Topological Quantum Phase Transitions in Metallic Shiba Lattices

Shiba bands formed by overlapping Yu-Shiba-Rusinov subgap states in magnetic impurities on a superconductor play an important role in topological superconductors. Here, we theoretically demonstrate the existence of a new type of Shiba bands (dubbed topological Shiba metal) on a magnetically doped $s$-wave superconducting surface with Rashba spin-orbit coupling in the presence of a weak in-plane magnetic field. Such topological gapless Shiba bands develop from gapped Shiba bands through Lifshitz phase transitions accompanied by second-order quantum phase transitions for the intrinsic thermal Hall conductance. We also find a mechanism in Shiba lattices that protects the first-order quantum phase transitions for the intrinsic thermal Hall conductance. Due to the long-range hopping in Shiba lattices, the topological Shiba metal exhibits intrinsic thermal Hall conductance with large nonquantized values. As a consequence, there emerge a large number of second-order quantum phase transitions.