Disorder-robust phase crystal in high-temperature superconductors stabilized by strong correlations

TL;DR

This paper reveals a new disorder-robust phase crystal state in high-temperature cuprate superconductors, arising from the interplay of strong correlations, topology, and disorder, characterized by modulated superconducting orders.

Contribution

It introduces a novel phase crystal state stabilized by strong correlations, which is robust to disorder and involves coexisting modulated $d$-wave and extended $s$-wave superconducting orders.

Findings

The phase crystal state breaks translational and time-reversal symmetry.

It remains stable despite disorder due to strong correlations.

The state involves a modulation of superconducting phases.

Abstract

The simultaneous interplay of strong electron-electron correlations, topological zero-energy states, and disorder is yet an unexplored territory but of immense interest due to their inevitable presence in many materials. Copper oxide high-temperature superconductors (cuprates) with pair breaking edges host a flat band of topological zero-energy states, making them an ideal playground where strong correlations, topology, and disorder are strongly intertwined. Here we show that this interplay in cuprates generates a new phase of matter: a fully gapped ``phase crystal" state that breaks both translational and time-reversal invariance, characterized by a modulation of the $d$-wave superconducting phase co-existing with a modulating extended $s$-wave superconducting order. In contrast to conventional wisdom, we find that this phase crystal state is remarkably robust to omnipresent disorder, but only in the presence of strong correlations, thus giving a clear route to its experimental realization.