📝 SummarXiv

Abstract

Pair-density-wave (PDW) states -- exotic superconductors with spatially modulated order -- are a long-sought-after phase of quantum materials, with the potential to unravel the mysteries of high-$T_c$ cuprates and other strongly correlated superconductors. Yet, surprisingly, a key signature of stable superconductivity, namely the positivity of the superfluid density, $n_s(T)$, has not yet been demonstrated. Here, we address this central issue by calculating $n_s(T)$, for a generic model two-dimensional PDW superconductor. We uncover a surprisingly large region of intrinsic instability, associated with negative $n_s(T)$, revealing that a significant portion of the parameter space thought to be physical cannot support superconducting order. This instability is driven by the large pairing momentum required to form the PDW state. In the remaining stable regime, we predict two striking and observable fingerprints: an anomalously small longitudinal superfluid response that is vulnerable to thermal fluctuations, and an unusual temperature dependence for $n_s(T)$ arising from the unique gapless excitation spectrum of the PDW state. These generally model independent, as well as experimentally relevant findings suggest that the fragility of the superfluid density poses a significant problem for the formation of stable, finite temperature PDW superconductivity.