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 for realizing topological superconductors. Here, we theoretically demonstrate the existence of topological gapless Shiba bands on a magnetically doped s-wave superconducting surface with Rashba spin-orbit coupling in the presence of a weak in-plane magnetic field. Such 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 emerges a large number of second-order quantum phase transitions. © 2022 American Physical Society.