Supercurrents and spontaneous time-reversal symmetry breaking by nonmagnetic disorder in unconventional superconductors

Abstract

Recently, a theoretical study [Z.-X. Li et al., npj Quantum Mater. 6, 36 (2021)] investigated a model of a disordered $d$-wave superconductor, and reported local time-reversal symmetry breaking current loops for sufficiently high disorder levels. Since the pure $d$-wave superconducting state does not break time-reversal symmetry, it is surprising that such persistent currents arise purely from nonmagnetic disorder. Here, we perform a detailed theoretical investigation of such disorder-induced orbital currents, and show that the occurrence of the currents can be traced to the emergence of local (extended) $s$-wave order coexisting with underlying disordered $d$-wave pairing, making it favorable to generate local $s\ifmmode\pm\else\textpm\fi{}id$ regions. We discuss the energetics leading to such regions of $s\ifmmode\pm\else\textpm\fi{}id$ order, which support spontaneous local current loops in the presence of inhomogeneous density modulations.