skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Evidence for a vestigial nematic state in the cuprate pseudogap phase
The CuO 2 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 T DW and T NE 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 Bi 2 Sr 2 CaCu 2 O 8 .  more » « less
Award ID(s):
1719875
PAR ID:
10146293
Author(s) / Creator(s):
; ; ; ; ; ; ; ; ; ; ;
Date Published:
Journal Name:
Proceedings of the National Academy of Sciences
Volume:
116
Issue:
27
ISSN:
0027-8424
Page Range / eLocation ID:
13249 to 13254
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    We use polarization-resolved electronic Raman spectroscopy to study quadrupolar charge dynamics in a nonmagnetic F e S e 1 − x S x superconductor. We observe two types of long-wavelength X Y symmetry excitations: 1) a low-energy quasi-elastic scattering peak (QEP) and 2) a broad electronic continuum with a maximum at 55 meV. Below the tetragonal-to-orthorhombic structural transition at T S ( x ) , a pseudogap suppression with temperature dependence reminiscent of the nematic order parameter develops in the X Y symmetry spectra of the electronic excitation continuum. The QEP exhibits critical enhancement upon cooling toward T S ( x ) . The intensity of the QEP grows with increasing sulfur concentration x and maximizes near critical concentration x c r ≈ 0.16 , while the pseudogap size decreases with the suppression of T S ( x ) . We interpret the development of the pseudogap in the quadrupole scattering channel as a manifestation of transition from the non-Fermi liquid regime, dominated by strong Pomeranchuk-like fluctuations giving rise to intense electronic continuum of excitations in the fourfold symmetric high-temperature phase, to the Fermi liquid regime in the broken-symmetry nematic phase where the quadrupole fluctuations are suppressed. 
    more » « less
  2. Abstract An unidentified quantum fluid designated the pseudogap (PG) phase is produced by electron-density depletion in the CuO 2 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 Bi 2 Sr 2 CaDyCu 2 O 8 at hole-density ~0.08 in the superconductive phase, we detect the 8 a 0 -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 8 a 0 -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 Bi 2 Sr 2 CaDyCu 2 O 8 pseudogap phase. 
    more » « less
  3. Abstract Search for novel electronically ordered states of matter emerging near quantum phase transitions is an intriguing frontier of condensed matter physics. In ruthenates, the interplay between Coulomb correlations among the 4delectronic states and their spin-orbit interactions, lead to complex forms of electronic phenomena. Here we investigate the double layered Sr3(Ru1−xMnx)2O7and its doping-induced quantum phase transition from a metal to an antiferromagnetic Mott insulator. Using spectroscopic imaging with the scanning tunneling microscope, we visualize the evolution of the electronic states in real- and momentum-space. We find a partial-gap at the Fermi energy that develops with doping to form a weak Mott insulating state. Near the quantum phase transition, we discover a spatial electronic reorganization into a commensurate checkerboard charge order. These findings bear a resemblance to the universal charge order in the pseudogap phase of cuprates and demonstrate the ubiquity of charge order that emanates from doped Mott insulators. 
    more » « less
  4. Abstract We model the pseudogap state of the hole- and electron-doped cuprates as a metal with hole and/or electron pocket Fermi surfaces. In the absence of long-range antiferromagnetism, such Fermi surfaces violate the Luttinger requirement of enclosing the same area as free electrons at the same density. Using the Ancilla theory of such a pseudogap state, we describe the onset of conventionald-wave superconductivity by the condensation of a chargeeHiggs boson transforming as a fundamental under the emergent SU(2) gauge symmetry of a backgroundπ-flux spin liquid. In all cases, we find that thed-wave superconductor has gapless Bogoliubov quasiparticles at 4 nodal points on the Brillouin zone diagonals with significant velocity anisotropy, just as in the BCS state. This includes the case of the electron-doped pseudogap metal with only electron pockets centered at wavevectors (π, 0), (0, π), and an electronic gap along the zone diagonals. Remarkably, in this case, too, gapless nodal Bogoliubov quasiparticles emerge within the gap at 4 points along the zone diagonals upon the onset of superconductivity. 
    more » « less
  5. null (Ed.)
    The defining characteristic of hole-doped cuprates is d -wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, d -symmetry form factor, pair density wave (PDW) state coexisting with d -wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states N r , E is predicted at the terminal BiO surface of Bi 2 Sr 2 CaCu 2 O 8 and compared with high-precision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations of N r , E , the modulations of the coherence peak energy Δ p r , and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space q - space . Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi 2 Sr 2 CaCu 2 O 8 does contain a PDW + DSC state. Moreover, in the model the PDW + DSC state becomes unstable to a pure DSC state at a critical hole density p *, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry-breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point at p * ≈ 19% occurs due to disappearance of this PDW. 
    more » « less