Triplet Pair-Density Wave Superconductivity on the $π$-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 π-flux square lattice model with on-site repulsion and moderate nearestneighbor 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 π-flux lattice is a special time-reversal symmetric case.

Emergence of Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model

“…On the other hand, defying expectations that the weak coupling regime (U W ) in Chern bands leads to a stable Fermi liquid (FL) fixed point, recent analysis [29,30] has uncovered new FL instabilities in partially filled Hofstadter bands [31] (generally supporting non-zero Chern number [32]) due to the interplay of repulsive interactions and logarithmic Van Hove singularities (VHS). In such fractal bands, the magnet flux per unit cell acts a control knob changing the landscape of VHSs and opening new interaction channels.…”