Multicriticality of Two-dimensional Class D Disordered Topological Superconductors

TL;DR

This paper investigates the phase diagram and critical behaviors of two-dimensional disordered topological superconductors in symmetry class D, revealing multiple phases, a tricritical point, and universality classes through numerical analysis.

Contribution

It provides the first detailed numerical study of phase transitions and critical behaviors in 2D class D disordered topological superconductors, identifying a tricritical point and universality classes.

Findings

Existence of a tricritical point where three phases meet.

Two metal-insulator transitions belong to the same universality class.

The tricritical point represents a distinct universality class.

Abstract

A generic two-dimensional disordered topological superconductor in symmetry class D exhibits rich phenomenology and multiple phases: diffusive thermal metal (DTM), Anderson insulator (AI), and thermal quantum Hall (TQH) phase (a topological superconductor). We numerically investigate the phase diagram of a lattice model of such class D superconductor, specifically focusing on transitions between the phases and the associated universal critical behaviors. We confirm the existence of a tricritical point and its repulsive nature at the point on the phase diagram where the three phases meet. We characterize the critical behaviors at various critical points and the tricritical point using numerical evaluation of the localization length, the conductance (or conductivity), and the density of states. We conclude that the two metal-insulator transitions (DTM-TQH and DTM-AI) belong to the same universality class, whereas the tricritical point (TCP) represents a distinct universality class.