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Spontaneous edge corner currents in $s+is$ superconductors and time reversal symmetry breaking surface states

We present a study of the basic microscopic model of an $s$-wave superconductor with frustrated interband interaction. When frustration is strong, such an interaction gives raise to a $s+is$ state. This is a $s$-wave superconductor that spontaneously breaks time reversal symmetry. We show that, in addition to the known $s+is$ state, there is additional phase, where the system's bulk is a conventional $s$-wave state, but superconducting surface states break time reversal symmetry. Furthermore, we show that $s+is$ superconductors can have spontaneous boundary currents and spontaneous magnetic fields. These arise at lower-dimensional boundaries, namely, the corners, in two-dimensional samples. This demonstrates that boundary currents effects in superconductors can arise in states which are not topological and not chiral according to the modern classification.