Atomically thin topological materials are attracting growing attention for their potential to radically transform classical and quantum electronic device concepts. Amongst them is the quantum spin Hall (QSH) insulator - a two-dimensional state of matter that arises from an interplay of topological band inversion and strong spin-orbit coupling, with large tunable bulk band gaps up to 800meV and gapless, one-dimensional edge states. Reviewing recent advances in materials science and engineering alongside theoretical description, this article surveys the QSH materials library with focus on their prospects for QSH-based device applications. In particular, this review discusses theoretical predictions of non-trivial superconducting pairing in the QSH state towards Majorana based topological quantum computing - the next frontier in QSH materials research.
We fabricate van der Waals heterostructure devices using few unit cell thick Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ for magnetotransport measurements. The superconducting transition temperature and carrier density in atomically thin samples can be maintained to close to that of the bulk samples. As in the bulk sample, the sign of the Hall conductivity is found to be opposite to the normal state near the transition temperature but with a drastic enlargement of the region of Hall sign reversal in the temperature-magnetic field phase diagram as the thickness of samples decreases. Quantitative analysis of …
Based on first-principles calculations and symmetry analysis, we predict atomically thin ($1-N$ layers) 2H group-VIB TMDs $MX_2$ ($M$ = Mo, W; $X$ = S, Se, Te) are large-gap higher-order topological crystalline insulators protected by $C_3$ rotation symmetry. We explicitly demonstrate the nontrivial topological indices and existence of the hallmark corner states with quantized fractional charge for these familiar TMDs with large bulk optical band gaps ($1.64-1.95$ eV for the monolayers), which would facilitate the experimental detection by STM. We find that the well-defined corner states exist…
The results of ultra-high vacuum low-temperature scanning-tunneling microscopy (STM) and spectroscopy (STS) of atomically clean (111) surface of the topological insulator Bi$_2$Se$_3$ are presented. We observed several types of new subsurface defects whose location and charge correspond to p-type conduction of grown crystals. The sign of the thermoelectric effect also indicates p-type conduction. STM and STS measurements demonstrate that the chemical potential is always located inside the bulk band gap. We also observed changes in the local density of states in the vicinity of the quintuple la…
The metal-insulator transition (MIT) is one of the remarkable electrical transport properties of atomically thin molybdenum disulphide (MoS2). Although the theory of electron-electron interactions has been used in modeling the MIT phenomena in MoS2, the underlying mechanism and detailed MIT process still remain largely unexplored. Here, we demonstrate that the vertical metal-insulator-semiconductor (MIS) heterostructures built from atomically thin MoS2 (monolayers and multilayers) are ideal capacitor structures for probing the electron states in MoS2. The vertical configuration of MIS heterost…
How to measure the optical conductivity of atomically thin crystals is an important but challenging issue due to the weak light-matter interaction at the atomic scale. Photonic spin Hall effect, as a fundamental physical effect in light-matter interaction, is extremely sensitive to the optical conductivity of atomically thin crystals. Here, we report a precision measurement of the optical conductivity of graphene, where the photonic spin Hall effect acts as a measurement pointer. By incorporating with the weak-value amplification technique, the optical conductivity of monolayer graphene taken …
Boosting the sensitivity of solid-state gas sensors by incorporating nanostructured materials as the active sensing element can be complicated by interfacial effects. Interfaces at nanoparticles, grains, or contacts may result in non-linear current-voltage response, high electrical resistance, and ultimately, electric noise that limits the sensor read-out. Here we report the possibility to prepare nominally one atom thin, electrically continuous metals, by straightforward physical vapor deposition on the carbon zero-layer grown epitaxially on silicon carbide. With platinum as the metal, its el…
The recent discovery of magnetism in atomically thin layers of van der Waals (vdW) crystals has created new opportunities for exploring magnetic phenomena in the two-dimensional (2D) limit. In most 2D magnets studied to date the c-axis is an easy axis, so that at zero applied field the polarization of each layer is perpendicular to the plane. Here, we demonstrate that atomically thin CrCl3 is a layered antiferromagnetic insulator with an easy-plane normal to the c-axis, that is the polarization is in the plane of each layer and has no preferred direction within it. Ligand field photoluminescen…
The interplay between band topology and magnetic order plays a key role in quantum states of matter. MnBi2Te4, a van der Waals magnet, has recently emerged as an exciting platform for exploring Chern insulator physics. Its layered antiferromagnetic order was predicted to enable even-odd layer-number dependent topological states, supported by promising edge transport measurements. Furthermore, it becomes a Chern insulator when all spins are aligned by an applied magnetic field. However, the evolution of the bulk electronic structure as the magnetic state is continuously tuned and its dependence…
Electrons hopping in two-dimensional honeycomb lattices possess a valley degree of freedom in addition to charge and spin. In the absence of inversion symmetry, these systems were predicted to exhibit opposite Hall effects for electrons from different valleys. Such valley Hall effects have been achieved only by extrinsic means, such as substrate coupling, dual gating, and light illuminating. Here, we report the first observation of intrinsic valley Hall transport without any extrinsic symmetry breaking in the non-centrosymmetric monolayer and trilayer MoS2, evidenced by considerable nonlocal r…
We report the growth of atomically smooth, single crystalline Bi2Se3 thin films on Si(111) by using molecular beam epitaxy. Scanning tunneling microscopy, low-energy electron diffraction, X-ray photoelectron emission spectroscopy and Raman spectroscopy were used to characterize the stoichiometry and crystallinity of the film. The film grows in a self-organized quintuple-layer by quintuple-layer mode, and atomically smooth film can be obtained with the thickness down to one quintuple-layer (~1nm).
A decade of intense research on two-dimensional (2D) atomic crystals has revealed that their properties can differ greatly from those of the parent compound. These differences are governed by changes in the band structure due to quantum confinement and are most profound if the underlying lattice symmetry changes. Here we report a high-quality 2D electron gas in few-layer InSe encapsulated in hexagonal boron nitride under an inert atmosphere. Carrier mobilities are found to exceed 1,000 and 10,000 cm2/Vs at room and liquid-helium temperatures, respectively, allowing the observation of the fully…
Spin-orbit coupling is a fundamental mechanism that connects the spin of a charge carrier with its momentum. Likewise, in the optical domain, a synthetic spin-orbit coupling is accessible, for instance, by engineering optical anisotropies in photonic materials. Both, akin, yield the possibility to create devices directly harnessing spin- and polarization as information carriers. Atomically thin layers of transition metal dichalcogenides provide a new material platform which promises intrinsic spin-valley Hall features both for free carriers, two-particle excitations (excitons), as well as for …
Despite topological protection and the absence of magnetic impurities, two-dimensional topological insulators display quantized conductance only in surprisingly short channels, which can be as short as 100 nm for atomically thin materials. We show that the combined action of short-range nonmagnetic impurities located near the edges and on site electron-electron interactions effectively creates noncollinear magnetic scatterers, and, hence, results in strong backscattering. The mechanism causes deviations from quantization even at zero temperature and for a modest strength of electron-electron i…
The recent discovery of magnetism in atomically thin layers of van der Waals crystals has created great opportunities for exploring light-matter interactions and magneto-optical phenomena in the two-dimensional limit. Optical and magneto-optical experiments have provided insights into these topics, revealing strong magnetic circular dichroism and giant Kerr signals in atomically thin ferromagnetic insulators. However, the nature of the giant magneto-optical responses and their microscopic mechanism remain unclear. Here, by performing first-principles GW and Bethe-Salpeter equation calculations…
A key feature of the topological surface state under a magnetic field is the presence of the zeroth Landau level at the zero energy. Nonetheless, it has been challenging to probe the zeroth Landau level due to large electron-hole puddles smearing its energy landscape. Here, by developing ultra-low-carrier density topological insulator Sb$_2$Te$_3$ films, we were able to reach an extreme quantum limit of the topological surface state and uncover a hidden phase at the zeroth Landau level. First, we discovered an unexpected quantum-Hall-to-insulator-transition near the zeroth Landau level. Then, …
We investigate the role of quantum fluctuations in topological quantum phase transitions of quantum spin Hall insulators and quantum anomalous Hall insulators. Employing the variational cluster approximation to obtain the single-particle Green's function of the interacting many-body system, we characterize different phases by direct calculation of the recently proposed topological order parameter for interacting systems. We pinpoint the influence of quantum fluctuations on the quantum spin Hall to Mott insulator transition in several models. Furthermore, we propose a general mechanism by which…
Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach …
The recently introduced classification of two-dimensional insulators in terms of topological crystalline invariants has been applied so far to "obstructed" atomic insulators characterized by a mismatch between the centers of the electronic Wannier functions and the ionic positions. We extend this notion to quantum spin Hall insulators in which the ground state cannot be described in terms of time-reversal symmetric localized Wannier functions. A system equivalent to graphene in all its relevant electronic and topological properties except for a real-space obstruction is identified and studied …
We report a proximity-driven large anomalous Hall effect in all-telluride heterostructures consisting of ferromagnetic insulator Cr2Ge2Te6 and topological insulator (Bi,Sb)2Te3. Despite small magnetization in the (Bi,Sb)2Te3 layer, the anomalous Hall conductivity reaches a large value of 0.2e2/h in accord with a ferromagnetic response of the Cr2Ge2Te6. The results show that the exchange coupling between the surface state of the topological insulator and the proximitized Cr2Ge2Te6 layer is effective and strong enough to open the sizable exchange gap in the surface state.
The chirality associated with broken time reversal symmetry in magnetically doped topological insulators has important implications to the quantum transport phenomena. Here we report the anomalous Hall effect studies in Mn- and Cr-doped Bi$_2$Te$_3$ topological insulators with varied thickness and doping content. By tracing the chirality of the Hall loops, we find that the Mn-type anomalous Hall effect with clockwise chirality is strengthened by the reduction of film thickness, which is opposite to that of the Cr-type anomalous Hall effect with counterclockwise chirality. We provide a phenomen…
We theoretically study the Josephson current in a superconductor/quantum anomalous Hall insulator/superconductor junction by using the lattice Green function technique. When an in-plane external Zeeman field is applied to the quantum anomalous Hall insulator, the Josephson current $J$ flows without a phase difference across the junction $θ$. The phase shift $φ$ appealing in the current-phase relationship $J\propto \sin(θ-φ$) is proportional to the amplitude of Zeeman fields and depends on the direction of Zeeman fields. A phenomenological analysis of the Andreev reflection processes explains t…
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.
The existence of conserved spin Hall currents is shown in a strongly correlated system without involving spin-orbit coupling. The spin Hall conductivity is determined by intrinsic bulk properties, which remains finite even when the charge resistivity diverges in strong magnetic fields at zero temperature. The state in the latter limit corresponds to a spin Hall insulator. Such a system is a doped Mott insulator described by the phase string theory, and spin Hall effect is predicted to coexist with the Nernst effect to characterize the intrinsic properties of the low-temperature pseudogap phase…
Quite generally, an insulator is theoretically defined by a vanishing conductivity tensor at the absolute zero of temperature. In classical insulators, such as band insulators, vanishing conductivities lead to diverging resistivities. In other insulators, in particular when a high magnetic field (B) is added, it is possible that while the magneto-resistance diverges, the Hall resistance remains finite, which is known as a Hall insulator. In this letter we demonstrate experimentally the existence of another, more exotic, insulator. This insulator, which terminates the quantum Hall effect series…
By breaking the time-reversal-symmetry in three-dimensional topological insulators with introduction of spontaneous magnetization or application of magnetic field, the surface states become gapped, leading to quantum anomalous Hall effect or quantum Hall effect, when the chemical potential locates inside the gap. Further breaking of inversion symmetry is possible by employing magnetic topological insulator heterostructures that host nondegenerate top and bottom surface states. Here, we demonstrate the tailored-material approach for the realization of robust quantum Hall states in the bilayer s…
An electric charge near the surface of a topological insulator induces an image magnetic monopole. Here, we show that if the topological insulator surface has a negative curvature, namely in the case of a semispherical cavity, the induced Hall current reverses its rotation as the electric charge crosses the semisphere geometric focus. Such a reversion is shown to be equivalent of inverting the charge of the image magnetic monopole. We also discuss upon the case of a semicylindrical cavity, where Hall current reversion appears to be feasible of probing in realistic experiments.
Recent theories predict dissipationless spin current induced by an electric field in doped semiconductors. Nevertheless, the charge current is still dissipative in these systems. In this work, we theoretically predict the dissipationless spin Hall effect, without any accompanying charge current, in some classes of band insulators, including zero-gap semiconductors such as HgTe and narrow-gap semiconductors such as PbTe. This effect is similar to the quantum Hall effect in that all the states below the gap contribute and there occurs no dissipation. However the spin Hall conductance is not quan…
In topological insulators, spin-orbit coupling and time-reversal symmetry combine to form a novel state of matter predicted to have exotic physical properties.
Fundamental research and technological applications of topological insulators are hindered by the rarity of materials exhibiting a robust topologically non-trivial phase, especially in two dimensions. Here, by means of extensive first-principles calculations, we propose a novel quantum spin Hall insulator with a sizeable band gap of $\sim$0.5 eV that is a monolayer of Jacutingaite, a naturally occurring layered mineral first discovered in 2008 in Brazil and recently synthesised. This system realises the paradigmatic Kane-Mele model for quantum spin Hall insulators in a potentially exfoliable t…
It is demonstrated that upon pulsed microwave excitation, the temporal behavior of a spin-wave induced inverse spin Hall voltage in a magnetic insulator-nonmagnetic metal structure is distinctly different from the temporal evolution of the directly excited spin-wave mode from which it originates. The difference in temporal behavior is attributed to the excitation of long-lived secondary spin-wave modes localized at the insulator-metal interface.
We study topological phases in Iridium (Ir) oxide superlattices of orthorhombic perovskite-type grown along the [001] crystallographic axis. Due to strong spin-orbit coupling of Ir 5d-orbitals and electronic correlation effects, Ir oxide bilayer superlattices display topological magnetic insulators exhibiting quantized anomalous Hall effects. Depending on stacking of two layers, we also found a valley Hall insulator with counter-propagating edge currents from two different valleys and a topological crystalline insulator with edge states protected by the crystal lattice symmetry. In a single la…
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…
The nature of a metal-insulator transition tuned by external gates in quantum Hall (QH) systems with point constrictions, as reported in recent experiments of Roddaro et al [1], is examined. We attribute this phenomenon to a splitting of the integer edge into conducting and insulating stripes, the latter wide enough to allow for the stability of the edge structure. Inter-channel impurity scattering and inter-channel Coulomb interactions do not destabilize this picture.
The Hall effect, the anomalous Hall effect and the spin Hall effect are fundamental transport processes in solids arising from the Lorentz force and the spin-orbit coupling respectively. The quantum versions of the Hall effect and the spin Hall effect have been discovered in recent years. However, the quantized anomalous Hall (QAH) effect has not yet been realized experimentally. In a QAH insulator, spontaneous magnetic moments and spin-orbit coupling combine to give rise to a topologically non-trivial electronic structure, leading to the quantized Hall effect without any external magnetic fie…
A mechanism for phonon Hall effect (PHE) in non-magnetic insulators under an external magnetic field is theoretically studied. PHE is known in (para)magnetic compounds, where the magnetic moments and spin-orbit interaction play an essential role. In sharp contrast, we here show that a non-zero Berry curvature of acoustic phonons is induced by an external magnetic field due to the correction to the adiabatic Born-Oppenheimer approximation. This results in the finite thermal Hall conductivity $κ_H$ in nonmagnetic band insulators. Our estimate of $κ_H$ for a simple model gives $κ_H \sim 1.0\times…
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 consider a four-terminal setup of a two-dimensional topological insulator (quantum spin Hall insulator) with local tunneling between the upper and lower edges. The edge modes are modeled as helical Luttinger liquids and the electron-electron interactions are taken into account exactly. Using perturbation theory in the tunneling, we derive the cumulant generating function for the inter-edge current. We show that different possible transport channels give rise to different signatures in the current noise and current cross-correlations, which could be exploited in experiments to elucidate the …
Quantum anomalous Hall (QAH) effect in magnetic topological insulator (TI) is a novel transport phenomenon in which the Hall resistance reaches the quantum plateau in the absence of external magnetic field. Recently, this exotic effect has been discovered experimentally in an ultrathin film of the Bi2Te3 family TI with spontaneous ferromagnetic (FM) order. An important question concerning the QAH state is whether it is simply a zero-magnetic-field version of the quantum Hall (QH) effect, or if there is new physics beyond the conventional paradigm. Here we report experimental investigations on …
Using the Chalker-Coddington network model as a drastically simplified, but universal model of integer quantum Hall physics, we investigate the plateau-to-insulator transition at strong magnetic field by means of a real-space renormalization approach. Our results suggest that for a fully quantum coherent situation, the quantized Hall insulator with R_H approx. h/e^2 is observed up to R_L ~25 h/e^2 when studying the most probable value of the distribution function P(R_H). Upon further increasing R_L ->\infty the Hall insulator with diverging Hall resistance R_H \propto R_L^kappa is seen. The cr…
We study the quantum Hall effect in the surface states of topological insulator in the presence of a perpendicular magnetic field in the framework of edge states. Motion of Dirac fermions will form descrete Landau levels, among which a fully saturated zero mode will have different behaviors near the boundary according to the sign of the effective mass for Dirac fermions. The Hall conductance is quantized to be n (n is an integer) in the unit of e^2/h for a positive mass, n+1 for a negative mass, and n+1/2 for massless fermions. In topological insulator the massive term to the Dirac fermions ca…
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.
The Dirac electrons occupying the surface states (SSs) of topological insulators (TIs) have been predicted to exhibit many exciting magneto-transport phenomena. Here we report on the first experimental observation of an unconventional planar Hall effect (PHE) and an electrically gate-tunable hysteretic planar magnetoresistance (PMR) in EuS/TI heterostructures, in which EuS is a ferromagnetic insulator (FMI) with an in-plane magnetization. In such exchange-coupled FMI/TI heterostructures, we find a significant (suppressed) PHE when the in-plane magnetic field is parallel (perpendicular) to the …
We investigate the algebraic structure of flat energy bands a partial filling of which may give rise to a fractional quantum anomalous Hall effect (or a fractional Chern insulator) and a fractional quantum spin Hall effect. Both effects arise in the case of a sufficiently flat energy band as well as a roughly flat and homogeneous Berry curvature, such that the global Chern number, which is a topological invariant, may be associated with a local non-commutative geometry. This geometry is similar to the more familiar situation of the fractional quantum Hall effect in two-dimensional electron sys…
Magneto-transport measurements are performed on two-dimensional GaAs electron systems to probe the quantum Hall (QH) effect at low magnetic fields. Oscillations following the Shubnikov-de Haas (SdH) formula are observed in the transition from the insulator to QH liquid when the observed almost temperature-independent Hall slope indicates insignificant interaction correction. Our study shows that the existence of SdH oscillations in such a transition can be understood based on the non-interacting model.
Based on a combination of $k \cdot p$ theory, band topology analysis and electronic structure calculations, we predict the (111) thin films of the SnTe class of three-dimensional (3D) topological crystalline insulators realize the quantum spin Hall phase in a wide range of thickness. The nontrivial topology originates from the inter-surface coupling of the topological surface states of TCI in the 3D limit. The inter-surface coupling changes sign and gives rise to topological phase transitions as a function of film thickness. Furthermore, this coupling can be strongly affected by an external el…
