Critical Behaviors of Anderson Transitions in Three Dimensional Orthogonal Classes with Particle-hole Symmetries

Abstract

From transfer-matrix calculation of localization lengths and their finite-size scaling analyses, we evaluate critical exponents of the Anderson metal-insulator transition in three dimensional (3D) orthogonal class with particle-hole symmetry, class CI, as $\nu =1.16\pm 0.02$. We further study disorder-driven quantum phase transitions in the 3D nodal line Dirac semimetal model, which belongs to class BDI, and estimate critical exponent as $\nu =0.80\pm 0.02$. From a comparison of the critical exponents, we conclude that a disorder-driven re-entrant insulator-metal transition from the topological insulator phase in the class BDI to the diffusive metal phase belongs to the same universality class as the Anderson transition in the 3D class BDI. We also argue that an infinitesimally small disorder drives the nodal line Dirac semimetal in the clean limit to the diffusive metal.

4 pages with two figures, 1 table and supplemental materials

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Cited by in corpus (12)

• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems
• Universality classes of the Anderson transition in three-dimensional symmetry classes AIII, BDI, C, D and CI
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Anisotropic Topological Anderson Transitions in Chiral Symmetry Classes
• Metal-insulator transition in a 2D system of chiral unitary class
• Topological effect on the Anderson transition in chiral symmetry classes
• Generalized multifractality in 2D disordered systems of chiral symmetry classes
• Intrinsic (Axion) Statistical Topological Insulator
• Disorder-induced instability of a Weyl nodal loop semimetal towards a diffusive topological metal with protected multifractal surface states
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors