Triplet Pair-Density Wave Superconductivity on the $\pi$-flux Square Lattice

Abstract

Pair-density waves (PDW) are superconducting states that spontaneously break translation symmetry in systems with time-reversal symmetry (TRS). Evidence for PDW has been seen in several recent experiments, as well as in the pseudogap regime in cuprates. Theoretical understanding of PDW has been largely restricted to phenomenological and numerical studies, while microscopic theories typically require strong-coupling or fine-tuning. In this work, we provide a novel symmetry-based mechanism under which PDW emerges as a weak coupling instability of a 2D TRS metal. Combining mean-field and renormalization group analyses, we identify a weak-coupling instability towards a triplet PDW realized in the $\pi$-flux square lattice model with on-site repulsion and moderate nearest-neighbor attraction when the Fermi level crosses Van Hove singularities at 1/4 and 3/4 fillings. This PDW is protected by the magnetic translation symmetries characteristic of Hofstadter systems, of which the $\pi$-flux lattice is a special time-reversal symmetric case.

7+9 pages, 3+5 figures

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• Self-consistent theory of $2\times 2$ pair density waves in kagome superconductors
• Pair-density-wave and $s\pm \mathrm{i}d$ superconductivity in a strongly coupled, lightly doped Kondo insulator
• Pair-density-wave superconductivity: a microscopic model on 2D honeycomb lattice
• Pair density wave characterized by a hidden string order parameter
• Density matrix renormalization group study of quantum-geometry-facilitated pair density wave order
• Pseudo-magnetic fields in square lattices
• Strong pair-density-wave fluctuations in an exactly solvable doped Mott insulator
• Vestigial $d$-wave charge-$4e$ Superconductivity from Bidirectional Pair Density Waves
• Efficiency of the superconducting diode effect of pair-density-wave states in two-dimensional $d$-wave altermagnets
• Enhanced pair-density-wave vertices in a bilayer Hubbard model at half-filling
• Pair-density-wave phase of strongly interacting electrons on the triangular lattice: A variational Monte Carlo study
• Spin-triplet pair density wave superconductors