Multicriticality of two-dimensional class-D disordered topological superconductors

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 represents a distinct universality class.

Automated summary

This study investigates the phase diagram of a generic two-dimensional disordered topological superconductor in symmetry class D and identifies a tricritical point as well as distinct universality classes. Critical behaviors at various critical points and the tricritical point are characterized using numerical evaluations of localization length, conductance (or conductivity), and density of states. The transitions between diffusive thermal metal (DTM) and thermal quantum Hall (TQH), as well as between DTM and Anderson insulator (AI), are found to belong to the same universality class, while the tricritical point represents a different universality class.