Spontaneous surface current in multi-component cubic superconductors with time-reversal symmetry breaking

TL;DR

This paper investigates spontaneous surface currents in multi-component cubic superconductors with time-reversal symmetry breaking, revealing conditions for their existence and extending theoretical models to include effects like gap anisotropy and surface disorder.

Contribution

It establishes the symmetry conditions for spontaneous currents in TRSB cubic superconductors and refines the Ginzburg-Landau theory with numerical BdG calculations, including effects of disorder and anisotropy.

Findings

Spontaneous surface currents occur only when TRSB pairing breaks specific mirror symmetries.

Numerical BdG calculations confirm the symmetry-based criteria for current existence.

A refined low-temperature effective theory is necessary in certain cases where GL theory is insufficient.

Abstract

In this work we present a comprehensive study of the spontaneous currents in time-reversal symmetry breaking (TRSB) multi-component superconductors with cubic crystalline symmetry. We argue, not limiting to cubic lattices, that spontaneous current on certain high-symmetry surfaces can exist only if the TRSB pairing simultaneously breaks a certain pair of mirror symmetries. This is shown to have exact correspondence with the Gingzburg-Landau (GL) theory and is verified by numerical Bogoliubov de-Gennes (BdG) calculations. In the course we extend the BdG to include effects of gap anisotropy and surface disorder, both of which could lead to a much suppressed current. The GL theory has been known to describe well the spontaneous current. However, we highlight a special case where it becomes less adequate, and show that a refined effective theory for low temperatures is needed. These results could shed light on the phenomenology of cubic superconductors such as U$_{1-x}$Th$_x$Be$_{13}$, the filled skutterudites PrOs$_4$Sb$_{12}$, PrPt$_4$Ge$_{12}$ and related compounds.