Global phase diagram of a three dimensional dirty topological superconductor

Abstract

We investigate the phase diagram of a three-dimensional, time-reversal symmetric topological superconductor in the presence of charge impurities and random $s$-wave pairing. Combining complimentary field theoretic and numerical methods, we show that the quantum phase transition between two topologically distinct paired states (or thermal insulators), described by thermal Dirac semimetal, remains unaffected in the presence of sufficiently weak generic randomness. At stronger disorder, however, these two phases are separated by an intervening thermal metallic phase of diffusive Majorana fermions. We show that across the insulator-insulator and metal-insulator transitions, normalized thermal conductance displays single parameter scaling, allowing us to numerically extract the critical exponents across them. The pertinence of our study in strong spin-orbit coupled, three-dimensional doped narrow gap semiconductors, such as Cu${}_x$Bi${}_2$Se${}_3$, is discussed.

Published version in PRL: 5+epsilon Pages, 4 Figures (Supplementary: 8 Pages, 3 Figures; as Ancillary File)

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• Dissolution of topological Fermi arcs in a dirty Weyl semimetal
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• Nodal points of Weyl semimetals survive the presence of moderate disorder
• Topological and conventional phases of a three dimensional electron glass
• Noncrystalline topological superconductors
• Universality classes of the Anderson transition in three-dimensional symmetry classes AIII, BDI, C, D and CI
• Itinerant quantum multi-criticality of two dimensional Dirac fermions
• Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
• Anisotropic Topological Anderson Transitions in Chiral Symmetry Classes
• Topological Anomalous Skin Effect in Weyl Superconductors
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• Quantum criticality of fermion velocities and critical temperature nearby a putative quantum phase transition in the $d$-wave superconductors
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene
• Quantized thermal and spin transports of dirty planar topological superconductors
• Hybrid symmetry class topological insulators
• Superconductivity in doped planar Dirac insulators: A renormalization group study
• Singular low-energy states of tilted Dirac semimetals induced by the fermion-fermion interactions
• Critical behavior around the fixed points driven by fermion-fermion interactions and disorders in the nodal-line superconductors
• Superconductivity in three-dimensional interacting doped topological insulators
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Critical fates induced by the interaction competition in three-dimensional tilted Dirac semimetals