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

We present a study of the basic microscopic model of a 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 super-conductor 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.