Fermi points and topological quantum phase transitions in a model of superconducting wires

TL;DR

This paper explores a two-band $sp$ model of spinless fermions with antisymmetric interactions, revealing diverse topological phases and phase transitions with unique critical behavior, extending understanding of topological quantum phase transitions beyond known models.

Contribution

It introduces a novel $sp$ two-band fermion model with antisymmetric hybridization and interactions, analyzing its rich phase diagram and unique critical exponents in topological phase transitions.

Findings

Identifies a Weyl superconductor, topological insulator, and trivial phases in the model.

Discovers that the topological transition has distinct critical exponents from Kitaev's model.

Shows the transition can be either continuous or discontinuous depending on parameters.

Abstract

The importance of models with an exact solution for the study of materials with non-trivial topological properties has been extensively demonstrated. Among these, the Kitaev model of a one-dimensional $p$-wave superconductor plays a guiding role in the search for Majorana modes in condensed matter systems. Also, the $sp$ chain, with an anti-symmetric mixing among the $s$ and $p$ bands provides a paradigmatic example of a topological insulator with well understood properties. There is an intimate relation between these two models and in particular their topological quantum phase transitions share the same universality class. Here we consider a two-band $sp$ model of spinless fermions with an attractive (inter-band) interaction. Both the interaction and hybridization between the $s$ and $p$ fermions are anti-symmetric. The zero temperature phase diagram of the model presents a variety of phases including a Weyl superconductor, topological insulator and trivial phases. The quantum phase transitions between these phases can be either continuous or discontinuous. We show that the transition from the topological superconducting phase to the trivial one has critical exponents different from those of an equivalent transition in Kitaev's model.