Disorder and Metal-Insulator Transitions in Weyl Semimetals

Higher-order topological phases in crystalline and non-crystalline systems: a review

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in non-periodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.

Room-temperature valley transistors for low-power neuromorphic computing

Valley pseudospin is an electronic degree of freedom that promises highly efficient information processing applications. However, valley-polarized excitons usually have short pico-second lifetimes, which limits the room-temperature applicability of valleytronic devices. Here, we demonstrate room-temperature valley transistors that operate by generating free carrier valley polarization with a long lifetime. This is achieved by electrostatic manipulation of the non-trivial band topology of the Weyl semiconductor tellurium (Te). We observe valley-polarized diffusion lengths of more than 7 μm and fabricate valley transistors with an ON/OFF ratio of 105 at room temperature. Moreover, we demonstrate an ion insertion/extraction device structure that enables 32 non-volatile memory states with high linearity and symmetry in the Te valley transistor. With ultralow power consumption (~fW valley contribution), we enable the inferring process of artificial neural networks, exhibiting potential for applications in low-power neuromorphic computing.

Anomalous Transport Signatures in Weyl Semimetals with Point Defects

We present the first theoretical study of transport properties of Weyl semimetals with point defects. Focusing on a class of time-reversal symmetric Weyl lattice models, we show that dilute lattice vacancies induce a finite density of quasilocalized states at and near the nodal energy, causing strong modifications to the low-energy spectrum. This generates novel transport effects, namely, (i) an oscillatory behavior of the dc conductivity with the charge carrier density in the absence of magnetic fields, and (ii) a plateau-shaped dissipative optical response for photon frequencies below the interband threshold, E_{F}≲ℏω≲2E_{F}. Our results provide a path to engineer unconventional quantum transport effects in Weyl semimetals by means of common point defects.

Topological Chern vectors in three-dimensional photonic crystals

The paradigmatic example of a topological phase of matter, the two-dimensional Chern insulator^1-5, is characterized by a topological invariant consisting of a single integer, the scalar Chern number. Extending the Chern insulator phase from two to three dimensions requires generalization of the Chern number to a three-vector^6,7, similar to the three-dimensional (3D) quantum Hall effect^8-13. Such Chern vectors for 3D Chern insulators have never been explored experimentally. Here we use magnetically tunable 3D photonic crystals to achieve the experimental demonstration of Chern vectors and their topological surface states. We demonstrate Chern vector magnitudes of up to six, higher than all scalar Chern numbers previously realized in topological materials. The isofrequency contours formed by the topological surface states in the surface Brillouin zone form torus knots or links, whose characteristic integers are determined by the Chern vectors. We demonstrate a sample with surface states forming a (2, 2) torus link or Hopf link in the surface Brillouin zone, which is topologically distinct from the surface states of other 3D topological phases. These results establish the Chern vector as an intrinsic bulk topological invariant in 3D topological materials, with surface states possessing unique topological characteristics.

Disorder- and Topology-Enhanced Fully Spin-Polarized Currents in Nodal Chain Spin-Gapless Semimetals

Recently discovered high-quality nodal chain spin-gapless semimetals MF_{3} (M=Pd, Mn) feature an ultraclean nodal chain in the spin up channel residing right at the Fermi level and displaying a large spin gap leading to a 100% spin polarization of transport properties. Here, we investigate both intrinsic and extrinsic contributions to anomalous and spin transport in this class of materials. The dominant intrinsic origin is found to originate entirely from the gapped nodal chains without the entanglement of any other trivial bands. The side-jump mechanism is predicted to be negligibly small, but intrinsic skew scattering enhances the intrinsic Hall and Nernst signals significantly, leading to large values of respective conductivities. Our findings open a new material platform for exploring strong anomalous and spin transport properties in magnetic topological semimetals.

Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals

Recently, higher-order topological matter and 3D quantum Hall effects have attracted a great amount of attention. The Fermi-arc mechanism of the 3D quantum Hall effect proposed to exist in Weyl semimetals is characterized by the one-sided hinge states, which do not exist in all the previous quantum Hall systems, and more importantly, pose a realistic example of the higher-order topological matter. The experimental effort so far is in the Dirac semimetal Cd_{3}As_{2}, where, however, time-reversal symmetry leads to hinge states on both sides of the top and bottom surfaces, instead of the aspired one-sided hinge states. We propose that under a tilted magnetic field, the hinge states in Cd_{3}As_{2}-like Dirac semimetals can be one sided, highly tunable by field direction and Fermi energy, and robust against weak disorder. Furthermore, we propose a scanning tunneling Hall measurement to detect the one-sided hinge states. Our results will be insightful for exploring not only the quantum Hall effects beyond two dimensions, but also other higher-order topological insulators in the future.

Topological Phase Transitions in Disordered Electric Quadrupole Insulators

We investigate disorder-driven topological phase transitions in quantized electric quadrupole insulators in two dimensions. We show that chiral symmetry can protect the quantization of the quadrupole moment q_{xy}, such that the higher-order topological invariant is well defined even when disorder has broken all crystalline symmetries. Moreover, nonvanishing q_{xy} and consequent corner modes can be induced from a trivial insulating phase by disorder that preserves chiral symmetry. The critical points of such topological phase transitions are marked by the occurrence of extended boundary states even in the presence of strong disorder. We provide a systematic characterization of these disorder-driven topological phase transitions from both bulk and boundary descriptions.

Semi-quantized Spin Pumping and Spin-Orbit Torques in Topological Dirac Semimetals

We study the time-development processes of spin and charge transport phenomena in a topological Dirac semimetal attached to a ferromagnetic insulator with a precessing magnetization. Compared to conventional normal metals, topological Dirac semimetals manifest a large inverse spin Hall effect when a spin current is pumped from the attached ferromagnetic insulator. It is shown that the induced charge current is semi-quantized, i.e., it depends only on the distance between the two Dirac points in momentum space and hardly depends on the disorder strength when the system remains in the topological Dirac semimetal phase. As an inverse effect, we show that the electric field applied to the topological Dirac semimetal exerts a spin torque on the local magnetization in the ferromagnetic insulator via the exchange interaction and the semi-quantized spin Hall effect. Our study demonstrates that the topological Dirac semimetal offers a less-dissipative platform for spin-charge conversion and spin switching.

Anomalous spin Nernst effect in Weyl semimetals

The spin Nernst effect describes a transverse spin current induced by the longitudinal thermal gradient in a system with the spin-orbit coupling. Here we study the spin Nernst effect in a mesoscopic four-terminal cross-bar Weyl semimetal device under a perpendicular magnetic field. Because the spin current is a tensor, it has three elements with the spin direction pointing to the x, y  and z directions when the spin current flows along the transverse lead. By using the tight-binding Hamiltonian combined with the nonequilibrium Green's function method, the three elements of the spin current in the transverse leads and the spin Nernst coefficients are obtained. The results show that the spin Nernst effect in the Weyl semimetal has an essential difference to the traditional Nernst effect: we found that the z direction spin current is zero without the magnetic field while it appears under the magnetic field, and the x and y  direction spin currents in the two transverse leads flow out or in together, in contrast to the traditional spin Nernst effect, in which the spin current is induced by the spin-orbit coupling and flows out from one lead and flows in on the other. We call it the anomalous spin Nernst effect. In addition, we show that the Weyl semimetals have inversion-type symmetry, mirror-reversal-type symmetry and electron-hole-type symmetry, which lead to the spin Nernst coefficients being either odd or even functions of the Fermi energy, the magnetic field and the transverse terminals. Moreover, the spin Nernst effect in the Weyl semimetals are strongly anisotropic and its coefficients are strongly dependent on both the direction of thermal gradient and the direction of the transverse lead connection. Three non-equivalent connection modes (x-z, z-x and x-y  modes) are studied in detail, and the spin Nernst coefficients for three different modes exhibit very different behaviors. These strongly anisotropic behaviors of the spin Nernst effect can be used as the characterization of magnetic Weyl semimetals.

Topological Amorphous Metals

We study amorphous systems with completely random sites and find that, through constructing and exploring a concrete model Hamiltonian, such a system can host an exotic phase of topological amorphous metal in three dimensions. In contrast to the traditional Weyl semimetals, topological amorphous metals break translational symmetry, and thus they cannot be characterized by the first Chern number defined based on the momentum space band structures. Instead, their topological properties will manifest in the Bott index and the Hall conductivity as well as the surface states. By studying the energy band and quantum transport properties, we find that topological amorphous metals exhibit a diffusive metal behavior. We further introduce a practical experimental proposal with electric circuits where the predicted phenomena can be observed using state-of-the-art technologies. Our results open the door to exploring topological gapless phenomena in amorphous systems.

Disorder-Driven Quantum Transition in Relativistic Semimetals: Functional Renormalization via the Porous Medium Equation

In the presence of randomness, a relativistic semimetal undergoes a quantum transition towards a diffusive phase. A standard approach relates this transition to the U(N) Gross-Neveu model in the limit of N→0. We show that the corresponding fixed point is infinitely unstable, demonstrating the necessity to include fluctuations beyond the usual Gaussian approximation. We develop a functional renormalization group method amenable to include these effects and show that the disorder distribution renormalizes following the so-called porous medium equation. We find that the transition is controlled by a nonanalytic fixed point drastically different from that of the U(N) Gross-Neveu model. Our approach provides a unique mechanism of spontaneous generation of a finite density of states and also characterizes the scaling behavior of the broad distribution of fluctuations close to the transition. It can be applied to other problems where nonanalytic effects may play a role, such as the Anderson localization transition.

Stability of Periodically Driven Topological Phases against Disorder

In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These nonequilibrium states, at high driving frequencies, exhibit the quintessential robustness against local disorder similar to equilibrium topological phases. However, proving the existence of such topological phases in a general setting is an open problem. We propose a universal effective theory that leverages on modern free probability theory and ideas in random matrices to analytically predict the existence of the topological phase for finite driving frequencies and across a range of disorder. We find that, depending on the strength of disorder, such systems may be topological or trivial and that there is a transition between the two. In particular, the theory predicts the critical point for the transition between the two phases and provides the critical exponents. We corroborate our results by comparing them to exact diagonalizations for driven-disordered 1D Kitaev chain and 2D Bernevig-Hughes-Zhang models and find excellent agreement. This Letter may guide the experimental efforts for exploring topological phases.

A generic phase between disordered Weyl semimetal and diffusive metal

Quantum phase transitions of three-dimensional (3D) Weyl semimetals (WSMs) subject to uncorrelated on-site disorder are investigated through quantum conductance calculations and finite-size scaling of localization length. Contrary to previous claims that a direct transition from a WSM to a diffusive metal (DM) occurs, an intermediate phase of Chern insulator (CI) between the two distinct metallic phases should exist due to internode scattering that is comparable to intranode scattering. The critical exponent of localization length is ν [Formula: see text] 1.3 for both the WSM-CI and CI-DM transitions, in the same universality class of 3D Gaussian unitary ensemble of the Anderson localization transition. The CI phase is confirmed by quantized nonzero Hall conductances in the bulk insulating phase established by localization length calculations. The disorder-induced various plateau-plateau transitions in both the WSM and CI phases are observed and explained by the self-consistent Born approximation. Furthermore, we clarify that the occurrence of zero density of states at Weyl nodes is not a good criterion for the disordered WSM, and there is no fundamental principle to support the hypothesis of divergence of localization length at the WSM-DM transition.

Accurate Determination of the Quasiparticle and Scaling Properties Surrounding the Quantum Critical Point of Disordered Three-Dimensional Dirac Semimetals

Exploiting the enabling power of the Lanczos method in momentum space, we determine accurately the quasiparticle and scaling properties of disordered three-dimensional Dirac semimetals surrounding the quantum critical point separating the semimetal and diffusive metal regimes. We unveil that the imaginary part of the quasiparticle self-energy obeys a common power law before, at, and after the quantum phase transition, but the power law is nonuniversal, whose exponent is dependent on the disorder strength. More intriguingly, whereas a common power law is also found for the real part of the self-energy before and after the phase transition, a distinctly different behavior is identified at the critical point, characterized by the existence of a nonanalytic logarithmic singularity. This nonanalytical correction serves as the very basis for the unusual power-law behaviors of the quasiparticles and many other physical properties surrounding the quantum critical point. Our approach also allows the ready and reliable determination of the scaling properties of the correlation length and dynamical exponents. We further show that the central findings are valid for both uncorrelated and correlated disorder distributions and should be directly comparable with future experimental observations.

Chiral magnetic conductivity and surface states of Weyl semimetals in topological insulator ultra-thin film multilayer

We investigate an ultra-thin film of topological insulator (TI) multilayer as a model for a three-dimensional (3D) Weyl semimetal. We introduce tunneling parameters t S, [Formula: see text], and t D, where the former two parameters couple layers of the same thin film at small and large momenta, and the latter parameter couples neighbouring thin film layers along the z-direction. The Chern number is computed in each topological phase of the system and we find that for [Formula: see text], the tunneling parameter [Formula: see text] changes from positive to negative as the system transits from Weyl semi-metallic phase to insulating phases. We further study the chiral magnetic effect (CME) of the system in the presence of a time dependent magnetic field. We compute the low-temperature dependence of the chiral magnetic conductivity and show that it captures three distinct phases of the system separated by plateaus. Furthermore, we propose and study a 3D lattice model of Porphyrin thin film, an organic material known to support topological Frenkel exciton edge states. We show that this model exhibits a 3D Weyl semi-metallic phase and also supports a 2D Weyl semi-metallic phase. We further show that this model recovers that of 3D Weyl semimetal in topological insulator thin film multilayer. Thus, paving the way for simulating a 3D Weyl semimetal in topological insulator thin film multilayer. We obtain the surface states (Fermi arcs) in the 3D model and the chiral edge states in the 2D model and analyze their topological properties.

Effect of Disorder in a Three-Dimensional Layered Chern Insulator

We studied the effects of disorder in a three-dimensional layered Chern insulator, which, in the clean limit, is either a Chern insulator or a Weyl semimetal depending on an interlayer coupling strength. By calculating the localization length by the transfer matrix method, we found two distinct types of metallic phases between the Anderson insulator and the Chern insulator: one is a diffusive metallic phase and the other is a renormalized Weyl semimetal phase. By calculating the conductance and density of states, we characterize these two metallic phases and reveal a critical nature of a quantum critical line between these two metallic phases.