📝 SummarXiv

Abstract

We study conditions of the appearance of \$U(1) \times \mathbb{Z}_2\$ superconducting states that spontaneously break time-reversal symmetry (BTRS) on a square lattice as a function of applied stress. We focus on the spin-singlet s+id state. Calculations show that if critical temperatures coincide at zero stress they exhibit linear kink and no kink otherwise. We find that in general, the microscopic calculations show a complex phase diagram, for example, non-monotonic behavior of BTRS transition. Another beyond-Ginzburg-Landau theory result is that \$U(1)\$ critical temperature can decrease under compressional strain for small Poisson ratio materials. In the second part of the paper we consider effects of boundaries and finiteness of the sample on the strain-induced splitting of \$T_c^{U(1)}\$ and \$T_c^{\mathbb{Z}_2}\$ transitions. A finite sample has BTRS boundary states with persistent superconducting currents over a wide range of band filling. Overall, the BTRS dome occupies a larger band filling--temperature phase space region for a mesoscopic sample with [110] surface compared to an infinite system. Hence, the presence of boundaries helps to stabilize the BTRS phase.