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 ($C eq 0$) phase is a quantum anomalous Hall (Q
AH) 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.
We study the disorder-induced phase transition of higher-order Weyl semimetals (HOWSMs) and the fate of the topological features of disordered HOWSMs. We obtain a global phase diagram of HOWSMs according to the scaling theory of Anderson localization
. Specifically, a phase transition from the Weyl semimetal (WSM) to the HOWSM is uncovered, distinguishing the disordered HOWSMs from the traditional WSMs. Further, we confirm the robustness of Weyl-nodes for HOWSMs. Interestingly, the unique topological properties of HOWSMs show different behaviors: (i) the quantized quadrupole moment and the corresponding quantized charge of hinge states are fragile to weak disorder; (ii) the hinge states show moderate stability which enables the feasibility in experimental observation. Our study deepens the understanding of the topological nature of HOWSMs and paves a possible way to the characterization of such a phase in experiments.
In this Letter, we study an Anderson-localization-induced quantized transport in disordered Chern insulators (CIs). By investigating the disordered CIs with a step potential, we find that the chiral interface states emerge along the interfaces of the
step potential, and the energy range for such quantized transport can be manipulated through the potential strength. Furthermore, numerical simulations on cases with a multi-step potential demonstrate that such chiral state can be spatially shifted by varying the Fermi energy, and the energy window for quantized transport is greatly enlarged. Experimentally, such chiral interface states can be realized by imposing transverse electric field, in which the energy window for quantized transport is much broader than the intrinsic band gap of the corresponding CI. These phenomena are quite universal for disordered CIs due to the direct phase transition between the CI and the normal 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 k~ 0.38 in agreement with recent high-precision numerical results on the correlation length exponent of the Chalker-Coddington model at v ~ 2.6, rather than the generally-accepted value of 2.33.
The noncentrosymmetric Td-WTe$_2$, previously known as a type-II Weyl semimetal, is expected to have higher order topological phases with topologically protected, helical one-dimensional (1D) hinge states when their scarcely separated Weyl points get
annihilated. However, the detection of these hinge states is difficult in the presence of the semimetallic behaviour of the bulk. Here, we spatially resolved the hinge states by analysing the magnetic field interference of supercurrent in Nb-WTe$_2$-Nb proximity Josephson junctions. The Josephson current along the a-axis of the WTe$_2$ crystal, but not along the b-axis, showed sharp enhancements at the edges of the junction; the amount of enhanced Josephson current was comparable to the upper limits of a single 1D conduction channel. Our experimental observations provide evidence of the higher order topological phase in WTe$_2$ and its corresponding anisotropic topological hinge states, in good agreement with theoretical calculations. Our work paves the way for hinge transport studies on topological semimetals in superconducting heterostructures, including their topological superconductivity.
Recently, a quantum anomalous Hall insulator (QAHI)/superconductor heterostructure has been realized and shows half-quantized conductance plateaus in two-terminal conductance measurements [Q. L. He textit{et al.}, Science {bf357}, 294 (2017)]. The ha
lf-quantized conductance plateaus are considered as a solid evidence of chiral Majorana edge modes. However, there is a strong debate over the origin of the half-quantized conductance plateaus. In this work, we propose a Josephson junction based on the QAHI/superconductor heterostructure to identify the existence of chiral Majorana edge modes. We find that the critical Josephson current dramatically increases to a peak value when a half-quantized conductance plateau $sigma_{12}=e^2/2h$ is showing up for the $N=1$ chiral topological superconductor phase with a single chiral Majorana mode. Furthermore, we show that the critical Josephson current of the $N=1$ chiral topological superconductor exhibits an $h/e$-period oscillation and is robust to disorder, in contrast to the behaviors of conventional two-dimensional electron gas systems. We also estimate experimentally relevant parameters and believe that the supercurrent can be observed in experiments.
Quantum anomalous Hall insulator/superconductor heterostructures emerged as a competitive platform to realize topological superconductors with chiral Majorana edge states as shown in recent experiments [He et al. Science {bf 357}, 294 (2017)]. Howeve
r, chiral Majorana modes, being extended, cannot be used for topological quantum computation. In this work, we show that quasi-one-dimensional quantum anomalous Hall structures exhibit a large topological regime (much larger than the two-dimensional case) which supports localized Majorana zero energy modes. The non-Abelian properties of a cross-shaped quantum anomalous Hall junction is shown explicitly by time-dependent calculations. We believe that networks of such quasi-one-dimensional quantum anomalous Hall systems can be easily fabricated for scalable topological quantum computation.
The Weyl semimetal (WSM) is a newly proposed quantum state of matter. It has Weyl nodes in bulk excitations and Fermi arcs surface states. We study the effects of disorder and localization in WSMs and find three exotic 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 (3D) 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 exotic phase transitions can be realized on a photonic lattice.
