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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.
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Ground-state phase diagram of the t-t ′ -J model
We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t - t ′ - J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative t ′ values ( t ′ / t = ± 0.2 ) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The t ′ < 0 (hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find t ′ < 0 strongly suppresses superconductivity. The t ′ > 0 (electron-doped) region shows the expected circular Fermi pocket of holes around the ( π , π ) point and a broad low-doped region of coexisting antiferromagnetism and d -wave pairing with a triplet p component at wavevector ( π , π ) induced by the antiferromagnetism and d -wave pairing. The pairing for the electron low-doped system with t ′ > 0 is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d -wave pairing and striped p -wave pairing appears. In a small doping region near x = 0.08 for t ′ ∼ − 0.2 , we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.
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- Award ID(s):
- 2110041
- PAR ID:
- 10322389
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 118
- Issue:
- 44
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1073/pnas.2109978118
