From the Fractional Quantum Hall Effect States on a torus with filling factor nu = 1/p, p odd, we found that for small values of nu such states describe triangular Wigner crystals which are stable configurations. Therefore, the insulator phase of the two-dimensional electron system can be described with the same wave function that the liquid phase, and the incompressible liquid freezes (or the Wigner crystal melts) without any quantum transition between states, thus the system phase changes by means of a direct transition. We found at least one stable configuration of a Wigner crystal with F = 3 electrons for cell and we investigate the behavior of the crystal when the lengths ratio Ly/Lx changes.
We propose a realization of a quantum Hall effect (QHE) in a second-order topological insulator (SOTI) in three dimensions (3D), which is mediated by hinge states on a torus surface. It results from the nontrivial interplay of the material structure, Zeeman effect, and the surface curvature. In contrast to the conventional 2D- and 3D-QHE, we show that the 3D-SOTI QHE is not affected by orbital effects of the applied magnetic field and exists in the presence of a Zeeman term only, induced e.g. by magnetic doping. To explain the 3D-SOTI QHE, we analyze the boundary charge for a 3D-SOTI and estab…
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.
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 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.
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.
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…
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…
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…
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.
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…
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 …
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…
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…
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…
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…
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…
In this article we consider the chiral Hall effect due to topologically protected kink states formed in topological insulators at boundaries between domains with differing topological invariants. Such systems include the surfaces of three dimensional topological insulators magnetically doped or in proximity with ferromagnets, as well as certain two dimensional topological insulators. We analyze the equilibrium charge current along the domain wall and show that it is equal to the sum of counter-propagating equilibrium currents flowing along external boundaries of the domains. In addition, we al…
The fabrication of bismuthene on top of SiC paved the way for substrate engineering of room temperature quantum spin Hall insulators made of group V atoms. We perform large-scale quantum transport calculations in these 2d materials to analyse the rich phenomenology that arises from the interplay between topology, disorder, valley and spin degrees of freedom. For this purpose, we consider a minimal multi-orbital real-space tight-binding hamiltonian and use a Chebyshev polynomial expansion technique. We discuss how the quantum spin Hall states are affected by disorder, sublattice resolved potent…
The anomalous Hall effect is caused by magnetic textures such as skyrmions. We derive an analytical formula of the Hall conductivity on the surface of a topological insulator up to third order in magnetization, $\boldsymbol{M}(\boldsymbol{x})$, based on a perturbative approach. We identify the magnetic textures that contribute to the Hall conductivity up to third order in magnetization and second order in spatial differentiation. We treat magnetization as a perturbation to calculate the Hall conductivity for each magnetic texture based on the linear response theory. Furthermore, we estimate th…
The search of novel topological phases, such as the quantum anomalous Hall insulator (QAHI) or the axion insulator, has motivated different schemes to introduce magnetism into topological insulators. One scheme is to introduce ferromagnetic dopants in topological insulators. However, it is generally challenging and requires carefully engineered growth/heterostructures or relatively low temperatures to observe the QAHI due to issues such as the added disorder with ferromagnetic dopants. Another promising scheme is using the magnetic proximity effect with a magnetic insulator to magnetize the to…
