Evidence for a vestigial nematic state in the cuprate pseudogap phase

Abstract

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.

Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity

“…3 G – L ) in the p < p* broken-symmetry state of Bi 2 Sr 2 CaCu 2 O 8. Indeed, the PDW + DSC model explains simply the microscopic origins of many enigmatic characteristics of this broken-symmetry state, including the dFF modulations ( 6 – 10 , 12 ), the concentration of their amplitude maxima ( 8 , 9 , 12 , 13 ) surrounding , and the periodic energy gap modulations observed in the superconducting state ( 42 ). Further, by considering scattering of k -space quasiparticles, we explore the QPI fingerprint of the PDW + DSC model ( Fig.…”

“…3 G – L show the measured in the energy range , with each panel shown side-by-side with the equivalent energy in the model. The most intense modulations occur at for all ( 8 , 13 ), and all through this energy range they exhibit a comprehensive dFF ( 8 , 12 , 13 ). Therefore, correspondence between theoretical from the PDW + DSC model ( Fig.…”

“…Bulk probes of charge density find translational symmetry breaking in a density wave (DW) state with axial wavevectors parallel to the CuO 2 axes ( 1 , 2 , 5 ). Similarly, direct visualization with subunit-cell resolution using single-electron tunneling in Bi 2 Sr 2 CaCu 2 O 8 and Ca 2− x Na x CuO 2 Cl 2 reveals intense electronic structure modulations ( 6 , 7 ) that are locally unidirectional ( 7 , 8 ), exhibit lattice-commensurate periodicity ( 9 , 10 ) for all ( 11 ), have a d -symmetry form factor ( 8 , 12 ), and are concentrated at particle-hole symmetric energies ( 13 ) . The spatial configurations consist of nanoscale regions within which the modulations are commensurate and unidirectional along either ( 7 , 8 , 10 , 12 ) .…”

Linking the pseudogap in the cuprates with local symmetry breaking: A commentary

“…Mukhopadhyay et al (1), in PNAS, venture a bold proposition as to the origin of the pseudogap on the basis of a careful examination of high-resolution scanning tunneling spectroscopy on Bi 2 Sr 2 CaCu 2 O 8+x (Bi-2212). They focus on 2 distinct forms of order: charge density wave (CDW), the breaking of lattice translation symmetry; and nematicity, the breaking of lattice rotational symmetry.…”

Hints for the nematic pseudogap in the nearly optimally doped La2−xSrxCuO4 superconductor

“…Notably, different models for the formation of the pseudogap predict that the electron system in this state should break various symmetries [12][13][14][15]. The electronic nematicity, which appears to be common among various families of unconventional superconductors [15][16][17][18][19][20][21], breaks the rotational (but preserves translational) symmetry and has been recently suggested to be the true foundation of the pseudogap phase [22,23].…”