Correlations between superconducting and resistive anisotropies

TL;DR

This paper theoretically investigates how transport anisotropies in metals and superconductors relate to different symmetry-breaking scenarios, providing insights into their origins through analysis of various models and experimental implications.

Contribution

It develops a comprehensive theoretical framework for understanding correlations of anisotropies in normal and superconducting phases, including vestigial order and finite-momentum pairing.

Findings

Transport anisotropies depend on the symmetry-breaking scenario.

Measurement of directional critical current constrains the origin of anisotropy.

Models relevant to twisted multilayer graphene and related materials are analyzed.

Abstract

There are multiple possible origins of transport anisotropies in metals and superconductors. For instance, rotational symmetry can be spontaneously broken in the normal state as a result of electronic nematic order inducing anisotropies in an otherwise $s$-wave superconducting phase. Another possibility is that the dominant source of rotational symmetry breaking is the superconductor itself and its vestiges that may survive in the normal state. We here theoretically analyze the correlations of transport anisotropies in the normal and the corresponding superconducting phase for different scenarios of broken symmetry, either coming solely from the normal state, solely from the superconductor and its vestiges in the metallic regimes, or from both simultaneously. We further include both zero-momentum and finite-momentum pairing; we develop a theory of vestigial order for the latter, characterized by broken rotational and translational symmetry. Our findings reveal that the relative transport anisotropies in the normal and superconducting phases sensitively depend on the scenario, including the form of vestigial order and, in some cases, the parity of the superconducting order parameter. As such, measuring the directional dependence of the critical current and resistivity can provide strong constraints on the origin of rotational symmetry breaking. We demonstrate our findings in minimal models relevant to twisted multilayer graphene, rhombohedral graphene, and twisted transition metal dichalcogenides.