Multicriticality of Two-dimensional Class D Disordered Topological Superconductors

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.

14 pages, 13 figures

References in corpus (46)

• Anyons in an exactly solved model and beyond
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Anderson Transitions
• The Kernel Polynomial Method
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Quantum-limited shot noise in graphene
• Evidence for Majorana bound state in an iron-based superconductor
• Zitterbewegung, chirality, and minimal conductivity in graphene
• Chiral Majorana edge state in a quantum anomalous Hall insulator-superconductor structure
• Corrections to scaling at the Anderson transition
• Quasiparticle localization in superconductors with spin-orbit scattering
• Random Network Models and Quantum Phase Transitions in Two Dimensions
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators
• Majorana bound states without vortices in topological superconductors with electrostatic defects
• Critical exponent for the quantum Hall transition
• Non-Majorana Origin of the Half-Quantized Conductance Plateau in Quantum Anomalous Hall Insulator and Superconductor Hybrid Structures
• The Anderson transition: time reversal symmetry and universality
• Critical exponent for the Anderson transition in the three dimensional orthogonal universality class
• The two-dimensional random-bond Ising model, free fermions and the network model
• Disordered 2d quasiparticles in class D: Dirac fermions with random mass, and dirty superconductors
• Thermal metal in network models of a disordered two-dimensional superconductor
• Random-bond Ising model in two dimensions, the Nishimori line, and supersymmetry
• Effect of Disorder in a Three-Dimensional Layered Chern Insulator
• Criticality in the two-dimensional random-bond Ising model
• Bond disordered spin liquid and the honeycomb iridate H${}_3$LiIr${}_2$O${}_6$ $-$ abundant low energy density of states from random Majorana hopping
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect
• Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
• Ballistic transport in disordered graphene
• Disorder-induced half-integer quantized conductance plateau in quantum anomalous Hall insulator-superconductor structures
• Learning Disordered Topological Phases by Statistical Recovery of Symmetry
• Disorder-induced Majorana metal in interacting non-Abelian anyon systems
• Effective mass and tricritical point for lattice fermions localized by a random mass
• Quantum phase transition of chiral Majorana fermion in the presence of disorder
• Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class D thermal quantum Hall effect
• Temperature enhancement of thermal Hall conductance quantization
• Anderson-Kitaev spin liquid
• Quantum Multicriticality in Disordered Weyl Semimetal
• Negative scaling dimensions and conformal invariance at the Nishimori point in the +/-J random-bond Ising model
• Griffiths phase in the thermal quantum Hall effect
• Conductance distributions in disordered quantum spin-Hall systems
• Universal critical exponent in class D superconductors
• Critical fixed points in class D superconductors
• Quantum transport phenomena in disordered electron systems with spin-orbit coupling in two dimensions and below
• Localization properties of random-mass Dirac fermions from real-space renormalization group

Cited by in corpus (13)

• Coherent error threshold for surface codes from Majorana delocalization
• Topological Random Fractals
• Surface codes, quantum circuits, and entanglement phases
• Anisotropic Topological Anderson Transitions in Chiral Symmetry Classes
• Zeros of Green Functions in Topological Insulators
• Generalized multifractality at metal-insulator transitions and in metallic phases of 2D disordered systems
• Topological effect on the Anderson transition in chiral symmetry classes
• Renormalization group analysis of Dirac fermions with random mass
• Majorana-metal transition in a disordered superconductor: percolation in a landscape of topological domain walls
• Genuine topological Anderson insulator from impurity induced chirality reversal
• Symmetry and Topology of Monitored Quantum Dynamics
• Generalized multifractality at the spin quantum Hall transition: Percolation mapping and pure-scaling observables
• Effect of Uncorrelated On-site Scalar Potential and Mass Disorder on Transport of Two-Dimensional Dirac Fermions