Localized Bulk States Research Articles

Mapping the topology-localization phase diagram with quasiperiodic disorder using a programmable superconducting simulator

We explore a topology-localization phase diagram by simulating a one-dimensional Su-Schrieffer-Heeger model with quasiperiodic disorder using a programmable superconducting simulator. We experimentally map out and identify various trivial and topological phases with extended, critical, and localized bulk states. We find that with increasing disorder strength, some extended states can be first replaced by localized states and then by critical states before the system finally becomes fully localized. The critical states exhibit typical features such as multifractality and self-similarity, which lead to surprisingly rich phases with different types of mobility edges and scaling behaviors on the phase boundaries. Our results shed light on the investigation of the topological and localization phenomena in condensed-matter physics. Published by the American Physical Society 2024

The size effect and analogous boundary states in a circular non-Hermitian chain

We investigate the size effect and boundary states based on a circular non-Hermitian chain under the nonreciprocal intra-cell coupling and inter-cell coupling regimes. We find that the circular non-Hermitian chain exhibits an even–odd effect on the unit cell corresponding to a large chain, which is different from the open non-Hermitian chain only exhibiting the same effect for a small chain. Moreover, we find that the originally localized bulk states become totally extended via designing the boundary coupling strength appropriately. The extended bulk states reveal the fact of the disappearance of the non-Hermitian skin effect. In particular, we show that the circular non-Hermitian chain also possesses the analogous edge states under some parameter regimes, which is pretty counterintuitive since the circular chain usually cannot define a boundary. Our investigations supply the different non-Hermitian phenomena in a circular non-Hermitian chain.

Giant atom induced zero modes and localization in the nonreciprocal Su–Schrieffer–Heeger chain

A notable feature of non-Hermitian systems with skin effects is the sensitivity of their spectra and eigenstates to the boundary conditions. In the literature, three types of boundary conditions–periodic boundary condition, open boundary condition (OBC) and a defect in the system as a boundary, are explored. In this work we introduce the other type of boundary condition provided by a giant atom. The giant atom couples to a nonreciprocal Su–Schrieffer–Heeger (SSH) chain at two points and plays the role of defects. We study the spectrum and localization of eigenstates of the system and find that the giant atom can induce asymmetric zero modes. A remarkable feature is that bulk states might localize at the left or the right chain-atom coupling sites in weak localization regimes. This bipolar localization leads to Bloch-like states, even though translational invariance is broken. Moreover, we find that the localization is obviously weaker than the case with two small atoms or OBCs even in strong coupling regimes. These intriguing results indicate that nonlocal coupling of the giant atom to a nonreciprocal SSH chain weakens the localization of the eigenstates. We also show that the Lyapunov exponent in the long-time dynamics in real space can act as a witness of the localized bulk states.

Dynamic Signatures of Non-Hermitian Skin Effect and Topology in Ultracold Atoms.

The non-Hermitian skin effect (NHSE), the accumulation of eigen-wave functions at boundaries of open systems, underlies a variety of exotic properties that defy conventional wisdom. While the NHSE and its intriguing impact on band topology and dynamics have been observed in classical or photonic systems, their demonstration in a quantum gas system remains elusive. Here we report the experimental realization of a dissipative Aharonov-Bohm chain-non-Hermitian topological model with NHSE-in the momentum space of a two-component Bose-Einstein condensate. We identify signatures of the NHSE in the condensate dynamics, and perform Bragg spectroscopy to resolve topological edge states against a background of localized bulk states. Our Letter sets the stage for further investigation on the interplay of many-body statistics and interactions with the NHSE, and is a significant step forward in the quantum control and simulation of non-Hermitian physics.

Pair-partitioned bulk localized states induced by topological band inversion

Photonic topological insulators have recently received widespread attention mainly due to their ability to provide directions in the development of photonic integration platforms. The proposal for a topological bulk cavity with a single-mode expands upon previous research works on topological cavities; thus, interest in topological edge states and corner states is beginning to shift into analysis on bulk properties and their applications. However, there remains a gap in research on a multi-mode cavity of the topological photonic crystals (PCs). In this Letter, a cavity of the topological PCs is proposed involving pair-partitioned bulk localized states (BLSs) from a two-dimensional inner and outer nested square lattice (2D IONSL), which can enable a multi-mode cavity for the topological PCs. First, the topological characteristics are described in terms of a Zak phase, and band inversions are achieved by changing the size of scatterers in the inner and outer circles that reside within the unit cell. Afterwards, analogous to the tight-binding model for electronic systems, the Hamiltonian and topological phase transition conditions of 2D IONSL PCs are derived. Furthermore, it is proposed that the demonstrated optical field reflection and confinement mechanism induced by topological band inversions due to the opposite parities of wavefunctions may lead to the phenomenon of pair-partitioned BLSs. This research increases the research works of bulk topological effects, creating a route for photonic integration platforms for near-infrared.

Topological Anderson insulators induced by random binary disorders

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 real and momentum spaces. We show that the topological phase boundaries are consistent with the analytical results of the self-consistent Born approach and the localization length of zero-energy modes, and discuss how the bimodal probability affects the disorder-induced topological phases. The topological characters can be detected from the mean chiral displacement in atomic or photonic systems. Our work provides an extension of the topological Anderson insulators to the case of correlated disorders.

Coexistence of Quantum Hall and Quantum Anomalous Hall Phases in Disordered MnBi2Te4

In most cases, to observe quantized Hall plateaux, an external magnetic field is applied in intrinsic magnetic topological insulators $\mathrm{MnBi_2Te_4}$. Nevertheless, whether the nonzero Chern number ($C\neq 0$) phase is a quantum anomalous Hall (QAH) state, or a quantum Hall (QH) state, or a mixing state of both is still a puzzle, especially for the recently observed $C=2$ phase [Deng \textit{et al}., Science \textbf{367}, 895 (2020)]. In this Letter, we propose a physical picture based on the Anderson localization to understand the observed Hall plateaux in disordered $\mathrm{MnBi_2Te_4}$. Rather good consistency between the experimental and numerical results confirms that the bulk states are localized in the absence of a magnetic field and a QAH edge state emerges with $C=1$. However, under a strong magnetic field, the lowest Landau band formed with the localized bulk states, survives disorder, together with the QAH edge state, leading to a $C=2$ phase. Eventually, we present a phase diagram of a disordered $\mathrm{MnBi_2Te_4}$ which indicates more coexistence states of QAH and QH to be verified by future experiments.

Bulk locality in the AdS/CFT correspondence

In this paper, we study the bulk local states in the $\mathrm{AdS}/\mathrm{CFT}$ correspondence in the large $N$ limit using the formula explicitly relating the bulk local operators and the conformal field theory (CFT) local operators. We identify the bulk local state in terms of CFT local states and find that the bulk local state corresponds to a CFT state supported in the whole space, which means a version of the subregion duality is not valid. On the other hand, CFT states supported in a space region are expressed in terms of the bulk states supported in a certain region. We find that the quantum error correction proposal is not realized although the puzzles of the radial locality which motivated the proposal are resolved in our analysis. For the understating of the bulk local states, an explicit realization of an analog of the Reeh-Schlieder theorem plays an important role.

Symmetry analysis of anomalous Floquet topological phases

The topological characterization of nonequilibrium topological matter is highly nontrivial because familiar approaches designed for equilibrium topological phases may not apply. In the presence of crystal symmetry, Floquet topological insulator states cannot be easily distinguished from normal insulators by a set of symmetry eigenvalues at high symmetry points in the Brillouin zone. This work advocates a physically motivated, easy-to-implement approach to enhance the symmetry analysis to distinguish between a variety of Floquet topological phases. Using a two-dimensional inversion-symmetric periodically-driven system as an example, we show that the symmetry eigenvalues for anomalous Floquet topological states, of both first-order and second-order, are the same as for normal atomic insulators. However, the topological states can be distinguished from one another and from normal insulators by inspecting the occurrence of stable symmetry inversion points in their microscopic dynamics. The analysis points to a simple picture for understanding how topological boundary states can coexist with localized bulk states in anomalous Floquet topological phases.

Dynamical Crystallites of Active Chiral Particles.

One of the intrinsic characteristics of far-from-equilibrium systems is the nonrelaxational nature of the system dynamics, which leads to novel properties that cannot be understood and described by conventional pathways based on thermodynamic potentials. Of particular interest are the formation and evolution of ordered patterns composed of active particles that exhibit collective behavior. Here we examine such a type of nonpotential active system, focusing on effects of coupling and competition between chiral particle self-propulsion and self-spinning. It leads to the transition between three bulk dynamical regimes dominated by collective translative motion, spinning-induced structural arrest, and dynamical frustration. In addition, a persistently dynamical state of self-rotating crystallites is identified as a result of a localized-delocalized transition induced by the crystal-melt interface. The mechanism for the breaking of localized bulk states can also be utilized to achieve self-shearing or self-flow of active crystalline layers.

Topological signatures in quantum transport in anomalous Floquet-Anderson insulators

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.

Enhanced localization and protection of topological edge states due to geometric frustration

Topologically nontrivial phases are linked to the appearance of localized modes in the boundaries of an open insulator. On the other hand, the existence of geometric frustration gives rise to degenerate localized bulk states. The interplay of these two phenomena may, in principle, result in an enhanced protection/localization of edge states. In this paper, we study a two-dimensional Lieb-based topological insulator with staggered hopping parameters and diagonal open boundary conditions. This system belongs to the ${C}_{2v}$ class and sustains one-dimensional (1D) boundary modes except at the topological transition point, where the ${C}_{4v}$ symmetry allows for the existence of localized (0D) corner states. Our analysis reveals that, while a large set of boundary states have a common well-defined topological phase transition, other edge states reflect a topological nontrivial phase for any finite value of the hopping parameters, are completely localized (compact) due to destructive interference, and evolve into corner states when reaching the higher symmetry point. We consider the robustness of these compact edge states with respect to time-dependent perturbations and indicate ways that these states could be prepared and measured in experiments with ultracold atoms.

Edge and bulk localization of Floquet topological superconductors

We study the bulk and edge properties of a driven Kitaev chain, where the driving is performed as instantaneous quenches of the on-site energies. We identify three periodic driving regimes: low period, which is equivalent to a static model, with renormalized parameters obtained from the Baker-Campbell-Hausdorff (BCH) expansion; intermediate period, where the first order BCH expansion breaks down; and high period when the quasienergy gap at $\omega/2$ closes. We investigate the dynamical localization properties for the case of quasiperiodic potential driving as a function of its amplitude and the pairing strength, obtaining regimes with extended, critical and localized bulk states, if the driving is performed at high frequencies. In these, we characterize wave-packet propagation, obtaining ballistic, subdiffusive and absence of spreading, respectively. In the intermediate period regime, we find an additional region in the phase diagram with a mobility edge between critical and localized states. Further, we investigate the stability of these phases under time-aperiodicity on the drivings, observing that the system eventually thermalizes: It results in featureless random states which can be described by the symmetry of the Hamiltonian. In a system with open edges, we find that both Majorana and fermionic localized edge modes can be engineered with a spatially quasiperiodic potential. Besides, we demonstrate the possibility of creating multiple Majorana $0$ and $\pi$ modes in a driven setting, even if the underlying static Hamiltonian is in its trivial phase. Lastly, we study the robustness of the Majorana modes against the aperiodicity in the driving period, showing that the ones created via quasiperiodic potential are more robust to the decoherence. Moreover, we find an example where Majorana mode is robust, provided that it is chosen from a special point in the topological region.

Electronic states in tin oxide thin films upon photo and electrochemical analysis

Sb-doped SnO2 thin films have been deposited by the dip-coating technique. The morphology analysis revealed that the surface is granular, crack-free and the average roughness varies with Sb-doping. The sub–band gap electronic transitions were successfully probed using the optical and Mott-Schottky measurements. Therefore, the energetic band diagrams were established to locate the conduction band (3.85 eV) and valence band (7.69 eV) below vacuum. The concentrations of shallow and deep donors were determined from the pseudo-slopes. The charge transport was achieved with bulk-localized states which mediate the carriers tunneling. The electrical conductivity above 1 V, involves electrons hopping between tail states and the current increases exponentially (I∼ ea.V). The ac-conductivity is enhanced with increasing the thermal energy, which promotes the carriers hopping. The photoconductivity revealed that the tunneling mechanism is sensitive to the localized states overlapping, thus generating donor and/or traps levels within the forbidden band.

CFT descriptions of bulk local states in the AdS black holes

We present a new method for reconstructing CFT duals of states excited by the bulk local operators in the three dimensional AdS black holes in the AdS/CFT context. As an important procedure for this, we introduce a map between the bulk points in AdS and those on the boundary where CFT lives. This gives a systematic and universal way to express bulk local states even inside black hole interiors. Our construction allows us to probe the interior structures of black holes purely from the CFT calculations. We analyze bulk local states in the single-sided black holes as well as the double-sided black holes.

Basic models in dielectric spectroscopy of heterogeneous materials with semiconductor inclusions

PurposeThe purpose of this paper is to develop the models of the dielectric permittivity dispersion of heterogeneous systems based on semiconductors to a level that would allow to apply effectively the method of broadband dielectric spectroscopy for the study of electronic processes in ceramic and composite materials.Design/methodology/approachThe new approach for determining the complex dielectric permittivity of heterogeneous systems with semiconductor particles is used. It includes finding the analytical expression of the effective dielectric permittivity of the separate semiconductor particle of spherical shape. This approach takes into account the polarization of the free charge carriers in this particle, including capturing to localized electron states. This enabled the authors to use the known equations for complex dielectric permittivity of two-component matrix systems and statistical mixtures.FindingsThe presented dispersion equations establish the relationship between the parameters of the dielectric spectrum and electronic processes in the structures like semiconductor particles in a dielectric matrix in a wide frequency range. Conditions of manifestation and location of the different dispersion regions of the complex dielectric heterogeneous systems based on semiconductors in the frequency axis and their features are established. The most high-frequency dispersion region corresponds to the separation of free charge carriers at polarization. After this region in the direction of reducing of the frequency, the dispersion regions caused by recharge bulk and/or surface localized states follow. The most low-frequency dispersion region is caused by recharging electron traps in the boundary layer of the dielectric matrix.Originality/valueDielectric dispersion models are developed that are associated with: electronic processes of separation of free charge carriers in the semiconductor component, recapture of free charge carriers in the localized electronic states in bulk and on the surface of the semiconductor and also boundary layers of the dielectric at the polarization. The authors have analyzed to situations that correspond applicable and promising materials: varistor ceramics and composite structure with conductive and semiconductor fillers. The modelling results correspond to the existing level of understanding of the electron phenomena in matrix systems and statistical mixtures based on semiconductors. It allows to raise efficiency of research and control properties of heterogeneous materials by dielectric spectroscopy.

Bulk local states and crosscaps in holographic CFT

In a weakly coupled gravity theory in the anti-de Sitter space, local states in the bulk are linear superpositions of Ishibashi states for a crosscap in the dual conformal field theory. The superposition structure can be constrained either by the microscopic causality in the bulk gravity or the bootstrap condition in the boundary conformal field theory. We show, contrary to some expectation, that these two conditions are not compatible to each other in the weak gravity regime. We also present an evidence to show that bulk local states in three dimensions are not organized by the Virasoro symmetry.

Causal evolutions of bulk local excitations from CFT

Bulk localized excited states in an AdS spacetime can be constructed from Ishibashi states with respect to the global conformal symmetry in the dual CFT. We study boundary two point functions of primary operators in the presence of bulk localized excitations in two dimensional CFTs. From two point functions in holographic CFTs, we observe causal propagations of radiations when the mass of dual bulk scalar field is close to the BF bound. This behavior for holographic CFTs is consistent with the locality and causality in classical gravity duals. We also show that this cannot be seen in free fermion CFTs. Moreover, we find that the short distance behavior of two point functions is universal and obeys the relation which generalizes the first law of entanglement entropy.

Discriminating a deep gallium antisite defect from shallow acceptors in GaAs using supercell calculations

For the purposes of making reliable first-principles predictions of defect energies in semiconductors, it is crucial to distinguish between effective-mass-like defects, which cannot be treated accurately with existing supercell methods, and deep defects, for which density functional theory calculations can yield reliable predictions of defect energy levels. The gallium antisite defect ${\mathrm{Ga}}_{As}$ is often associated with the 78/203 meV shallow double acceptor in Ga-rich gallium arsenide. Within a conceptual framework of level patterns, analyses of structure and spin stabilization can be used within a supercell approach to distinguish localized deep defect states from shallow acceptors such as ${\mathrm{B}}_{As}$. This systematic approach determines that the gallium antisite supercell results has signatures inconsistent with an effective mass state and cannot be the 78/203 shallow double acceptor. The properties of the Ga antisite in GaAs are described, total energy calculations that explicitly map onto asymptotic discrete localized bulk states predict that the Ga antisite is a deep double acceptor and has at least one deep donor state.

Quantum Hall resistance standards from graphene grown by chemical vapour deposition on silicon carbide.

Replacing GaAs by graphene to realize more practical quantum Hall resistance standards (QHRS), accurate to within 10−9 in relative value, but operating at lower magnetic fields than 10 T, is an ongoing goal in metrology. To date, the required accuracy has been reported, only few times, in graphene grown on SiC by Si sublimation, under higher magnetic fields. Here, we report on a graphene device grown by chemical vapour deposition on SiC, which demonstrates such accuracies of the Hall resistance from 10 T up to 19 T at 1.4 K. This is explained by a quantum Hall effect with low dissipation, resulting from strongly localized bulk states at the magnetic length scale, over a wide magnetic field range. Our results show that graphene-based QHRS can replace their GaAs counterparts by operating in as-convenient cryomagnetic conditions, but over an extended magnetic field range. They rely on a promising hybrid and scalable growth method and a fabrication process achieving low-electron-density devices.