Recent progress on disorder-induced topological phases

TL;DR

This article surveys disorder-induced topological phases, centered on TAIs, and extends to quasiperiodic and non-Hermitian settings, dynamical pumps, and interacting many-body regimes. It presents real-space topological markers, theory for disorder-driven topology via SCBA and percolation concepts, and an array of experimental realizations in ultracold atoms, photonics, and solids. Key contributions include unified real-space invariants (winding, Chern, Bott, quadrupole), demonstrations of TAI physics across dimensions and systems, and the emergence of non-Hermitian and Floquet TAIs, as well as disorder-induced topological phenomena in dynamical and many-body contexts. The findings highlight disorder as a versatile tool to induce and control topological phases, with implications for robust transport, engineered materials, and quantum simulators in both equilibrium and driven-dissipative settings.

Abstract

Topological states of matter in disordered systems without translation symmetry have attracted great interest in recent years. These states with topological characters are not only robust against certain disorders, but also can be counterintuitively induced by disorders from a topologically trivial phase in the clean limit. In this review, we summarize the current theoretical and experimental progress on disorder-induced topological phases in both condensed-matter and artificial systems. We first introduce the topological Anderson insulators (TAIs) induced by random disorders and their topological characterizations and experimental realizations. We then discuss various extensions of TAIs with unique localization phenomena in quasiperiodic and non-Hermitian systems. We also review the theoretical and experimental studies on the disorder-induced topology in dynamical and many-body systems, including topological Anderson-Thouless pumps, disordered correlated topological insulators and average-symmetry protected topological orders acting as interacting TAI phases. Finally, we conclude the review by highlighting potential directions for future explorations.

Figures (16)

• Figure 1: (color online) (a) Conductance $G$ as a function of random disorder strength $W$ for two Fermi energies. The inset show the energy spectrum, where horizontal lines mark Fermi energies. (b) and (c) 2D Phase diagrams showing $G$ versus $W$ and $\varepsilon_\mathrm{F}$, with the TAI phase regime. Theoretical phase boundaries from effective medium theory in (c) show as two curves $A$ (renormalized topological mass $\bar{m}$ sign reversal) and $B$ (crossover between renormalized $|\bar{\mu}|$ and band edge). (a) and (b) are adapted from Ref. JLi2009a. (c) is adapted from Ref. Groth2009a. (d) 3D phase diagram in parameter space spanned by $E_F$, $W$ and Dirac mass $\Delta$. Contour boundaries combined with dotted line enclose the quantum spin Hall phase regimes, with shaded regime for the TAI. Adapted from Ref. Prodan2011a.
• Figure 2: Observation of the TAI in disordered atomic wires. (a) Schematic lattice of the chiral symmetric wire. (b) Schematic of the experimental implementation of the tight-binding model engineered with atomic momentum states. (c) Topological phase diagram calculated by the real-space winding number $\nu$. (d) Experimental measurement of time- and disorder-averaged chiral displacement $\langle\bar{C}\rangle$ as a function of disorder strength $W$. Solid and dashed lines are simulations for the same lattice and for larger system, respectively. Dotted gray curve denotes $\nu$ in the thermodynamic limit. Adapted from Ref. Meier2018a.
• Figure 3: Photonic TAIs. (a) Schematic of the 2D waveguide configuration and a 1D straw, through which the edge modes are excited. (b-d) The formation of chiral edge states when sufficient disorder is added. (e) Topological Phase diagram showing the real-space Chern number as a function of the detuning mass $m_{\delta}$ and disorder strength $W$. Adapted from Ref. Stuetzer2018a.
• Figure 4: (Color online) (a) Real-space winding number $\nu$ versus $W$ and $m$. Topological phase boundaries (red dashed: zero-energy state localization length divergence; black solid: SCBA analysis) are shown. (b) For $m=1.02$, $\nu$ (red dashed) and $\Delta E$ (blue solid) versus $W$, with topological transitions at $W_{1T}$ and $W_{2T}$. (c) OBC eigenenergies (middle 100 states) versus $W$ at $m=1.02$, highlighting zero-energy edge modes (red) in the topological regime $W_{1T}<W<W_{2T}$. Mean IPRs $\bar{I}_x$ (d) and quantity $\eta$ (f), and IPR $I_{x}^{(j)}$ versus $W$ at fixed $m=1.02$ (e). Regions labeled 'Ext.', 'Loc.', and 'Int.' in (d, f) denote extended, localized, and intermediate phases, respectively. Vertical lines in (e) mark the first ($W_{1L}\approx0.57$) and second ($W_{2L}\approx1.02$) localization transitions. Adapted from Ref. LZTang2022a.
• Figure 5: (Color online) (a) Global phase diagram in the $W$-$m$ parameter space, identifying six distinct phase: I: Extended topological phase, II: Topological intermediate phase, III: Topological localized phase, IV: Trivial extended phase, V: Trivial intermediate phase, VI: Trivial localized phase. (b) Disorder strength dependence of three different types of TAIs for fixed $m=1.02$. Adapted from Ref. LZTang2022a.