Broken translational symmetry at edges of unconventional superconductors

Flat bands of zero-energy states at edges of d-wave superconductors have a topological origin. However, a mechanism that can shift the band to finite energies would lower the free energy, break the initial topological protection, and thereby enable a phase transition. We present results [1] for a second-order phase transition at T≈0.2T_c, where T_c is the superconducting transition temperature, where time-reversal and continuous translational symmetry along the surface are spontaneously broken. The order parameter, the superfluid momentum p_s, forms a non-trivial planar vector field with sources and sinks, that satisfies a generalized Poincaré-Hopf theorem, relating the sum of Poincaré indices to the Euler characteristics of the system. We discuss the robustness of this phase against an external magnetic field, mesoscopic surface roughness, and system size. We also present signatures for experimental verification by calorimetry and magnetometry.

[1] P. Holmvall, A.B. Vorontsov, M. Fogelström, T. Löfwander, Nat. Commun. 9, 2190 (2018).