Revisiting vestigial order in nematic superconductors: gauge-field mechanisms and model constraints

TL;DR

This study investigates the emergence of vestigial nematic phases in superconductors, confirming their absence in common models and identifying specific conditions where gauge-field interactions can stabilize such phases.

Contribution

The paper provides large-scale simulations showing the absence of vestigial nematic phases in typical models and proposes mechanisms involving gauge fields for their potential stabilization.

Findings

Common models do not exhibit vestigial nematic phases.

Gauge-field coupling can stabilize vestigial order under certain conditions.

Numerical results align with recent analytical conclusions.

Abstract

An electronic nematic order that originates from superconducting fluctuation but persists above the superconducting transition temperature is often referred to as a vestigial nematic phase. Such a vestigial order belongs to the broader class of composite orders discussed in earlier literature, characterized by ordering in gauge-invariant combinations of superconducting order parameters while the individual superconducting order parameters remain disordered. These states include metallic superfluids, paired phases, and composite (charge-4e) superconductors. Whether and under what conditions such a vestigial phase can emerge in realistic models of nematic superconductors remains an open question. Recent analytical work [P. T. How and S. K. Yip, Phys. Rev. B 107, 104514 (2023)] concluded that vestigial nematic phases--and related mechanisms--do not appear in the widely studied models proposed for, e.g., Bi$_2$Se$_3$-based candidates. To shed light on this question, we perform large-scale Monte Carlo simulations of a three-dimensional Ginzburg-Landau model of a nematic superconductor. Consistent with the findings of How and Yip, our numerical results confirm that commonly considered models do not exhibit vestigial nematic phases or nematic-fluctuation-induced charge-4e superconductivity. Extending the analysis to include coupling to a gauge field, we show that vestigial nematic order can, under restrictive conditions, be stabilized through an alternative mechanism: intercomponent coupling mediated by the gauge field or the effects of strong correlations.