Topological Anderson Insulator Phase Research Articles

Different topological phase transitions in the Su–Schrieffer–Heeger model under different disorder structures

Abstract We investigate the topological phase transition in the Su–Schrieffer–Heeger model with the long-range hopping and quasi-periodic modulation. By numerically calculating the real-space winding number, we obtain topological phase diagrams for different disordered structures. These diagrams suggest that topological phase transitions are different by selecting the specific disordered structure. When quasi-periodic modulation is applied to intracell hopping, the resulting disorder induces topological Anderson insulator (TAI) phase with high winding number (W = 2), but the topological states are destroyed as the disorder increases. Conversely, when intercell hoppings are modulated quasi-periodically, both TAI phase and the process of destruction and restoration of topological zero modes can be induced by disorder. These topological states remain robust even under strong disorder conditions. Our work demonstrates that disorder effects do not always disrupt topological states; rather, with a judicious selection of disordered structures, topological properties can be preserved.

Topological Anderson insulator via disorder-recovered average symmetry

We propose that the topological Anderson insulator (TAI) can be realized by introducing special disorder into a graphene with a modified Kane-Mele model. The disorder recovers symmetry under statistical averaging, which turns a trivial insulator into a topologically nontrivial insulator. When graphene is subjected to nonmagnetic adatoms in one sublattice or global uniform magnetic adatoms, the sublattice or time-reversal (TR) symmetry is broken, respectively, making the system topologically trivial. For the former one, randomly spatial distributed adatoms result in gapless edge states and quantized transport characteristics. Such randomization preserves the sublattice symmetry on average and the system becomes a TAI phase. For the latter one, the average TR symmetry is recovered by randomizing magnetization directions and the topological phase is protected. We demonstrate the existence of gapless edge states, but the differential conductance is no longer quantized. Moreover, we construct our proposal in electric circuits and observe the disorder-induced edge state through the circuit simulation. Our work provides a more simplified scheme to realize the TAI, and deepens the understanding of the relationship between the TAI and average symmetries.

Probing of the topological phase transition in a disordered 1D acoustic system

The methods to determine the Zak phase introduced by previous studies are usually limited to the periodic systems protected by the inversion symmetry. In this work, we build a one-dimensional chiral symmetric acoustic chain with controllable disorder to break its inversion symmetry. By the mean chiral displacement method, we detect the Zak phase in order to observe the topological phase transition induced purely by disorder. The finding exhibits the topological Anderson insulator phase, in which an otherwise trivial acoustic Su–Schrieffer–Heeger model is driven non-trivial by disorder accompanied by the change of the topological sign. This method could also be utilized in chiral symmetry broken and non-Hermitian systems. The result reveals that disorder introduced in the acoustic devices may induce the change of the topological phase, which is promising for the design of new acoustic devices.

Exact Mobility Edges and Topological Anderson Insulating Phase in a Slowly Varying Quasiperiodic Model

AbstractThe relationship of topology and disorder in a 1D Su–Schrieffer–Heeger chain subjected to a slowly varying quasi‐periodic modulation is uncovered. By numerically calculating the disorder‐averaged winding number and analytically studying the localization length of the zero modes, the topological phase diagram is obtained, which implies that the topological Anderson insulator (TAI) can be induced by a slowly varying quasi‐periodic modulation. Moreover, unlike the localization properties in the TAI phase caused by random disorder, mobility edges can enter into the TAI region identified by the fractal dimension, the inverse participation ratio, and the spatial distributions of the wave functions, the boundaries of which coincide with the analytical results presented here.

Topological Anderson insulators in an Ammann-Beenker quasicrystal and a snub-square crystal

The quest for the topological phases of matter in an aperiodic system has been greatly developed recently. Here we investigate the effects of disorder on topological phases of a two-dimensional Ammann-Beenker tiling quasicrystalline lattice. For comparison purposes, we also consider the case of a periodic snub-square crystalline lattice, which has the same primitive tiles as the Ammann-Beenker tiling quasicrystalline lattice. By calculating the spin Bott index and the two-terminal conductance, we confirm that the topological phases with disorder share the similar properties in the two systems which possess different symmetry and periodicity. It is shown that the quantum spin Hall states are robust against weak disorder in both the quasicrystalline lattice and the crystalline lattice. More interesting is that topological Anderson insulator phases induced by disorder appear in the two systems. Furthermore, the quantized conductance plateau contributed by the topological Anderson insulator phase is verified by the distribution of local currents.

Disorder-Induced Signal Filtering with Topological Metamaterials.

Disorder, ubiquitously present in realistic structures, is generally thought to disturb the performance of analog wave devices, as it often causes strong multiple scattering effects that largely arrest wave transportation. Contrary to this general view, here, it is shown that, in some wave systems with nontrivial topological character, strong randomness can be highly beneficial, acting as a powerful stimulator to enable desired analog filtering operations. This is achieved in a topological Anderson sonic crystal that, in the regime of dominating randomness, provides a well-defined filtering response characterized by a Lorentzian spectral line-shape. The theoretical and experimental results, serving as the first realization of topological Anderson insulator phase in acoustics, suggest the striking possibility of achieving specific, nonrandom analog filtering operations by adding randomness to clean structures.

Topological Anderson insulator in two-dimensional non-Hermitian systems**Project supported by the National Basic Research Program of China (Grant No. 2019YFA0308403), the National Natural Science Foundation of China (Grant No. 11822407), Undergraduate Training Program for Innovation and Entrepreneurship, Soochow University (Grant No. 201810285022Z), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, China.

We study the disorder-induced phase transition in two-dimensional non-Hermitian systems. First, the applicability of the noncommutative geometric method (NGM) in non-Hermitian systems is examined. By calculating the Chern number of two different systems (a square sample and a cylindrical one), the numerical results calculated by NGM are compared with the analytical one, and the phase boundary obtained by NGM is found to be in good agreement with the theoretical prediction. Then, we use NGM to investigate the evolution of the Chern number in non-Hermitian samples with the disorder effect. For the square sample, the stability of the non-Hermitian Chern insulator under disorder is confirmed. Significantly, we obtain a nontrivial topological phase induced by disorder. This phase is understood as the topological Anderson insulator in non-Hermitian systems. Finally, the disordered phase transition in the cylindrical sample is also investigated. The clean non-Hermitian cylindrical sample has three phases, and such samples show more phase transitions by varying the disorder strength: (1) the normal insulator phase to the gapless phase, (2) the normal insulator phase to the topological Anderson insulator phase, and (3) the gapless phase to the topological Anderson insulator phase.

Topological Anderson insulator phase in a quasicrystal lattice

Motivated by the recent experimental realization of the topological Anderson insulator and research interest on the topological quasicrystal lattices, we investigate the effects of disorder on topological properties of a two-dimensional Penrose-type quasicrystal lattice that supports the quantum spin Hall insulator (QSHI) and normal insulator (NI) phases in the clean limit. It is shown that the helical edge state of the QSHI phase is robust against weak disorder. Most saliently, it is found that disorder can induce a phase transition from NI to QSHI phase in the quasicrystal system. The numerical results based on a two-terminal device show that a quantized conductance plateau can arise inside the energy gap of NI phase for moderate Anderson disorder strength. Further, it is confirmed that the local current distributions of the disorder-induced quantized conductance plateau are located on the two edges of sample. Finally, we identify this disorder-induced phase as topological Anderson insulator phase by computing the disorder-averaged spin Bott index.

Observation of the topological Anderson insulator in disordered atomic wires.

Topology and disorder have a rich combined influence on quantum transport. To probe their interplay, we synthesized one-dimensional chiral symmetric wires with controllable disorder via spectroscopic Hamiltonian engineering, based on the laser-driven coupling of discrete momentum states of ultracold atoms. Measuring the bulk evolution of a topological indicator after a sudden quench, we observed the topological Anderson insulator phase, in which added disorder drives the band structure of a wire from topologically trivial to nontrivial. In addition, we observed the robustness of topologically nontrivial wires to weak disorder and measured the transition to a trivial phase in the presence of strong disorder. Atomic interactions in this quantum simulation platform may enable realizations of strongly interacting topological fluids.

Topological Anderson insulator phase in a Dirac-semimetal thin film

The recently discovered topological Dirac semimetal represents a new exotic quantum state of matter. Topological Dirac semimetals can be viewed as three dimensional analogues of graphene, in which the Dirac nodes are protected by crystalline symmetry. It has been found that quantum confinement effect can gap out Dirac nodes and convert Dirac semimetal to a band insulator. The band insulator is either normal insulator or quantum spin Hall insulator depending on the thin film thickness. We present the study of disorder effects in thin film of Dirac semimetals. It is found that moderate Anderson disorder strength can drive a topological phase transition from normal band insulator to topological Anderson insulator in Dirac semimetal thin film. The numerical calculation based on the model parameters of Dirac semimetal Na$_{3}$Bi shows that in the topological Anderson insulator phase a quantized conductance plateau occurs in the bulk gap of band insulator, and the distributions of local currents further confirm that the quantized conductance plateau arises from the helical edge states induced by disorder. Finally, an effective medium theory based on Born approximation fits the numerical data.

Disordered Chern insulator with a two-step Floquet drive

We explore the physics of a Chern insulator subjected to a two step Floquet drive. We analytically obtain the phase diagram and show that the system can exhibit different topological phases characterized by presence and chirality of edge-modes in the two bulk gaps of the Floquet quasienergy spectrum, around $0$ and $\pi$. We find that the phase of the system depends on the mean but not on the amplitude of the drive. The bulk topological invariants characterizing the phases can be extracted by mapping the unitary evolution within a time period to an energetically trivial but topologically non-trivial time evolution. An extensive numerical study of the bulk topological invariants in the presence of quenched disorder reveals new transitions induced by strong disorder (i) from the different topological to trivial insulator phases and (ii) from a trivial to a topological Anderson insulator phase at intermediate disorder strengths. Careful analysis of level statistics of the quasienergy spectrum indicates a `levitation-annihilation' mechanism near these transitions.

The topological Anderson insulator phase in the Kane-Mele model.

It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase.

Topological insulator in the presence of spatially correlated disorder

We investigate the effect of spatially correlated disorder on two-dimensional topological insulators and on the quantum spin Hall effect which the helical edge states in these systems give rise to. Our work expands the scope of previous investigations which found that uncorrelated disorder can induce a nontrivial phase called the topological Anderson insulator (TAI). In extension of these studies, we find that spatial correlations in the disorder can entirely suppress the emergence of the TAI phase. We show that this phenomenon is associated with a quantum percolation transition and quantify it by generalizing an existing effective medium theory to the case of correlated disorder potentials. The predictions of this theory are in good agreement with our numerics and may be crucial for future experiments.

Disorder dependence of helical edge states in HgTe/CdTe quantum wells

In recent years, extensive attention has been focused on a new topological phase induced by nonmagnetic disorder, known as the topological Anderson insulator (TAI). In this work, we study the disorder strength dependence of the edge states in TAI phase in disordered HgTe/CdTe quantum wells. It is shown clearly that the disorder-induced edge states appear above a critical disorder strength after a gap-closing phase transition. These edge states are then found to decline with an increase of disorder strength in a stepwise pattern due to the finite-width effect, where the opposite edges couple to each other through the localized bulk states. This is in sharp contrast with the localization of the edge states themselves by time-reversal symmetry breaking. The size-independent phase boundaries are further obtained through scaling analysis, where a metallic phase is found separating two topologically distinct phases, which is due to the Fermi energy and mass renormalization.