Topological Anderson Insulator Research Articles

Phase transitions and scale invariance in topological Anderson insulators

Phase transitions and scale invariance in topological Anderson insulators

Realization of Gapped and Ungapped Photonic Topological Anderson Insulators.

It is commonly believed that topologically nontrivial one-dimensional systems support edge states rather than bulk states at zero energy. In this work, we find an unanticipated case of topological Anderson insulator (TAI) phase where two bulk modes are degenerate at zero energy, in addition to degenerate edge modes. We term this "ungapped TAI" to distinguish it from the previously known gapped TAIs. Our experimental realization of both gapped and ungapped TAIs relies on coupled photonic resonators, in which the disorder in coupling is judiciously engineered by adjusting the spacing between the resonators. By measuring the local density of states both in the bulk and at the edges, we demonstrate the existence of these two types of TAIs, together forming a TAI plateau in the phase diagram. Our experimental findings are well supported by theoretical analysis. In the ungapped TAI phase, we observe stable coexistence of topological edge states and localized bulk states at zero energy, highlighting the distinction between TAIs and traditional topological insulators.

Four-dimensional topological Anderson insulator with an emergent second Chern number

Four-dimensional topological Anderson insulator with an emergent second Chern number

Observation of an acoustic non-Hermitian topological Anderson insulator

Observation of an acoustic non-Hermitian topological Anderson insulator

Photonic topological Anderson insulator in a two-dimensional atomic lattice

Disorder in atomic positions can induce a topologically nontrivial phase - topological Anderson insulator (TAI) - for transverse electric optical quasimodes of a two-dimensional honeycomb lattice of immobile atoms. TAI requires both time-reversal and inversion symmetries to be broken to similar extents. It is characterized by a nonzero topological invariant, a reduced density of states and spatially localized quasimodes in the bulk, as well as propagating edge states. A transition from TAI to the topological insulator (TI) phase can take place at a constant value of the topological invariant, showing that TAI and TI represent the same topological phase.

Single-point spin Chern number in a supercell framework

We present an approach for the calculation of the topological invariant in non-crystalline two-dimensional quantum spin Hall insulators. While topological invariants were originally mathematically introduced for crystalline periodic systems, and crucially hinge on tracking the evolution of occupied states through the Brillouin zone, the introduction of disorder or dynamical effects can break the translational symmetry and imply the use of larger simulation cells, where the k-point sampling is typically reduced to the single Γ-point. Here, we introduce a single-point formula for the spin Chern number that enables to adopt the supercell framework, where a single Hamiltonian diagonalisation is performed. Inspired by the work of Prodan (2009 Phys. Rev. B 80 125327), our single-point approach allows to calculate the spin Chern number even when the spin operator does not commute with the Hamiltonian, as in the presence of Rashba spin–orbit coupling. We validate our method on the Kane–Mele model, both pristine and in the presence of Anderson disorder. Finally, we investigate the disorder-driven transition from the trivial phase to the topological state known as topological Anderson insulator. Beyond disordered systems, our approach is particularly useful to investigate the role of defects, to study topological alloys and in the context of ab-initio molecular dynamics simulations at finite temperature.

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.

Quantized topological Anderson-Thouless pump

Thouless pump with quantized transports is topologically robust against small perturbations and disorders, while breaks down under sufficiently strong disorders. Here we propose counter-intuitive topological pumps induced by disorders in noninteracting and interacting systems. We first show an extrinsic topological pump driven by the on-site quasiperiodic potential for a two-loop sequence, where the disorder inequivalently suppresses the topology of two pump loops. Moreover, we reveal an intrinsic topological pump induced by the hopping quasiperiodic disorder from a trivial single-loop pump in the clean limit, dubbed the topological Anderson-Thouless pump (TATP) as a dynamical analogue of topological Anderson insulators. We demonstrate that the mechanism of the TATP is the disorder-induced shift of gapless critical points and the TATP can even exhibit in the dynamic disorder and interacting cases. Finally, we extend the TATP to higher-order topological systems with disorder-induced quantized corner transports. Our proposed TATPs present new members of the topological pump family and could be realized with ultracold atoms or photonic waveguides.

Weak quantization of noninteracting topological Anderson insulator

We study the transition between the two-dimensional topological insulator (TI) featuring quantized edge conductance and the trivial Anderson insulator (AI) induced by strong disorder. We discover a distinct scaling behavior of TI near the phase transition where the longitudinal conductance approaches the quantized value by a power law with system size, instead of an exponential law in clean TI. This region is thus called the weak quantization topological insulator (WQTI). By using the self-consistent Born approximation, we associate the emergence of the weak quantization with the imaginary part of the effective self-energy acquiring a finite value at strong disorder. We use our analytical theory, supported by direct numerical simulations, to study the effect of disorder range on the topological Anderson insulator. Interestingly, while this phase is quite generic for uncorrelated or short-range disorder, it is strongly suppressed by long-range disorder, perhaps explaining why it has never been seen in solid state systems.

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.

Photonic Z2 Topological Anderson Insulators

That disorder can induce nontrivial topology is a surprising discovery in topological physics. As a typical example, Chern topological Anderson insulators (TAIs) have been realized in photonic systems, where the topological phases exist without symmetry protection. In this Letter, by taking transverse magnetic and transverse electric polarizations as pseudospin degrees of freedom, we theoretically propose a scheme to realize disorder-induced symmetry-protected topological phase transitions in two-dimensional photonic crystals with a combined time-reversal, mirror, and duality symmetry T_{f}=TM_{z}D. In particular, we demonstrate that the disorder-induced symmetry-protected topological phase persists even without pseudospin conservation, thereby realizing a photonic Z_{2} TAI, in contrast to a Z-classified quantum spin Hall (QSH) TAI with decoupled spins. By formulating a new scattering approach, we show that the topology of both the QSH and Z_{2} TAIs can be manifested by the accumulated spin rotations of the reflected waves from the photonic crystals. Using a transmission structure, we also illustrate the trivialization of a disordered QSH phase with an even integer topological index caused by spin coupling.

Correlated disorder induced anomalous transport in magnetically doped topological insulators

We examine the transport properties of magnetically doped topological insulator (TI) thin films subject to correlated non-magnetic disorder. For the disorder we choose a quasi-periodic potential with a random phase. We restrict the disorder to a central region, which is coupled to two leads in a clean quantum spin Hall insulator (QSHI) state and concentrate on different orientations of the quasi-periodicity in the two-dimensional central region. In the case of a diagonally oriented or purely longitudinal quasi-periodicity we find different topological Anderson insulator (TAI) phases, with a quantum anomalous Hall insulator (QAHI), a quantum spin Chern insulator (QSCI), or a QSHI phase being realized before the Anderson insulation takes over at large disorder strength. Quantized transport from extended bulk states is found for diagonal quasi-periodicity in addition to the above TAI phases that are also observed for the case of uncorrelated disorder. For a purely transverse orientation of the quasi-periodicity the emerging QSHI and QSCI phases persist to arbitrarily strong disorder potential. These topological phase transitions (except to the Anderson insulator phase), can be understood from a self consistent Born approximation.

Topological and dynamical phase transitions in the Su–Schrieffer–Heeger model with quasiperiodic and long-range hoppings

Disorders and long-range hoppings can induce exotic phenomena in condensed matter and artificial systems. We study the topological and dynamical properties of the quasiperiodic Su–Schrier–Heeger model with long-range hoppings. It is found that the interplay of quasiperiodic disorder and long-range hopping can induce topological Anderson insulator phases with non-zero winding numbers and the phase boundaries can be consistently revealed by the divergence of zero-energy mode localization length. We also investigate the nonequilibrium dynamics by ramping the long-range hopping along two different paths. The critical exponents extracted from the dynamical behavior agree with the Kibble–Zurek mechanic prediction for the path with In particular, the dynamical exponent of the path crossing the multicritical point is numerical obtained as which agrees with the unconventional finding in the previously studied XY spin model. Besides, we discuss the anomalous and non-universal scaling of the defect density dynamics of topological edge states in this disordered system under open boundary condictions.

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 with different bulk states in quasiperiodic chains

We investigate the topology and localization of one-dimensional Hermitian and non-Hermitian Su-Schrieffer-Heeger chains with quasiperiodic hopping modulations. In the Hermitian case, phase diagrams are obtained by numerically and analytically calculating various topological and localization characters. We show the presence of topological extended, intermediate, and localized phases due to the coexistence of independent topological and localization phase transitions driven by the quasiperiodic disorder. Unlike the gapless and localized TAI phase in one-dimensional random disordered systems, we uncover three types of quasiperiodic-disorder-induced gapped topological Anderson insulators (TAIs) with extended, intermediate (with mobility edges), and localized bulk states in this chiral chain. Moreover, we study the non-Hermitian effects on the TAIs by considering two kinds of non-Hermiticities from the non-conjugate complex hopping phase and asymmetric hopping strength, respectively. We demonstrate that three types of TAIs preserve under the non-Hermitian perturbations with some unique localization and topological properties, such as the non-Hermitian real-complex and localization transitions and their topological nature. Our work demonstrates that the disorder-induced TAIs in Hermitian and non-Hermitian quasiperiodic systems are not tied to Anderson transitions and have various localization properties.

Observation of non-Hermitian topological Anderson insulator in quantum dynamics

Disorder and non-Hermiticity dramatically impact the topological and localization properties of a quantum system, giving rise to intriguing quantum states of matter. The rich interplay of disorder, non-Hermiticity, and topology is epitomized by the recently proposed non-Hermitian topological Anderson insulator that hosts a plethora of exotic phenomena. Here we experimentally simulate the non-Hermitian topological Anderson insulator using disordered photonic quantum walks, and characterize its localization and topological properties. In particular, we focus on the competition between Anderson localization induced by random disorder, and the non-Hermitian skin effect under which all eigenstates are squeezed toward the boundary. The two distinct localization mechanisms prompt a non-monotonous change in profile of the Lyapunov exponent, which we experimentally reveal through dynamic observables. We then probe the disorder-induced topological phase transitions, and demonstrate their biorthogonal criticality. Our experiment further advances the frontier of synthetic topology in open systems.

Chern insulator in a hyperbolic lattice

Motivated by the recent experimental realizations of hyperbolic lattices in circuit quantum electrodynamics and the research interest in the non-Euclidean generalization of topological phenomena, we investigate the Chern insulator phases in a hyperbolic $\{8,3\}$ lattice, which is made from regular octagons ($8$-gons) such that the coordination number of each lattice site is $3$. Based on the conformal projection of the hyperbolic lattice into the Euclidean plane, i.e., the Poincar\'{e} disk model, by calculating the Bott index ($B$) and the two-terminal conductance, we reveal two Chern insulator phases (with $B=1$ and $B=-1$, respectively) accompanied with quantized conductance plateaus in the hyperbolic $\{8,3\}$ lattice. The numerical calculation results of the nonequilibrium local current distribution further confirm that the quantized conductance plateau originates from the chiral edge states and the two Chern insulator phases exhibit opposite chirality. Moreover, we explore the effect of disorder on topological phases in the hyperbolic lattice. It is demonstrated that the chiral edge states of Chern insulators are robust against weak disorder in the hyperbolic lattice. More fascinating is the discovery of disorder-induced topological non-trivial phases exhibiting chiral edge states in the hyperbolic lattice, realizing a non-Euclidean analog of topological Anderson insulator. Our work provides a route for the exploration of topological non-trivial states in hyperbolic geometric systems.

Topological transitions and Anderson localization of light in disordered atomic arrays

We explore the interplay of disorder and topological phenomena in honeycomb lattices of atoms coupled by the electromagnetic field. On the one hand, disorder can trigger transitions between distinct topological phases and drive the lattice into the topological Anderson insulator state. On the other hand, the nontrivial topology of the photonic band structure suppresses Anderson localization of modes that disorder introduces inside the band gap of the ideal lattice. Furthermore, we discover that disorder can both open a topological pseudogap in the spectrum of an otherwise topologically trivial system and introduce spatially localized modes inside it.

Current carrying states in the disordered quantum anomalous Hall effect

In a quantum Hall effect, flat Landau levels may be broadened by disorder. However, it has been found that in the thermodynamic limit, all extended (or current carrying) states shrink to one single energy value within each Landau level. On the other hand, a quantum anomalous Hall effect consists of dispersive bands with finite widths. We numerically investigate the picture of current carrying states in this case. With size scaling, the spectrum width of these states in each bulk band still shrinks to a single energy value in the thermodynamic limit, in a power law way. The magnitude of the scaling exponent at the intermediate disorder is close to that in the quantum Hall effects. The number of current carrying states obeys similar scaling rules, so that the density of states of current carrying states is finite. Other states in the bulk band are localized and may contribute to the formation of a topological Anderson insulator.

Hermitian chiral boundary states in non-Hermitian topological insulators

Eigenenergies of a non-Hermitian system without parity-time symmetry are complex in general. Here, we show that the chiral boundary states of higher-dimensional (two-dimensional and three-dimensional) non-Hermitian topological insulators without parity-time symmetry can be Hermitian with real eigenenergies under certain conditions. Our approach allows one to construct Hermitian chiral edge and hinge states from non-Hermitian two-dimensional Chern insulators and three-dimensional second-order topological insulators, respectively. Such Hermitian chiral boundary channels have perfect transmission coefficients (quantized values) and are robust against disorders. Furthermore, a non-Hermitian topological insulator can undergo the topological Anderson insulator transition from a topological trivial non-Hermitian metal or insulator to a topological Anderson insulator with quantized transmission coefficients at finite disorders.