Phase transitions and scale invariance in topological Anderson insulators

Abstract

We investigate disordered-driven transitions between trivial and topological insulator (TI) phases in two-dimensional (2D) systems. Our study primarily focuses on the BHZ model with Anderson disorder, while other standard 2DTI models exhibit equivalent features. The analysis is based on the local Chern marker (LCM), a local quantity that allows for the characterization of topological transitions in finite and disordered systems. Our simulations indicate that disorder-driven trivial to topological insulator transitions are nicely characterized by ${\mathcal{C}}_0$, the disorder averaged LCM near the central cell of the system. We show that ${\mathcal{C}}_0$ is characterized by a single-parameter scaling, namely, ${\mathcal{C}}_0(M,W,L)\equiv {\mathcal{C}}_0(z)$ with $z=[W^{\mu }-W_c^{\mu }(M)]L$, where $M$ is the Dirac mass, $W$ is the disorder strength and $L$ is the system size, while $W_c(M)\propto \sqrt{M}$ and $\mu \approx 2$ stand for the critical disorder strength and critical exponent, respectively. Our numerical results are in agreement with a theoretical prediction based on a first-order Born approximation (1BA) analysis. These observations lead us to speculate that the universal scaling function we have found is rather general for amorphous and disorder-driven topological phase transitions.

7 pages, 4 figures, and a supplemental material with 7 pages, 4 figures

References in corpus (19)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• The Kernel Polynomial Method
• Topological Anderson Insulator
• Photonic Topological Anderson Insulators
• Disorder-induced Floquet Topological Insulators
• Topological Anderson Insulator in Three Dimensions
• The dependence of topological Anderson insulator on the type of disorder
• Disorder effect on 3-dimensional $Z_2$ quantum spin Hall systems
• Three-dimensional phase diagram of disordered HgTe/CdTe Quantum spin-Hall wells
• Toward Realistic Amorphous Topological Insulators
• Universality classes of topological phase transitions with higher-order band crossing
• Temperature-induced topological phase transitions: promoted vs. suppressed non-trivial topology
• Amorphous topological matter: theory and experiment
• Quantised Bulk Conductivity as a Local Chern Marker
• Topological marker approach to an interacting Su-Schrieffer-Heeger model
• Robustness of topological order against disorder
• Local Chern Marker for Periodic Systems
• Strain-gradient induced topological transition in bent nanoribbons of the Dirac semimetal Cd3As2
• Topological Anderson insulating phases in the interacting Haldane model

Cited by in corpus (15)

• Theory of local ${\mathbb{Z}}_2$ topological markers for finite and periodic two-dimensional systems
• Scaling of the Integrated Quantum Metric in Disordered Topological Phases
• Reentrant topological phases and spin density wave induced by 1D moiré potentials
• Structure-driven phase transitions in paracrystalline topological insulators
• Topological Phases in Fractals: Local Spin Chern Marker in the Sierpinski carpet Kane-Mele-Rashba Model
• Reentrant topological phases and entanglement scalings in moiré-modulated extended Su-Schrieffer-Heeger Model
• Topological characterization of modified Kane-Mele-Rashba models via local spin Chern marker
• Evaluation of real-space second Chern number using the kernel polynomial method
• Interacting Virtual Topological Phases in Defect-Rich 2D Materials
• Aharanov-Bohm oscillations and perfectly transmitted mode in amorphous topological insulator nanowires
• Finite-temperature topological transitions in the presence of quenched uncorrelated disorder
• Multiple reentrant topological windows induced by generalized Bernoulli disorder
• Anomalous Non-Hermitian Topological Anderson Insulator
• Coarse geometric approach to topological phases: Invariants from real-space representations
• Physical Pictures for Quasisymmetry in Crystals