◽

Charge Density ◽

Charge Density Wave ◽

Density Wave ◽

Phonon Coupling ◽

Electronic Nature ◽

Electron Phonon Coupling ◽

Gap Opening ◽

Fermi Surface Reconstruction

AbstractThe Kagome superconductors AV3Sb5 (A = K, Rb, Cs) have received enormous attention due to their nontrivial topological electronic structure, anomalous physical properties and superconductivity. Unconventional charge density wave (CDW) has been detected in AV3Sb5. High-precision electronic structure determination is essential to understand its origin. Here we unveil electronic nature of the CDW phase in our high-resolution angle-resolved photoemission measurements on KV3Sb5. We have observed CDW-induced Fermi surface reconstruction and the associated band folding. The CDW-induced band splitting and the associated gap opening have been revealed at the boundary of the pristine and reconstructed Brillouin zones. The Fermi surface- and momentum-dependent CDW gap is measured and the strongly anisotropic CDW gap is observed for all the V-derived Fermi surface. In particular, we have observed signatures of the electron-phonon coupling in KV3Sb5. These results provide key insights in understanding the nature of the CDW state and its interplay with superconductivity in AV3Sb5 superconductors.

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Effect of Multiple Orders on Superconducting Transition Temperature of Hole Doped Cuprates

Journal of Scientific Research ◽

10.3329/jsr.v9i4.32598 ◽

2017 ◽

Vol 9 (4) ◽

pp. 341-349

Author(s):

I. Qabid ◽

S. H. Naqib

Keyword(s):

Transition Temperature ◽

Superconducting Transition Temperature ◽

Cuprate Superconductors ◽

Energy Gap ◽

Density Wave ◽

Spin Density Wave ◽

Superconducting Transition ◽

Electronic Density ◽

Special Cases ◽

Multiple Orders

Hole doped high-Tc cuprate superconductors are strongly correlated electronic systems. In these materials, various electronic orders are often found, but whether they support or compete with superconducting order is not unambiguous. Superconductivity normally manifests itself by a superconducting gap in the electronic density of states (EDOS). In cuprates, a gap appears even in the normal state called the pseudogap (PG). For certain doping range, spin density wave and charge density wave coexist with superconductivity by inducing corresponding additional gaps in the EDOS. In this study, we have tried to obtain expression for superconducting transition temperature, Tc by solving the BCS (Bardeen-Cooper-Schrieffer) energy gap equation in the presence of depleted EDOS of various origins and types. We have been successful to solve the weak-coupling BCS integral equation analytically in some special cases and also in the general case by using numerical integration. We have found that depending on conditions these non-pairing gaps/orders can enhance as well as reduce Tc.

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CRITICAL EXPONENTS OF THE TRANSPORT PROPERTIES AT THE B2⇔IC⇔C(R) TRANSITIONS IN Ti-Ni-Me SHAPE MEMORY ALLOYS

International Journal of Modern Physics B ◽

10.1142/s021797920000159x ◽

2000 ◽

Vol 14 (17) ◽

pp. 1729-1742 ◽

Cited By ~ 1

Author(s):

V. KOLOMYTSEV ◽

V. NEVDACHA ◽

L. BATAILLARD ◽

R. GOTTHARDT

Keyword(s):

Shape Memory Alloys ◽

Shape Memory ◽

Energy Gap ◽

Density Wave ◽

Normal Pressure ◽

Gap Formation ◽

Resistance Change ◽

Total Enthalpy ◽

Β Phase ◽

Gap Opening

Critical behaviour of the physical properties at the B2⇔IC ⇔C(R) phase transitions in TiNi-based shape memory alloys has been analyzed in the frame of the charge density wave (CDW) model. Variation of total resistance at the Peierls-type B2⇔IC ⇔C(R) transition in TiNiMe (Me=Cr, Fe, Al, Ge) alloys has been found to be a sum of the β-phase normal contribution, fluctuating CDW resistance ρ f (T) in the incommensurate state and resistance change due to the energy gap formation ρc(T) in the commensurate state. The fitting parameters such as the energy gap at saturation Δ(0) and the number of electrons involved in the process of the CDW's formation ψ(0) have been determined as a function of the alloy chemical composition and thermal treatment at moderate temperature. The critical resistive fluctuations in the incommensurate phase follow a power law dρ f /dt*~t*m with critical exponent m=-1. In the frame of the CDW model this means that the process of electron scattering from periodic distortion is strongly limited to a definite plane of the crystal and system is two-dimensional. The change of ρ c with temperature is controlled by the activation energy law corresponding to electron single excitations through the gap Δ(T), with a varying ψ(T) effective number of the electrons involved in the process. The total enthalpy measured during cooling is compared with the heat calculated for the energy gap opening at the Fermi level during the IC⇒C(R) transition in the frame of the Shottky anomaly approximation. Both values are of the same order. When hydrostatic pressure is applied to the material, a small drop in the conductivity is observed around P~2 GPa and interpreted as CDW pinning by commensurability locking at a temperature higher than the transition temperature at normal pressure.

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Scattering interference signature of a pair density wave state in the cuprate pseudogap phase

Nature Communications ◽

10.1038/s41467-021-26028-x ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Shuqiu Wang ◽

Peayush Choubey ◽

Yi Xue Chong ◽

Weijiong Chen ◽

Wangping Ren ◽

...

Keyword(s):

Temperature Dependence ◽

Energy Gap ◽

Density Wave ◽

Real Space ◽

Hole Density ◽

Wave State ◽

Electron Pairs ◽

Pseudogap Phase ◽

Pair Density ◽

Pair Density Wave

AbstractAn unidentified quantum fluid designated the pseudogap (PG) phase is produced by electron-density depletion in the CuO2 antiferromagnetic insulator. Current theories suggest that the PG phase may be a pair density wave (PDW) state characterized by a spatially modulating density of electron pairs. Such a state should exhibit a periodically modulating energy gap $${\Delta }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{r}}}}}})$$ Δ P ( r ) in real-space, and a characteristic quasiparticle scattering interference (QPI) signature $${\Lambda }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{q}}}}}})$$ Λ P ( q ) in wavevector space. By studying strongly underdoped Bi2Sr2CaDyCu2O8 at hole-density ~0.08 in the superconductive phase, we detect the 8a0-periodic $${\Delta }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{r}}}}}})$$ Δ P ( r ) modulations signifying a PDW coexisting with superconductivity. Then, by visualizing the temperature dependence of this electronic structure from the superconducting into the pseudogap phase, we find the evolution of the scattering interference signature $$\Lambda ({{{{{\boldsymbol{q}}}}}})$$ Λ ( q ) that is predicted specifically for the temperature dependence of an 8a0-periodic PDW. These observations are consistent with theory for the transition from a PDW state coexisting with d-wave superconductivity to a pure PDW state in the Bi2Sr2CaDyCu2O8 pseudogap phase.

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“Nodal Gap” Induced by the Incommensurate Diagonal Spin Density Modulation in Underdoped High-TcSuperconductors

Advances in Condensed Matter Physics ◽

10.1155/2015/652424 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Tao Zhou ◽

Yi Gao ◽

Jian-Xin Zhu

Keyword(s):

Fermi Surface ◽

Spin Density ◽

Energy Gap ◽

Local Density ◽

Density Wave ◽

Spin Density Wave ◽

Finite Energy ◽

Pairing Symmetry ◽

Nodal Lines ◽

Density Modulation

Recently it was revealed that the whole Fermi surface is fully gapped for several families of underdoped cuprates. The existence of the finite energy gap along thed-wave nodal lines (nodal gap) contrasts the common understanding of thed-wave pairing symmetry, which challenges the present theories for the high-Tcsuperconductors. Here we propose that the incommensurate diagonal spin-density-wave order can account for the above experimental observation. The Fermi surface and the local density of states are also studied. Our results are in good agreement with many important experiments in high-Tcsuperconductors.

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Change of the de Haas – van Alphen frequency of potassium with pressure

Canadian Journal of Physics ◽

10.1139/p80-053 ◽

1980 ◽

Vol 58 (3) ◽

pp. 370-375 ◽

Cited By ~ 16

Author(s):

Z. Altounian ◽

W. R. Datars

Keyword(s):

Band Structure ◽

Fermi Surface ◽

Pressure Dependence ◽

Charge Density Wave ◽

Energy Gap ◽

Density Wave ◽

Surface Anisotropy ◽

Band Structure Calculations ◽

Structure Calculations ◽

Fermi Surface Anisotropy

The pressure dependence of the de Haas – van Alphen frequency in oriented potassium samples has been investigated with pressures up to 4.6 kbar. The change of frequency with pressure is less than that expected from free-electron scaling and the Fermi surface anisotropy increases from 0.13% at zero pressure to 0.47% at 4 kbar. These results are discussed in terms of band structure calculations and the charge density wave (CDW) model of potassium. The CDW energy gap changes with pressure for the CDW model to be applicable.

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