Disorder-Induced Topological Phases in a Two-Dimensional Chern Insulator with Strong Magnetic Disorder

Abstract

Strong directional disorder in local magnetic moments coupled to a Chern insulator gives rise to topological phases that cannot be continuously connected to the clean limit and are therefore genuinely disorder-driven. We demonstrate this in a spinful Qi-Wu-Zhang model of a two-dimensional Chern insulator coupled to disordered classical spins of unit length. The topological phase diagram is computed numerically using two complementary approaches: twisted boundary conditions and the topological Hamiltonian technique. Our results show that strong disorder can act as a fundamental topological mechanism rather than merely a perturbation. For strong exchange coupling, tuning the mass parameter reveals a transition between phases with different Chern numbers $C$. Remarkably, this transition is driven by zeros, rather than poles, of the disorder-averaged Green's function crossing the chemical potential, and has no analogue in any clean system. We further identify a strong-coupling phase with $C=0$ that is nonetheless topologically nontrivial, characterized by a distinct Chern number $C^{(\mathrm{S})}\ne 0$ over the manifold of classical spin configurations. This phase is also disorder-driven, as $C^{(\mathrm{S})}=0$ in the clean limit.

16 pages, 10 figures, v2 with minor changes, as published

References in corpus (41)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Spin Anisotropy and Quantum Hall Effect in the Kagome Lattice - Chiral Spin State based on a Ferromagnet-
• Topological Anderson Insulator
• The Non-Commutative Geometry of the Quantum Hall Effect
• Berry Phase Theory of Anomalous Hall Effect: Application to Colossal Magnetoresistance Manganites
• Theory of the topological Anderson insulator
• Interacting topological insulators: a review
• Single particle Green's functions and interacting topological insulators
• Mapping topological order in coordinate space
• Numerical study of the topological Anderson insulator in HgTe/CdTe quantum wells
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Simplified topological invariants for interacting insulators
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Topological Anderson Insulator in Three Dimensions
• Disordered Topological Insulators: A Non-Commutative Geometry Perspective
• Observation of non-Hermitian topological Anderson insulator in quantum dynamics
• K-Theory and Pseudospectra for Topological Insulators
• Non-Commutative Tools for Topological Insulators
• Three-dimensional phase diagram of disordered HgTe/CdTe Quantum spin-Hall wells
• Almost Commuting Matrices, Localized Wannier Functions, and the Quantum Hall Effect
• Disorder-Induced Multiple Transition involving Z2 Topological Insulator
• Mott insulators with boundary zeros
• Many-body Chern number without integration
• Self-energy-functional theory for systems of interacting electrons with disorder
• Quantum criticality at the Chern-to-normal insulator transition
• Topological phase transition driven by magnetic field and topological Hall effect in an antiferromagnetic skyrmion lattice
• Magnetic skyrmion crystal at a topological insulator surface
• Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae
• Antiferromagnetic chiral spin density wave and strain-induced Chern insulator in the square lattice Hubbard model with frustration
• Topological Hall effect induced by classical large-spin background: $su(2)$ path-integral approach
• Spin Berry curvature of the Haldane model
• Chern insulating state with double-$Q$ ordering wave vectors at the Brillouin zone boundary
• Bound states and local topological phase diagram of classical impurity spins coupled to a Chern insulator
• Coherent cellular dynamical mean-field theory: a real-space quantum embedding approach to disorder in strongly correlated electron systems