The interplay between magnetism and strong topological insulator gives rise to distinct new topological phases and various intriguing phenomena, attracting significant attention in recent years. However, magnetic effects in weak topological insulators remain largely unexplored. In this work, we systematically investigate the magnetic effect on thin films of weak topological insulators. We focus on ferromagnetic and antiferromagnetic effects, which have been extensively studied in strong topological insulators, as well as the recently highlighted altermagnetic effect. We reveal that the interplay between magnetism and weak topological insulators leads to a variety of Hall effects in the absence of an external magnetic field, including the metallic quantum anomalous Hall effect without chiral edge states, the quantum anomalous Hall effect with a higher Hall conductance plateau, the quantized layer Hall effect, the metallic half-quantized valley-like Hall effect, and a quantized valley-like Hall effect. This work provides valuable insights for exploring magnetic effect on weak topological insulators.
We examine the magnetic field driven insulator-quantum Hall-insulator transitions of the two dimensional hole gas in a Ge/SiGe quantum well. We observe direct transitions between low and high magnetic field insulators and the $ν=1$ quantum Hall state. With increasing magnetic field, the transitions from insulating to quantum Hall and quantum Hall to insulating are very similar with respect to their transport properties. We address the temperature dependence around the transitions and show that the characteristic energy scale for the high field transition is larger.
Intrinsic contribution to the spin Hall effect in a two-dimensional silicene is considered theoretically within the linear response theory and Green function formalism. When an external voltage normal to the silicene plane is applied, the spin Hall conductivity is shown to reveal a transition from the spin Hall insulator phase at low voltages to the conventional insulator phase at higher voltages. This transition resembles recently reported phase transition in a bilayer graphene. The spin-orbit interaction responsible for this transition in silicene is much stronger than in graphene, which sho…
We study responses to metric perturbation in topological insulator models. In this paper we introduce a novel quantity, Hall viscosity to particle density ratio, which is analogous to the viscosity to entropy ratio suggested by AdS/CFT correspondence. This quantity corresponds to the filling fraction which characterizes the quantum Hall states, and hence it could be discussed in Haldane's zero-field quantum Hall system. We also consider dissipationless viscosity in the time reversal invariant quantum spin Hall system, which is related to a spin current.
Statistics of level spacing and magnetization are studied for the phase diagram of the integer quantum Hall effect in a 2D finite lattice model with Anderson disorder.
We describe a new phase transition of the bilayer quantum Hall ferromagnet at filling fraction $ν= 1$. In the presence of static disorder (modeled by a periodic potential), bosonic $S=1/2$ spinons can undergo a superfluid-insulator transition while preserving the ferromagnetic order. The Mott insulating phase has an emergent U(1) photon, and the transition is between Higgs and Coulomb phases of this photon. Physical consequences for charge and counterflow conductivity, and for interlayer tunneling conductance in the presence of quenched disorder are discussed.
We study an unconventional quantum Hall effect for the surface states of ultrathin Floquet topological insulators in a perpendicular magnetic field. The resulting band structure is modified by photon dressing and the topological property is governed by the low-energy dynamics of a single surface. An exchange of symmetric and antisymmetric surface states occurs by reversing the light's polarization. We find a novel quantum Hall state in which the zeroth Landau level undergoes a phase transition from a trivial insulator state, with Hall conductivity $σ_{yx}=0$ at zero Fermi energy, to a Hall ins…
Fundamental insight into the nature of the quantum phase transition from a superconductor to an insulator in two dimensions, or from one plateau to the next or to an insulator in quantum Hall effect, has been revealed through the study of its scaling behavior. Here, we report on the experimental observation of a quantum phase transition from a quantum-anomalous-Hall (QAH) insulator to an Anderson insulator in a magnetic topological insulator by tuning the chemical potential. Our experiment demonstrates the existence of scaling behavior from which we extract the critical exponent for this quant…
We studied the insulator-quantum Hall conductor transition which separates the low-field insulator from the quantum Hall state of the filling factor $ν=4$ on a gated two-dimensional GaAs electron system containing self-assembled InAs quantum dots. To enter the $ν=4$ quantum Hall state directly from the low-field insulator, the two-dimensional system undergoes a crossover from the low-field localization to Landau quantization. The crossover, in fact, covers a wide range with respect to the magnetic field rather than only a small region near the critical point of the insulator-quantum Hall condu…
We study spin conductivity of the surface states in a thin film of a topological insulator with Kubo formulas. Hybridization between the different sides of the film opens a gap at the Dirac point. We found that in the gapped region spin conductivity remains finite. In the gapless region near the band gap spin conductivity is enhanced. These findings make a thin film of a topological insulator as a promising material for spintronic applications.
Phase transitions between the quantum spin Hall and the insulator phases in three dimensions are studied. We find that in inversion-asymmetric systems there appears a gapless phase between the quantum spin Hall and insulator phases in three dimensions, which is in contrast with the two-dimensional case. Existence of this gapless phase stems from a topological nature of gapless points (diabolical points) in three dimensions, but not in two dimensions.
We present an analytical scaling theory for localization in a two-dimensional hierarchical network model that is designed to represent phase-coherent electron transport in the quantum-Hall regime. Scaling expressions for both the longitudinal and Hall resistivities are derived. In agreement with recent numerical studies, we find that the Hall resistivity is quantized in the metallic phase but diverges in the insulating phase. This suggests that the characteristics of a quantized Hall insulator can occur only in the presence of a strong dephasing mechanism.
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…
Electron spin-momentum locking together with background magnetic textures can significantly alter the electron transport properties. We theoretically investigate the electron transport at the interface between a topological insulator and a magnetic insulator with magnetic skyrmions on the top. In contrast to the conventional topological Hall effect in normal metals, the skyrmions yield an additional contribution to the anomalous Hall conductivity even in the absence of in-plane magnetic texture, arising from the phase factor characteristic to Dirac electrons acquired at skyrmion boundary.
We have studied the tachyonic excitations in the junction of two topological insulators in the presence of an external magnetic field. The Landau levels, evaluated from an effective two-dimensional model for tachyons, and from the junction states of two topological insulators, show some unique properties not seen in conventional electrons systems or in graphene. The $ν=1/3$ fractional quantum Hall effect has also a strong presence in the tachyon system.
The mapping between the metal-insulator transition of the quantum Hall system and a superfluid-to-insulator transition is revisited based on a disordered anyon model. The one-parameter scaling of the superfluid-to-insulator transition is employed for the analysis of the scaling behavior of the integer quantum Hall transitions. The analysis reveals the direct transition from a quantum Hall plateau to the insulator in weak disorder limit, and a float-down transition for strong disorders. In either cases, the transition corresponds to a non-chirality superfluid-to-insulator transition, with the l…
The anomalous Hall effect, a hallmark of broken time-reversal symmetry and spin-orbit coupling, is frequently observed in magnetically polarized systems. Its realization in non-magnetic systems, however, remains elusive. Here, we report on the observation of anomalous Hall effect in nominally non-magnetic KTaO3. Anomalous Hall effect emerges in reduced KTaO3 and shows an extrinsic to intrinsic crossover. A paramagnetic behavior is observed in reduced samples using first principles calculations and quantitative magnetometry. The observed anomalous Hall effect follows the oxygen vacancy-induced …
This is a Reply to a Comment by Tanaka and Machida. We provide some details of the derivation of the effective field theory for integer quantum Hall transitions using the non-Abelian chiral anomaly.
Based on ab initio calculations, we predict that a monolayer of Cr-doped (Bi,Sb)2Te3 and GdI2 heterostructure is a quantum anomalous Hall insulator with a non-trivial band gap up to 38 meV. The principle behind our prediction is that the band inversion between two topologically trivial ferromagnetic insulators can result in a non-zero Chern number, which offers a better way to realize the quantum anomalous Hall state without random magnetic doping. In addition, a simple effective model is presented to describe the basic mechanism of spin polarized band inversion in this system. Moreover, we pr…
We report a current scaling study of a quantum phase transition between a quantum anomalous Hall insulator and a trivial insulator on the surface of a heterostructure film of magnetic topological insulators. The transition was observed by tilting the magnetization while measuring the Hall conductivity $σ_{xy}$. The transition curves of $σ_{xy}$ taken under various excitation currents cross each other at a single point, exemplifying a quantum critical behavior of the transition. The slopes of the transition curves follow a power law dependence of the excitation current, giving a scaling exponen…
We demonstrate a new quantum state of matter---valley-polarized quantum anomalous Hall effect in monolayer silicene. In the presence of extrinsic Rashba spin-orbit coupling and exchange field, monolayer silicene can host a quantum anomalous-Hall state with Chern number C=2. We find that through tuning Rashba spin-orbit coupling, a topological phase transition gives rise to a valley polarized quantum anomalous Hall state, i.e. a quantum state which exhibits electronic properties of both quantum valley-Hall effect (valley Chern number C_V=3) and quantum anomalous Hall effect with C=-1.
In this paper, we study topological properties and Hall conductivities in PbC/MnSe heterostructure under the illumination of a circularly polarized light. At high frequency regime, energy gap, Chern numbers, and Hall conductivities are studied based on the Floquet theory and Green's function formalism, respectively. The interplay between spin orbit coupling and light leads to topological phase transition between anomalous Hall states and spin Hall states, which is related to the emission and absorption of two virtual photons. The anomalous Hall conductivities are dependent on polarization of l…
When charge current passes through a normal metal that exhibits spin Hall effect, spin accumulates at the edge of the sample in the transverse direction. We predict that this spin accumulation, or spin voltage, enables quantum tunneling of spin through an insulator or vacuum to reach a ferromagnet without transferring charge. In a normal metal/insulator/ferromagnetic insulator trilayer (such as Pt/oxide/YIG), the quantum tunneling explains the spin-transfer torque and spin pumping that exponentially decay with the thickness of the insulator. In a normal metal/insulator/ferromagnetic metal tril…
The original motivation of great interest to topological insulators was the hope to observe the quantum spin Hall effect. Therefore if a material is in the topological insulator state they frequently call it the quantum spin Hall state. However, despite impressive experimental results confirming the existence of the quantum spin Hall state, the quantum spin Hall effect has not yet been detected. After a short overview of what was originally suggested as the quantum spin Hall effect (quantum spin conductance determined by the topological Chern number) the paper analyzes the crucial role of the …
Negative longitudinal magnetoresistance, in the presence of an external magnetic field parallel to the direction of an applied current, has recently been experimentally verified in Weyl semimetals and topological insulators in the bulk conduction limit. The appearance of negative longitudinal magnetoresistance in topological semimetals is understood as an effect of chiral anomaly, whereas it is not well-defined in topological insulators. Another intriguing phenomenon, planar Hall effect - appearance of a transverse voltage in the plane of applied co-planar electric and magnetic fields not perf…
The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may have potential applications in future electronic devices. In recent years, quantum anomalous Hall effect has been proposed theoretically and realized experimentally. In this review article, we provide a systematic overview of the theoretical and experimental developments in this field.
We study the quantum Hall effect of Dirac fermions on the surface of a Wilson-Dirac type topological insulator thin film in the strong topological insulating phase. Although a magnetic field breaks time reversal symmetry of the bulk, the surface states can survive even in a strong field regime. We examine how the Landau levels of the surface states are affected by symmetry breaking perturbations.
We present a theoretical realization of quantum spin and quantum valley Hall effects in silicene. We show that combination of an electric field and intrinsic spin-orbit interaction leads to quantum phase transitions at the charge neutrality point. This phase transition from a two dimensional topological insulator to a trivial insulating state is accompanied by a quenching of the quantum spin Hall effect and the onset of a quantum valley Hall effect, providing a tool to experimentally tune the topological state of silicene. In contrast to graphene and other conventional topological insulators, …
With the recent observation of graphene-like Landau levels at the surface of topological insulators, the possibility of fractional quantum Hall effect, which is a fundamental signature of strong correlations, has become of interest. Some experiments have reported intra-Landau level structure that is suggestive of fractional quantum Hall effect. This paper discusses the feasibility of fractional quantum Hall effect from a theoretical perspective, and argues that while this effect should occur, ideally, in the $n=0$ and $|n|=1$ Landau levels, it is ruled out in higher $|n|$ Landau levels. Unlike…
We study the phase structure and Hall conductance quantization in weakly coupled multi-layer electron systems in the integer quantum Hall regime. We derive an effective field theory and perform a two-loop renormalization group calculation. It is shown that (i) finite interlayer tunnelings (however small) give rise to successive metallic and insulating phases and metal-insulator transitions in the unitary universality class. (ii) The Hall conductivity is not renormalized in the metallic phases in the 3D regime. (iii) The Hall conductances are quantized in the insulating phases. In the bulk quan…
The integer quantum Hall effect is a topological state of quantum matter in two dimensions, and has recently been observed in three-dimensional topological insulator thin films. Here we study the Landau levels and edge states of surface Dirac fermions in topological insulators under strong magnetic field. We examine the formation of the quantum plateaux of the Hall conductance and find two different patterns, in one pattern the filling number covers all integers while only odd integers in the other. We focus on the quantum plateau closest to zero energy and demonstrate the breakdown of the qua…
We show that a weak hexagonal periodic potential could transform a two-dimensional electron gas with an even-denominator magnetic filling factor to a quantum anomalous Hall insulator of composite fermions, giving rise to fractionally quantized Hall effect. The system provides a realization of the Haldane honeycomb-net model, albeit in a composite fermion system. We further propose a trial wave function for the state, and numerically evaluate its relative stability against the competing Hofstadter state. Possible sets of experimental parameters are proposed.
Nonlinear anomalous Hall effect is the Berry curvature dipole induced second-order Hall voltage or temperature difference in response to a longitudinal electric field or temperature gradient. These are the prominent Hall responses in time reversal symmetric systems. Here, we investigate the family of second-order nonlinear anomalous Hall effects, the electrical, thermoelectric and thermal nonlinear Hall effects in the moiré system of twisted double bilayer graphene. We demonstrate that the nonlinear anomalous Hall signals can be used to probe the topological phase-transitions in moiré systems,…
Both quantum spin Hall and quantum anomalous Hall states are novel states of quantum matter with promising applications. We propose junction quantum wells comprising II-VI, III-V or IV semiconductors as a large class of new materials realizing the quantum spin Hall state. Especially, we find that the bulk band gap for the quantum spin Hall state can be as large as 0.1 eV. Further more, magnetic doping would induce the ferromagnetism in these junction quantum wells due to band edge singularities in the band-inversion regime and to realize the quantum anomalous Hall state.
CrSb is an attractive material for room-temperature antiferromagnetic spintronic applications because of its high Néel temperature $\sim$700 K and semi-metallic character. We study the magnetic properties of CrSb bilayers on few-layer topological insulator thin films using \emph{ab initio} density functional theory. We find that the intrinsic parts of the total anomalous Hall conductivities of the thin films are non-zero, and approximately quantized. The Néel temperature of CrSb bilayers on few-layer topological insulator thin films is found to be approximately two times larger than that of an…
Clean topological insulators exposed to a magnetic field develop Landau levels accompanied by a nonzero Hall conductivity for the infinite slab geometry. In this work we consider the case of disordered topological insulator nanowires and find, in contrast, that a zero Hall plateau emerges within a broad energy window close to the Dirac point. We numerically calculate the conductance and its distribution for a statistical ensemble of disordered nanowires, and use the conductance fluctuations to study the dependence of the insulating phase on system parameters, such as the nanowire length, disor…
The magneto-transport and magnetization measurements of Sb1.90Cu0.10Te3 were performed at different temperatures and different fields. Magneto-transport measurement at high field indicates the coexistence of both bulk and surface states. The magnetization shows the induced antiferromagnetic ordering with Cu doping and the observed quantum oscillation in it indicates that magnetization in Sb1.90Cu0.10Te3 is the bulk property. The non linearity in Hall data suggests the existence of anomalous and topological Hall effect. The anomalous and topological Hall effect (THE) from measured hall data of …
A key step towards dissipationless transport devices is the quantum anomalous Hall effect, which is characterized by an integer quantized Hall conductance in a ferromagnetic insulator with strong spin-orbit coupling. In this work, the anomalous Hall effect due to the impurity scattering, namely the extrinsic anomalous Hall effect, is studied when the Fermi energy crosses with the topologically nontrivial conduction band of a quantum anomalous Hall system. Two major extrinsic contributions, the side-jump and skew-scattering Hall conductivities, are calculated using the diagrammatic techniques i…
We demonstrate the van der Waals epitaxy of the topological insulator compound Bi2Te3 on the ferromagnetic insulator Cr2Ge2Te6. The layers are oriented with (001) of Bi2Te3 parallel to (001) of Cr2Ge2Te6 and (110) of Bi2Te3 parallel to (100) of Cr2Ge2Te6. Cross-sectional transmission electron microscopy indicates the formation of a sharp interface. At low temperatures, bilayers consisting of Bi2Te3 on Cr2Ge2Te6 exhibit a large anomalous Hall effect (AHE). Tilted field studies of the AHE indicate that the easy axis lies along the c-axis of the heterostructure, consistent with magnetization meas…
We study theoretically the anomalous Hall effect due to the vector spin chirality carried by the local spins in the $s$-$d$ model. We will show that the vector spin chirality indeed induces local Hall effect in the presence of the electron spin polarization, while the global Hall effect vanishes if electron transport is homogeneous. This anomalous Hall effect can be interpreted in terms of the rotational component of the spin current associated with the vector chirality.
Thanks to its unique symmetry, the unidirectional spin Hall and Rashba-Edelstein magnetoresistance (USRMR) is of great fundamental and practical interest, particularly in the context of reading magnetization states in two-terminal spin-orbit torque switching memory and logic devices. Recent studies show that topological insulators could improve USRMR amplitude. However, the topological insulator device configurations studied so far in this context, namely ferromagnetic metal/topological insulator bilayers and magnetically doped topological insulators, suffer from current shunting by the metall…
The reentrant integer quantum Hall effects (RIQHE) are due to formation of electronic crystals. We show analytically and numerically that topological textures in the charge density distribution in these crystals in the vicinity of charged defects strongly reduce energy required for current-carrying excitations. The theory quantitatively explains sharp insulator-metal transitions experimentally observed in RIQHE states. The insulator to metal transition in RIQHE emerges as a thermodynamic unbinding transition of topological charged defects.
We investigate the Hall conductance of a two-dimensional Chern insulator coupled to an environment causing gain and loss. Introducing a biorthogonal linear response theory, we show that sufficiently strong gain and loss lead to a characteristic non-analytical contribution to the Hall conductance. Near its onset, this contribution exhibits a universal power-law with a power 3/2 as a function of Dirac mass, chemical potential and gain strength. Our results pave the way for the study of non-Hermitian topology in electronic transport experiments.
The ferromagnet-topological insulator-ferromagnet (FM-TI-FM) junction exhibits thermal and electrical quantum Hall effects. The generated Hall voltage and transverse temperature gradient can be controlled by the directions of magnetizations in the FM leads, which inspires the use of FM-TI-FM junctions as electrical and as heat switches in spintronic devices. Thermal and electrical Hall coefficients are calculated as functions of the magnetization directions in ferromagnets and the spin-relaxation time in TI. Both the Hall voltage and the transverse temperature gradient decrease but are not com…
It is shown that the presence of matrix dipole moments induced by external electric fields can modify the Hall response in two dimensional Topological insulators. In the case of the Quantum Anomalous Hall effect the induced transverse currents acquire an extra term being proportional to the Hall conductance and the time derivative of the applied electric field. In the case of the Quantum Spin Hall effect both a spin and charge transverse currents appear simultaneously. In virtue of the bulk-edge correspondence the coupling between the chiral edge channels and the electromagnetic field changes …
We study the temperature dependence of spin Hall magnetoresistance (SMR) in antiferromagnetic insulator (AFI)/metal bilayer systems. We calculate the amplitude of the SMR signal by using a quantum Monte Carlo simulation and examine how the SMR depends on the amplitude of the spin, thickness of the AFI layer, and randomness of the exchange interactions. Our results for simple quantum spin models provide a useful starting point for understanding SMR measurements on atomic layers of magnetic compounds.
Interfacing topological insulators (TIs) with magnetic insulators (MIs) has been widely used to study the interaction between topological surface states and magnetism. Previous transport studies typically interpret the suppression of weak antilocalization or appearance of the anomalous Hall effect as signatures of magnetic proximity effect (MPE) imposed to TIs. Here, we report the observation of nonlinear planar Hall effect (NPHE) in Bi2Se3 films grown on MI thulium and yttrium iron garnet (TmIG and YIG) substrates, which is an order of magnitude larger than that in Bi2Se3 grown on nonmagnetic…
We numerically study disorder effects in Bernevig-Hughes-Zhang (BHZ) model, and find that Anderson transition of quantum spin-Hall insulator (QSHI) is determined by model parameters. The BHZ Hamiltonian is equivalent to two decoupled spin blocks that belong to the unitary class. In contrast to the common belief that a two-dimensional unitary system scales to an insulator except at certain critical points, we find, through calculations scaling properties of the localization length, level statistics, and participation ratio, that a possible exotic metallic phase emerges between a QSHI and a norm…
Direct transitions, driven by disorder, from several integral quantum Hall states to an insulator have been observed in experiment. This finding is enigmatic in light of a theoretical phase diagram, based on rather general considerations, that predicts a sequence of transitions in which the integer $n$ characterizing the Hall conductivity is reduced successively by unity, eventually going from $n=1$ into an insulator. In this work, we suggest that the direct transition occurs because, in certain parameter regime, the edge states of different Landau levels are strongly coupled and behave as a s…
We present the theoretical description for a class of experimental setups that measure quantum Hall coefficients in ferromagnet-topological insulator-ferromagnet (FM-TI-FM) junctions. We predict that varying the magnetization direction in ferromagnets, one can change the induced Hall voltage and transverse temperature gradient from the maximal values, corresponding to the quantized Hall coefficients, down to their complete suppression to zero. We provide detailed analysis of thermal and electrical Hall resistances as functions of the magnetization directions in ferromagnets, the spin-scatterin…
We study mesoscopic spin Hall effect on the surface of topological insulator with a step-function potential. The giant spin polarization induced by a transverse electric current is derived analytically by using McMillan method in the ballistic transport limit, which oscillates across the potential boundary with no confinement from the potential barrier due to the Klein paradox, and should be observable in spin resolved scanning tunneling microscope.
Silicene have been proposed to host multiple topological phases depending on the environmental parameters such as gated voltage and proximity induced exchange field. Two typical topological phase are quantum spin Hall phase and quantum anomalous Hall phase. We found that in the presence of antiferromagnetic exchange field and (or) gated voltage, the bilayer silicene host a topological phase that the Chern numbers of the two spin are different in both sign and magnitude, .i.e the anomalous Hall effects of the two spins are imbalanced. The topological phase is generated by triple band inversion …
We study the coupled dynamics of spin and charge currents in a two-dimensional electron gas in the transport diffusive regime. For systems with inversion symmetry there are established relations between the spin Hall effect, the anomalous Hall effect and the inverse spin Hall effect. However, in two-dimensional electron gases of semiconductors like GaAs, inversion symmetry is broken so that the standard arguments do not apply. We demonstrate that in the presence of a Rashba type of spin-orbit coupling (broken structural inversion symmetry) the anomalous Hall effect, the spin Hall and inverse s…
In two-dimensional anomalous Floquet insulators, non-Hermitian boundary state engineering can be used to completely separate chiral boundary states from bulk bands in the quasienergy spectrum. The topological properties of such spectrally separated boundary states are no longer restricted by the strict bulk-boundary correspondence of Hermitian systems. We show that this additional topological freedom enables one to faithfully transfer the topological properties of a boundary attached to a Floquet insulator to a non-Hermitian Floquet chain obtained by physically cutting off the boundary from th…
We present a theory of the anomalous Hall effect in ferromagnetic (Mn,III)V semiconductors. Our theory relates the anomalous Hall conductance of a homogeneous ferromagnet to the Berry phase acquired by a quasiparticle wavefunction upon traversing closed paths on the spin-split Fermi surface of a ferromagnetic state. It can be applied equally well to any itinerant electron ferromagnet. The quantitative agreement between our theory and experimental data in both (In,Mn)As and (Ga,Mn)As systems suggests that this disorder independent contribution to the anomalous Hall conductivity dominates in dil…
