Spontaneous edge and 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\nsuperconductor with frustrated interband interaction. When frustration is\nstrong, such an interaction gives raise to a $s+is$ state. This is a $s$-wave\nsuperconductor that spontaneously breaks time reversal symmetry. We show that,\nin addition to the known $s+is$ state, there is additional phase, where the\nsystem's bulk is a conventional $s$-wave state, but superconducting surface\nstates break time reversal symmetry. Furthermore, we show that $s+is$\nsuperconductors can have spontaneous boundary currents and spontaneous magnetic\nfields. These arise at lower-dimensional boundaries, namely, the corners, in\ntwo-dimensional samples. This demonstrates that boundary currents effects in\nsuperconductors can arise in states which are not topological and not chiral\naccording to the modern classification.\n