Recently, a new family of symmetry-protected higher-order topological insulators has been proposed and was shown to host lower-dimensional boundary states. However, with the existence of the strong disorder in the bulk, the crystal symmetry is broken, and the associated corner states are disappeared. It is well known that the emergence of robust edge states and quantized transport can be induced by adding sufficient disorders into a topologically trivial insulator, that is the so-called topological Anderson insulator. The question is whether disorders can also cause the higher-order topological phase. This is not known so far, because interactions between disorders and the higher-order topological phases are completely different from those with the first-order topological system. Here, we demonstrate theoretically that the disorderinduced higher-order topological corner state and quantized fraction corner charge can appear in a modified Haldane model. In experiments, we construct the classical analog of such higherorder topological Anderson insulators using electric circuits and observe the disorder-induced corner state through the voltage measurement. Our work defies the conventional view that the disorder is detrimental to the higher-order topological phase, and offers a feasible platform to investigate the interaction between disorders and higher-order topological phases.
Different disorders lead to various localization and topological phenomena in condensed matter and artificial systems. Here we study the topological and localization properties in one-dimensional Su-Schrieffer-Heeger model with spatially correlated random binary disorders. It is found that random binary disorders can induce the topological Anderson insulating phase from the trivial insulator in various parameter regions. The topological Anderson insulators are characterized by the disorder-averaged winding number and localized bulk states revealed by the inverse participation ratio in both rea…
The realization of the quantum anomalous Hall (QAH) effect without magnetic doping attracts intensive interest since magnetically doped topological insulators usually possess inhomogeneity of ferromagnetic order. Here, we propose a different strategy to realize intriguing QAH states arising from the interplay of light and non-magnetic disorder in two-dimensional topologically trivial systems. By combining the Born approximation and Floquet theory, we show that a time-reversal invariant disorder-induced topological insulator, known as the topological Anderson insulator (TAI), would evolve into …
We study the characterization and realization of higher-order topological Anderson insulator (HOTAI) in non-Hermitian systems, where the non-Hermitian mechanism ensures extra symmetries as well as gain and loss disorder.We illuminate that the quadrupole moment $Q_{xy}$ can be used as the real space topological invariant of non-Hermitian higher-order topological insulator (HOTI). Based on the biorthogonal bases and non-Hermitian symmetries, we prove that $Q_{xy}$ can be quantized to $0$ or $0.5$. Considering the disorder effect, we find the disorder-induced phase transition from normal insulato…
Shift current is a photovoltaic current in bulk noncentrosymmetric insulator. Studies on shift current have so far focused on the extended Bloch waves, such as in semiconductors and perovskites. In contrast, it is unknown whether the localized wavefunctions support the dc photocurrent. Here, we show theoretically that the dc shift current appears in a noncentrosymmetric disordered one-dimensional insulator with random potential. When the light illuminates the entire sample, the photocurrent forms in presence of the electron-phonon coupling. We find this photocurrent remains robustly even when …
We study disorder effects in a two-dimensional system with chiral symmetry and find that disorder can induce a quadrupole topological insulating phase (a higher-order topological phase with quadrupole moments) from a topologically trivial phase. Their topological properties manifest in a topological invariant defined based on effective boundary Hamiltonians, the quadrupole moment, and zero-energy corner modes. We find gapped and gapless topological phases and a Griffiths regime. In the gapless topological phase, all the states are localized, while in the Griffiths regime, the states at zero en…
Recent breakthrough on topological Anderson insulators revealed the breakdown of the traditional perception that sufficiently strong disorder may induce the appearance of topological protected transport states instead of destruction. Although topological Anderson insulators have been observed in various time-reversal symmetry breaking systems, the observation of topological Anderson insulators protected by time-reversal symmetry remains scarce, which are considered to be more promising in applications such as the integrated devices. Here, we report the experimental observation of topological A…
The topological Anderson and Mott insulators are two phases that have so far been separately and widely explored beyond topological band insulators. Here we combine the two seemingly different topological phases into a system of spin-1/2 interacting fermionic atoms in a disordered optical lattice. We find that the topological Anderson and Mott insulators in the noninteracting and clean limits can be adiabatically connected without gap closing in the phase diagram of our model. Lying between the two phases, we uncover a disordered correlated topological insulator, which is induced from a trivia…
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 numeri…
The disorder effects on higher-order topological phases in periodic systems have attracted much attention. However, in aperiodic systems, such as quasicrystalline systems, the interplay between disorder and higher-order topology is still unclear. In this paper, we investigate the effects of disorder on two types of second-order topological insulators, including a quasicrystalline quadrupole insulator and a modified quantum spin Hall insulator, in a two-dimensional Amman-Beenker tiling quasicrystalline lattice. We demonstrate that the higher-order topological insulators are robust against weak …
Topological states require the presence of extended bulk states, as usually found in the picture of energy bands and topological states bridging the bulk gaps. But in driven systems this can be circumvented, and one can get topological states coexisting with fully localized bulk states, as in the case of the anomalous Floquet-Anderson insulator. Here, we show the fingerprints of this peculiar topological phase in the transport properties and their dependence on the disorder strength, geometrical configuration (two-terminal and multiterminal setups) and details of the driving protocol.
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 par…
Time-periodic (Floquet) drive can give rise to novel symmetry breaking and topological phases of matter. Recently, we showed that a quintessential Floquet topological phase known as the anomalous Floquet-Anderson insulator is stable to noise on the timing of its Floquet drive. Here, we perturb the anomalous Floquet-Anderson insulator at a single incommensurate frequency, resulting in a quasiperiodic 2-tone drive. Our numerics indicate that a robust topological phase survives at weak noise with topological pumping that is more stable than the case of white noise. Within the topological phase, w…
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 l…
Abstract: Using ab initio calculations supported by experimental transport measurements, we present the first credible candidate for the realization of a disorder-induced Topological Anderson Insulator in a real material system. High energy reactive ball-milling produces a polymorph of Cu2ZnSnS4 with high cation disorder, which shows an inverted ordering of bands at the Brillouin zone center, in contrast to its ordered phase. Adiabatic continuity arguments establish that this disordered Cu2ZnSnS4 can be connected to the closely related Cu2ZnSnSe4, previously predicted to be a 3D topological in…
We study two-terminal transport through two-dimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We focus on the Anomalous Floquet-Anderson Insulator (AFAI) phase, a topologically-nontrivial phase within this class, which hosts topologically protected chiral edge modes coexisting with its fully localized bulk. We show that the unique properties of the AFAI yield remarkable far-from-equilibrium transport signatures: for a large bias between leads, a quantized amount of charge is transported through the system each driving period. Upon increasi…
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 …
Non-Hermitian systems can exhibit unique topological and localization properties. Here we elucidate the non-Hermitian effects on disordered topological systems by studying a non-Hermitian disordered Su-Schrieffer-Heeger model with nonreciprocal hoppings. We show that the non-Hermiticity can enhance the topological phase against disorders by increasing energy gaps. Moreover, we uncover a topological phase which emerges only under both moderate non-Hermiticity and disorders, and is characterized by localized insulating bulk states with a disorder-averaged winding number and zero-energy edge mode…
First microscopic theory for electron-phonon energy exchange in Anderson insulators is developed. The major contribution to the cooling power as a function of electron temperature is shown to be directly related to the correlation function of the local density of electron states at small energy difference argument. In Anderson insulators not far from localization transition, this correlation function is strongly enhanced by wave-function's multi-fractality and, additionally, by the presence of Mott's resonant pairs of localized states. The theory we develop explains huge enhancement of the coo…
The interplay among topology, disorder, and non-Hermiticity can induce some exotic topological and localization phenomena. Here we investigate this interplay in a two-dimensional non-Hermitian disordered Chern-insulator model with two typical kinds of non-Hermiticities, the nonreciprocal hopping and on-site gain-and-loss effects. The topological phase diagrams are obtained by numerically calculating two topological invariants in the real space, which are the disorder-averaged open-bulk Chern number and the generalized Bott index, respectively. We reveal that the nonreciprocal hopping (the gain…
The hallmark property of two-dimensional topological materials is the incredible robustness of the quantized Hall conductivity to disorder. That robustness arises from the fact that in the topological band gap, transport can occur only along the edges modes, which are immune to scattering. However, for sufficiently strong disorder, the band gap closes and the system becomes topologically trivial as all states become localized, such that all transport vanishes -- in accordance with Anderson localization. It therefore came as a surprise when it was suggested that, for a two-dimensional quantum s…
Using a combination of analytic and numerical methods, we study the polarizability of a (non-interacting) Anderson insulator in one, two, and three dimensions and demonstrate that, in a wide range of parameters, it scales proportionally to the square of the localization length, contrary to earlier claims based on the effective-medium approximation. We further analyze the effect of electron-electron interactions on the dielectric constant in quasi-1D, quasi-2D and 3D materials with large localization length, including both Coulomb repulsion and phonon-mediated attraction. The phonon-mediated at…
