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

TL;DR

This paper introduces a new weak-coupling mechanism for triplet pair-density wave superconductivity on a $\

Contribution

It reveals a symmetry-protected triplet PDW state in a $\\pi$-flux square lattice model, expanding understanding of PDW origins in weak-coupling regimes.

Findings

Identified a weak-coupling instability towards triplet PDW at Van Hove singularities.

Demonstrated the role of magnetic translation symmetries in protecting the PDW state.

Established the relevance of the $\\pi$-flux lattice as a time-reversal symmetric Hofstadter system.

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.