Born approximation study of the strong disorder in magnetized surface states of topological insulator

Abstract

In this study we investigate the effect of random point disorder on the surface states of a topological insulator with out-of-plane magnetization. We consider the disorder within a high order Born approximation. The Born series converges to the one branch of the self-consistent Born approximation (SCBA) solution at low disorder. As the disorder strength increases, the Born series converges to another SCBA solution with the finite density of states within the magnetization induced gap. Further increase of the disorder strength leads to a divergence of the Born series, showing the limits of the applicability of the Born approximation. We find that the convergence properties of this Born series are closely related to the properties of the logistic map, which is known as a prototypical model of chaos. We also calculate the longitudinal and Hall conductivities within the Kubo formulas at zero temperature with the vertex corrections for the velocity operator. Vertex corrections are important for describing transport properties in the strong disorder regime. In the case of strong disorder, the longitudinal conductivity is weakly dependent on the disorder strength, while the Hall conductivity decreases with increasing disorder.

arXiv comment9 pages, 7 figures

References in corpus (27)

• Topological Insulators
• Anomalous Hall effect
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Classification of topological quantum matter with symmetries
• High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
• Trajectory of Anomalous Hall Effect toward the Quantized State in a Ferromagnetic Topological Insulator
• Electron transport in disordered graphene
• Effect of Disorder on Transport in Graphene
• Theory of the anomalous Hall effect from the Kubo formula and the Dirac equation
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Imaging Dirac-Mass Disorder from Magnetic Dopant-Atoms in the Ferromagnetic Topological Insulator Cr${}_x$(Bi${}_{0.1}$Sb${}_{0.9}$)${}_{2-x}$Te${}_3$
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Critical transport in weakly disordered semiconductors and semimetals
• Quantum anomalous Hall effect in magnetic topological insulators
• Breakdown of traditional many-body theories for correlated electrons
• A mechanism of $\frac{e^2}{2h}$ conductance plateau without 1D chiral Majorana fermions
• Anomalous Hall effect in a two-dimensional electron gas
• Half-Magnetic Topological Insulator
• Disorder-induced half-integer quantized conductance plateau in quantum anomalous Hall insulator-superconductor structures
• Magnetic-proximity-induced magnetoresistance on topological insulators
• Anomalous Hall effect in 2D Rashba ferromagnet
• From weak to strong disorder in Weyl semimetals: Self-consistent Born approximation
• Criticality of two-dimensional disordered Dirac fermions in the unitary class and universality of the integer quantum Hall transition
• Magnetic-field-induced topological phase transition in Fe-doped (Bi,Sb)${}_2$Se${}_3$ heterostructures
• Distinct quantum anomalous Hall ground states induced by magnetic disorders
• Topological Phase Transitions Induced by Disorder in Magnetically Doped (Bi, Sb)${}_2$Te${}_3$ Thin Films
• The Anomalous Hall Effect in Magnetic Topological Insulators

Cited by in corpus (1)

• Simple model for the gap in the surface states of the antiferromagnetic topological insulator MnBi${}_2$Te${}_4$