skip to main content

Title: Magnetic field–induced pair density wave state in the cuprate vortex halo
High magnetic fields suppress cuprate superconductivity to reveal an unusual density wave (DW) state coexisting with unexplained quantum oscillations. Although routinely labeled a charge density wave (CDW), this DW state could actually be an electron-pair density wave (PDW). To search for evidence of a field-induced PDW, we visualized modulations in the density of electronic states N ( r ) within the halo surrounding Bi 2 Sr 2 CaCu 2 O 8 vortex cores. We detected numerous phenomena predicted for a field-induced PDW, including two sets of particle-hole symmetric N ( r ) modulations with wave vectors Q P and 2 Q P , with the latter decaying twice as rapidly from the core as the former. These data imply that the primary field-induced state in underdoped superconducting cuprates is a PDW, with approximately eight CuO 2 unit-cell periodicity and coexisting with its secondary CDWs.
Authors:
; ; ; ; ; ; ; ; ; ;
Award ID(s):
1664842
Publication Date:
NSF-PAR ID:
10112673
Journal Name:
Science
Volume:
364
Issue:
6444
Page Range or eLocation-ID:
976 to 980
ISSN:
0036-8075
Sponsoring Org:
National Science Foundation
More Like this
  1. 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,more »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.« 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 2more »O 8 pseudogap phase.« less
  3. 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 openingmore »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 .« less
  4. Abstract

    A pair-density-wave (PDW) is a superconducting state with an oscillating order parameter. A microscopic mechanism that can give rise to it has been long sought but has not yet been established by any controlled calculation. Here we report a density-matrix renormalization-group (DMRG) study of an effectivet-J-Vmodel, which is equivalent to the Holstein-Hubbard model in a strong-coupling limit, on long two-, four-, and six-leg triangular cylinders. While a state with long-range PDW order is precluded in one dimension, we find strong quasi-long-range PDW order with a divergent PDW susceptibility as well as the spontaneous breaking of time-reversal and inversion symmetries. Despite the strong interactions, the underlying Fermi surfaces and electron pockets around theKand$${K}^{\prime}$$Kpoints in the Brillouin zone can be identified. We conclude that the state is valley-polarized and that the PDW arises from intra-pocket pairing with an incommensurate center of mass momentum. In the two-leg case, the exponential decay of spin correlations and the measured central chargec ≈ 1 are consistent with an unusual realization of a Luther-Emery liquid.

  5. ABSTRACT

    GW190425 was the second gravitational wave (GW) signal compatible with a binary neutron star (BNS) merger detected by the Advanced LIGO and Advanced Virgo detectors. Since no electromagnetic counterpart was identified, whether the associated kilonova was too dim or the localization area too broad is still an open question. We simulate 28 BNS mergers with the chirp mass of GW190425 and mass ratio 1 ≤ q ≤ 1.67, using numerical-relativity simulations with finite-temperature, composition dependent equations of state (EOS) and neutrino radiation. The energy emitted in GWs is $\lesssim 0.083\mathrm{\, M_\odot }c^2$ with peak luminosity of 1.1–$2.4\times ~10^{58}/(1+q)^2\, {\rm {erg \, s^{-1}}}$. Dynamical ejecta and disc mass range between 5 × 10−6–10−3 and 10−5–$0.1 \mathrm{\, M_\odot }$, respectively. Asymmetric mergers, especially with stiff EOSs, unbind more matter and form heavier discs compared to equal mass binaries. The angular momentum of the disc is 8–$10\mathrm{\, M_\odot }~GM_{\rm {disc}}/c$ over three orders of magnitude in Mdisc. While the nucleosynthesis shows no peculiarity, the simulated kilonovae are relatively dim compared with GW170817. For distances compatible with GW190425, AB magnitudes are always dimmer than ∼20 mag for the B, r, and K bands, with brighter kilonovae associated to more asymmetric binaries and stiffer EOSs. We suggest that,more »even assuming a good coverage of GW190425’s sky location, the kilonova could hardly have been detected by present wide-field surveys and no firm constraints on the binary parameters or EOS can be argued from the lack of the detection.

    « less