Disorder-Broadened Phase Boundary with Enhanced Amorphous Superconductivity in Pressurized In2Te5.

As an empirical tool in materials science and engineering, the iconic phase diagram owes its robustness and practicality to the topological characteristics rooted in the celebrated Gibbs phase law free variables (F) = components (C) - phases (P) + 2. When crossing the phase diagram boundary, the structure transition occurs abruptly, bringing about an instantaneous change in physical properties and limited controllability on the boundaries (F = 1). Here, the sharp phase boundary is expanded to an amorphous transition region (F = 2) by partially disrupting the long-range translational symmetry, leading to a sequential crystalline-amorphous-crystalline (CAC) transition in a pressurized In2Te5 single crystal. Through detailed in situ synchrotron diffraction, it is elucidated that the phase transition stems from the rotation of immobile blocks [In2Te2]2+, linked by hinge-like [Te3]2- trimers. Remarkably, within the amorphous region, the amorphous phase demonstrates a notable 25% increase of the superconducting transition temperature (Tc), while the carrier concentration remains relatively constant. Furthermore, a theoretical framework is proposed revealing that the unconventional boost in amorphous superconductivity might be attributed to an intensified electron correlation, triggered by a disorder-augmented multifractal behavior. These findings underscore the potential of disorder and prompt further exploration of unforeseen phenomena on the phase boundaries.

Half-quantized helical hinge currents in axion insulators.

Fractional quantization can emerge in noncorrelated systems due to the parity anomaly, while its condensed matter realization is a challenging problem. We propose that in axion insulators (AIs), parity anomaly manifests a unique fractional boundary excitation: the half-quantized helical hinge currents. These helical hinge currents microscopically originate from the lateral Goos-Hänchen (GH) shift of massless side-surface Dirac electrons that are totally reflected from the hinges. Meanwhile, due to the presence of the massive top and bottom surfaces of the AI, the helical current induced by the GH shift is half-quantized. The semiclassical wave packet analysis uncovers that the hinge current has a topological origin and its half quantization is robust to parameter variations. Lastly, we propose an experimentally feasible six-terminal device to identify the half-quantized hinge channels by measuring the nonreciprocal conductances. Our results advance the realization of the half-quantization and topological magnetoelectric responses in AIs.

Direct visualization of edge state in even-layer MnBi2Te4 at zero magnetic field.

Being the first intrinsic antiferromagnetic (AFM) topological insulator (TI), MnBi2Te4 is argued to be a topological axion state in its even-layer form due to the antiparallel magnetization between the top and bottom layers. Here we combine both transport and scanning microwave impedance microscopy (sMIM) to investigate such axion state in atomically thin MnBi2Te4 with even-layer thickness at zero magnetic field. While transport measurements show a zero Hall plateau signaturing the axion state, sMIM uncovers an unexpected edge state raising questions regarding the nature of the "axion state". Based on our model calculation, we propose that the edge state of even-layer MnBi2Te4 at zero field is derived from gapped helical edge states of the quantum spin Hall effect with time-reversal-symmetry breaking, when a crossover from a three-dimensional TI MnBi2Te4 to a two-dimensional TI occurs. Our finding thus signifies the richness of topological phases in MnB2Te4 that has yet to be fully explored.

Transport Theory of Half-Quantized Hall Conductance in a Semimagnetic Topological Insulator.

Recently, a half-quantized Hall conductance (HQHC) plateau was experimentally observed in a semimagnetic topological insulator heterostructure. However, the heterostructure was metallic with a nonzero longitudinal conductance, which contradicts the common belief that quantized Hall conductance is usually observed in insulators. In this work, we systematically study the surface transport of a semimagnetic topological insulator with both gapped and gapless Dirac surfaces in the presence of dephasing process. In particular, we reveal that the HQHC is directly related to the half-quantized chiral current along the edge of a strongly dephasing metal. The Hall conductance keeps a half-quantized value for large dephasing strengths, while the longitudinal conductance varies with Fermi energies and dephasing strengths. Furthermore, we evaluate both the conductance and resistance as a function of the temperature, which is consistent with the experimental results. Our results not only provide the microscopic transport mechanism of the HQHC, but also are instructive for the probe of the HQHC in future experiments.

Coexistence of Quantum Hall and Quantum Anomalous Hall Phases in Disordered MnBi_{2}Te_{4}.

In most cases, to observe quantized Hall plateaus, an external magnetic field is applied in intrinsic magnetic topological insulators MnBi_{2}Te_{4}. Nevertheless, whether the nonzero Chern number (C≠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 et al., Science 367, 895 (2020)SCIEAS0036-807510.1126/science.aax8156]. In this Letter, we propose a physical picture based on the Anderson localization to understand the observed Hall plateaus in disordered MnBi_{2}Te_{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 MnBi_{2}Te_{4} which indicates more coexistence states of QAH and QH to be verified by future experiments.

Critical Behavior and Universal Signature of an Axion Insulator State.

Recently, the search for an axion insulator state in the ferromagnetic-3D topological insulator (TI) heterostructure and MnBi_{2}Te_{4} has attracted intense interest. However, its detection remains difficult in experiments. We systematically investigate the disorder-induced phase transition of the axion insulator state in a 3D TI with antiparallel magnetization alignment surfaces. It is found that there exists a 2D disorder-induced phase transition on the surfaces of the 3D TI which shares the same universality class with the quantum Hall plateau to plateau transition. Then, we provide a phenomenological theory which maps the random mass Dirac Hamiltonian of the axion insulator state into the Chalker-Coddington network model. Therefore, we propose probing the axion insulator state by investigating the universal signature of such a phase transition in the ferromagnetic-3D TI heterostructure and MnBi_{2}Te_{4}. Our findings not only show a global phase diagram of the axion insulator state, but also stimulate further experiments to probe it.

Scaling behavior of the quantum phase transition from a quantum-anomalous-Hall insulator to an axion insulator.

The phase transitions from one plateau to the next plateau or to an insulator in quantum Hall and quantum anomalous Hall (QAH) systems have revealed universal scaling behaviors. A magnetic-field-driven quantum phase transition from a QAH insulator to an axion insulator was recently demonstrated in magnetic topological insulator sandwich samples. Here, we show that the temperature dependence of the derivative of the longitudinal resistance on magnetic field at the transition point follows a characteristic power-law that indicates a universal scaling behavior for the QAH to axion insulator phase transition. Similar to the quantum Hall plateau to plateau transition, the QAH to axion insulator transition can also be understood by the Chalker-Coddington network model. We extract a critical exponent κ ~ 0.38 ± 0.02 in agreement with recent high-precision numerical results on the correlation length exponent of the Chalker-Coddington model at ν ~ 2.6, rather than the generally-accepted value of 2.33.

Author Correction: Evidence of higher-order topology in multilayer WTe2 from Josephson coupling through anisotropic hinge states.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Evidence of higher-order topology in multilayer WTe2 from Josephson coupling through anisotropic hinge states.

Td-WTe2 (non-centrosymmetric and orthorhombic), a type-II Weyl semimetal, is expected to have higher-order topological phases with topologically protected, helical one-dimensional hinge states when its Weyl points are annihilated. However, the detection of these hinge states is difficult due to the semimetallic behaviour of the bulk. In this study, we have spatially resolved the hinge states by analysing the magnetic field interference of the supercurrent in Nb-WTe2-Nb proximity Josephson junctions. The Josephson current along the a axis of the WTe2 crystal, but not along the b axis, showed a sharp enhancement at the edges of the junction, and the amount of enhanced Josephson current was comparable to the upper limits of a single one-dimensional helical channel. Our experimental observations suggest a higher-order topological phase in WTe2 and its corresponding anisotropic topological hinge states, in agreement with theoretical calculations. Our work paves the way for the study of hinge states in topological transition-metal dichalcogenides and analogous phases.

Higher-Order Topological Insulators in Quasicrystals.

Current understanding of higher-order topological insulators (HOTIs) is based primarily on crystalline materials. Here, we propose that HOTIs can be realized in quasicrystals. Specifically, we show that two distinct types of second-order topological insulators (SOTIs) can be constructed on the quasicrystalline lattices (QLs) with different tiling patterns. One is derived by using a Wilson mass term to gap out the edge states of the quantum spin Hall insulator on QLs. The other is the quasicrystalline quadrupole insulator (QI) with a quantized quadrupole moment. We reveal some unusual features of the corner states (CSs) in the quasicrystalline SOTIs. We also show that the quasicrystalline QI can be simulated by a designed electrical circuit, where the CSs can be identified by measuring the impedance resonance peak. Our findings not only extend the concept of HOTIs into quasicrystals but also provide a feasible way to detect the topological property of quasicrystals in experiments.

Spectroscopic fingerprint of chiral Majorana modes at the edge of a quantum anomalous Hall insulator/superconductor heterostructure.

With the recent discovery of the quantum anomalous Hall insulator (QAHI), which exhibits the conductive quantum Hall edge states without external magnetic field, it becomes possible to create a topological superconductor (SC) by introducing superconductivity into these edge states. In this case, 2 distinct topological superconducting phases with 1 or 2 chiral Majorana edge modes were theoretically predicted, characterized by Chern numbers (N) of 1 and 2, respectively. We present spectroscopic evidence from Andreev reflection experiments for the presence of chiral Majorana modes in an Nb/(Cr0.12Bi0.26Sb0.62)2Te3 heterostructure with distinct signatures attributed to 2 different topological superconducting phases. The results are in qualitatively good agreement with the theoretical predictions.

Effects of Random Domains on the Zero Hall Plateau in the Quantum Anomalous Hall Effect.

Recently, a zero Hall conductance plateau with random domains was experimentally observed in the quantum anomalous Hall (QAH) effect. We study the effects of random domains on the zero Hall plateau in QAH insulators. We find that the structure inversion symmetry determines the scaling property of the zero Hall plateau transition in the QAH systems. In the presence of structure inversion symmetry, the zero Hall plateau state shows a quantum-Hall-type critical point, originating from the two decoupled subsystems with opposite Chern numbers. However, the absence of structure inversion symmetry leads to a mixture between these two subsystems, gives rise to a line of critical points, and dramatically changes the scaling behavior. Hereinto, we predict a Berezinskii-Kosterlitz-Thouless-type transition during the Hall conductance plateau switching in the QAH insulators. Our results are instructive for both theoretic understanding of the zero Hall plateau transition and future transport experiments in the QAH insulators.

Topological Transitions Induced by Antiferromagnetism in a Thin-Film Topological Insulator.

Magnetism in topological insulators (TIs) opens a topologically nontrivial exchange band gap, providing an exciting platform for manipulating the topological order through an external magnetic field. Here, we show that the surface of an antiferromagnetic thin film can magnetize the top and the bottom TI surface states through interfacial couplings. During the magnetization reversal, intermediate spin configurations are ascribed from unsynchronized magnetic switchings. This unsynchronized switching develops antisymmetric magnetoresistance spikes during magnetization reversals, which might originate from a series of topological transitions. With the high Néel ordering temperature provided by the antiferromagnetic layers, the signature of the induced topological transition persists up to ∼90 K.

Disorder and Metal-Insulator Transitions in Weyl Semimetals.

The Weyl semimetal (WSM) is a newly proposed quantum state of matter. It has Weyl nodes in bulk excitations and Fermi arc surface states. We study the effects of disorder and localization in WSMs and find three novel phase transitions. (i) Two Weyl nodes near the Brillouin zone boundary can be annihilated pairwise by disorder scattering, resulting in the opening of a topologically nontrivial gap and a transition from a WSM to a three-dimensional quantum anomalous Hall state. (ii) When the two Weyl nodes are well separated in momentum space, the emergent bulk extended states can give rise to a direct transition from a WSM to a 3D diffusive anomalous Hall metal. (iii) Two Weyl nodes can emerge near the zone center when an insulating gap closes with increasing disorder, enabling a direct transition from a normal band insulator to a WSM. We determine the phase diagram by numerically computing the localization length and the Hall conductivity, and propose that the novel phase transitions can be realized on a photonic lattice.