Phase transition and fractionalization in the superconducting Kondo lattice model

Abstract

Topology, symmetry, electron correlations, and the interplay between them have formed the cornerstone of our understanding of quantum materials in recent years and are used to identify new emerging phases. While the first two give a fair understanding of noninteracting and, in many cases, weakly interacting wave function of electron systems, the inclusion of strong correlations could change the picture substantially. The Kondo lattice model is a paradigmatic example of the interplay of electron correlations and conduction electrons of a metallic system, describing heavy fermion materials and also fractionalized Fermi liquid pertaining to an underlying gauge symmetry and topological orders. In this work, we study a superconducting Kondo lattice model, a network of 1D Kitaev superconductors Kondo coupled to a lattice of magnetic moments. Using slave-particle representation of spins and exact numerical calculations, we obtain the phase diagram of the model in terms of Kondo coupling $J_K$ and identify a topological order phase for $J_{K}<J_{K}^c$ and a Kondo compensated phase for $J_{K}>J_{K}^c$, where $J_{K}^c$ is the critical point. Setting the energy scales of electron hopping and pairing to unity, the mean-field theory calculations achives $J_{K}^c=2$ and in exact numerics we found $J_{K}^c\simeq 1.76$, both of which show that the topological order is a robust phase. We argue that in terms of slave particles, the compensated phase corresponds to an invertible phase, and a Mott insulating transition leads to a topological order phase. Furthermore, we show that in the regime $J_{K}<J_{K}^c$ in addition to the low-energy topological states, a branch of subgap states appears inside the superconducting gap.