Spin-Hall insulator

First-principles investigation of possible room-temperature topological insulators in monolayers

A Quantum Spin Hall (QSH) insulator with a large bulk band gap and tunable topological properties is crucial for both fundamental research and practical application. Chemical function-alization has been proposed as an effective route to realize the QSH effect. Using the ABINIT package, we have investigated the properties of (1) TlP, the functionalized monolayers TlPX2 (X = F, Cl, Br, I); (2) TlAs, the functionalized monolayers TlAsX2 (X = F, Cl, Br, I), and (3) GaGeTe, InGeTe, and InSnTe systems. The topological nature is verified by the calculation of the Z2 topo-logical invariant. We discovered TlPF2, TlPCl2, TlPBr2, TlPI2, TlAs, TlAsF2, TlAsCl2, TlAsBr2, and TlAsI2 were promising 2D TIs with bulk band gaps as large as 0.21 eV. Each monolayer was suitable for room-temperature application, and show great potential for their future applications in quantum computers, nanoelectronics, and spintronics.

Two-Dimensional Metal-Organic Frameworks Towards Spintronics

The intrinsic properties of predesignable topologies and tunable electronic structures, coupled with the increase of electrical conductivity, make two-dimensional metal-organic frameworks (2D MOFs) highly prospective candidates for next-generation electronic/spintronic devices. In this Minireview, we present an outline of the design principles of 2D MOF-based spintronics materials. Then, we highlight the spin-transport properties of 2D MOF-based organic spin valves (OSVs) as a notable achievement in the progress of 2D MOFs for spintronics devices. After that, we discuss the potential for spin manipulation in 2D MOFs with bipolar magnetic semiconductor (BMS) properties as a promising field for future research. Finally, we provide a brief summary and outlook to encourage the development of novel 2D MOFs for spintronics applications.

Spin polarization in quantum point contact based on wurtzite topological quantum well

Manipulating spin polarization in wide-gap wurtzite semiconductors is crucial for the development of high-temperature spintronics applications. A topological insulator revealed recently in wurtzite quantum wells (QWs) provides a platform to mediate spin-polarized transport through the polarization field-driven topological edges and large Rashba spin-orbit coupling (SOC). Here, we propose a spin-polarized device in a quantum point contact (QPC) structure based on ZnO/CdO wurtzite topological QWs. The results show that the QPC width can sufficiently control the lateral spin-orbit coupling (SOC) as well as the band gap of the edge states through the quantum size effect. As a result, the spin-polarized conductance exhibits oscillation due to the spin precession, which can be controlled by adjusting the voltage imposed on the split gate. The QPC-induced large spin splitting is highly nonlinear and becomes strong close to the gap. The spin splitting of the edge states will be suppressed for QPC widths greater than 50 nm, and thus lead to an extremely long spin precession length. This QPC width-dependent lateral SOC effect provides an emerging electrical approach to manipulate spin-polarized electron transport in topological wurtzite systems.

Influence of the physical properties of the layered oxyselenides Bi2YO4Cu2Se2 through Ni doping

We have synthesized a series of Ni-doped layered oxyselenides Bi2YO4Cu2-xNixSe2 (0 ≤ x ≤ 0.4). The crystal structure and physical properties were studied through X-ray diffraction, and electric and thermo transport measurements. We also performed DFT calculations to study the electric structure of the designed Bi2YO4Ni2Se2, which is similar to that of KNi2Se2.

Efficient Time-Domain Approach for Linear Response Functions

We derive the general Kubo formula in a form that solely utilizes the time evolution of displacement operators. The derivation is based on the decomposition of the linear response function into its time-symmetric and time-antisymmetric parts. We relate this form to the well-known fluctuation-dissipation formula and discuss theoretical and numerical aspects of it. The approach is illustrated with an analytical example for magnetic resonance as well as a numerical example where we analyze the electrical conductivity tensor and the Chern insulating state of the disordered Haldane model. We introduce a highly efficient time-domain approach that describes the quantum dynamics of the resistivity of this model with an at least 1000-fold better performance in comparison to existing time-evolution schemes.

Anomalous circular photogalvanic effect in p-GaAs

The anomalous circular photogalvanic effect (ACPGE) is observed in p-GaAs with a thickness of 2 μm at room temperature, in which circularly polarized light is used to inject spin-polarized carriers and the spin diffusion can generate a macroscopic detectable charge current due to the inverse spin Hall effect. The normalized ACPGE signals show first increasing and then decreasing with increasing the doping concentration. The role of the doping impurities is discussed by both extrinsic and intrinsic models, and both can well explain the variation of ACPGE with the doping concentration.

Bulk spin conductivity of three-dimensional topological insulators

We study the spin conductivity of the bulk states of three-dimensional topological insulators within Kubo formalism. Spin Hall effect is the generation of the spin current that is perpendicular to the applied voltage. In the case of a three-dimensional topological insulator, applied voltage along x direction generates transverse spin currents along y and z directions with comparable values. We found that finite non-universal value of the spin conductivity exists in the gapped region due to the inversion of bands. Contribution to the spin conductivity from the vertex corrections enhances the spin conductivity from the filled states. These findings explain large spin conductivity that has been observed in topological insulators.

Phonon Angular Momentum Hall Effect

The spin Hall effect is the transverse flow of the electron spin in response to an external electric field. Similarly, the temperature gradient in magnets can drive a transverse flow of the magnon spin, which provides a thermal alternative for spin manipulation. Recently, phonon angular momentum (PAM), the angular momentum of atoms resulting from their orbital motion around their equilibrium positions, has garnered attention as a quantity analogous to the magnon spin. Here, we report that the temperature gradient generally induces a transverse flow of PAM, which we term the phonon angular momentum Hall effect (PAMHE). The PAMHE arises whenever there are transverse and longitudinal acoustic phonons, and it is therefore ubiquitous in condensed matter systems. As a consequence of the PAMHE, PAM accumulates at the crystal edges. When the atoms in the crystal carry a non-zero Born effective charge, the edge PAM induces edge magnetization, which can be observed through optical measurement.

Critical Spin Fluctuation Mechanism for the Spin Hall Effect

We propose mechanisms for the spin Hall effect in metallic systems arising from the coupling between conduction electrons and local magnetic moments that are dynamically fluctuating. Both a side-jump-type mechanism and a skew-scattering-type mechanism are considered. In either case, dynamical spin fluctuation gives rise to a nontrivial temperature dependence in the spin Hall conductivity. This leads to the enhancement in the spin Hall conductivity at nonzero temperatures near the ferromagnetic instability. The proposed mechanisms could be observed in 4d or 5d metallic compounds.

Cu2Te-Ag2Te lateral topological insulator heterojunction: stability and properties

Different from most of the two-dimensional (2D) topological insulators (TIs) with small bulk band gaps, 2D TIs of Cu₂Te and Ag₂Te have been found to exhibit sizeable bulk gaps with potentials for device applications in room-temperature. Here we have further explored the stability and electronic properties of a lateral heterojunction consisting of Cu₂Te and Ag₂Te. We have found that this heterojunction has buckled geometrical configuration that is dynamically stable, and it is a TI as identified by calculating the Z ₂ topological invariant and the edge states. The band gap of the lateral heterojunction is between those of pristine Cu₂Te and Ag₂Te sheets, and it can be effectively tuned by varying the relative width of the two ribbons in this heterojunction.

Strain-induced nonlinear spin Hall effect in topological Dirac semimetal

We show that an electric field applied to a strained topological Dirac semimetal, such as Na₃Bi and Cd₃As₂, induces a spin Hall current that is quadratic in the electric field. By regarding the strain as an effective "axial magnetic field" for the Dirac electrons, we investigate the electron and spin transport semiclassically in terms of the chiral kinetic theory. The nonlinear spin Hall effect arises as the cross effect between the regular Hall effect driven by the axial magnetic field and the anomalous Hall effect coming from the momentum-space topology. It provides an efficient way to generate a fully spin-polarized and rectified spin current out of an alternating electric field, which is sufficiently large and can be directly tuned by the gate voltage and the strain.

Intrinsic Spin and Orbital Hall Effects from Orbital Texture

We show theoretically that both the intrinsic spin Hall effect (SHE) and orbital Hall effect (OHE) can arise in centrosymmetric systems through momentum-space orbital texture, which is ubiquitous even in centrosymmetric systems unlike spin texture. The OHE occurs even without spin-orbit coupling (SOC) and is converted into the SHE through SOC. The resulting spin Hall conductivity is large (comparable to that of Pt) but depends on the SOC strength in a nonmonotonic way. This mechanism is stable against orbital quenching. This work suggests a path for an ongoing search for materials with stronger SHE. It also calls for experimental efforts to probe orbital degrees of freedom in the OHE and SHE. Possible ways for experimental detection are briefly discussed.

One-dimensional quantum matter: gold-induced nanowires on semiconductor surfaces

Interacting electrons confined to only one spatial dimension display a wide range of unusual many-body quantum phenomena, ranging from Peierls instabilities to the breakdown of the canonical Fermi liquid paradigm to even unusual spin phenomena. The underlying physics is not only of tremendous fundamental interest, but may also have bearing on device functionality in future micro- and nanoelectronics with lateral extensions reaching the atomic limit. Metallic adatoms deposited on semiconductor surfaces may form self-assembled atomic nanowires, thus representing highly interesting and well-controlled solid-state realizations of such 1D quantum systems. Here we review experimental and theoretical investigations on a few selected prototypical nanowire surface systems, specifically Ge(0 0 1)-Au and Si(hhk)-Au, and the search for 1D quantum states in them. We summarize the current state of research and identify open questions and issues.

Topological phases in double layers of bismuthene and antimonene

Two-dimensional topological insulators show great promise for spintronic applications. Much attention has been placed on single atomic or molecular layers, such as bismuthene. The selections of such materials are, however, limited. To broaden the base of candidate materials with desirable properties for applications, we report herein an exploration of the physics of double layers of bismuthene and antimonene. The electronic structure of a film depends on the number of layers, and it can be modified by epitaxial strain, by changing the effective spin-orbit coupling strength, and by the manner in which the layers are geometrically stacked. First-principles calculations for the double layers reveal a number of phases, including topological insulators, topological semimetals, Dirac semimetals, trivial semimetals, and trivial insulators. Their phase boundaries and the stability of the phases are investigated. The results illustrate a rich pattern of phases that can be realized by tuning lattice strain and effective spin-orbit coupling.

Enhancement of the Bulk Photovoltaic Effect in Topological Insulators

We investigate the shift current bulk photovoltaic response of materials close to a band inversion topological phase transition. We find that the bulk photocurrent reverses direction across the band inversion transition, and that its magnitude is enhanced in the vicinity of the phase transition. These results are demonstrated with first principles density functional theory calculations of BiTeI and CsPbI_{3} under hydrostatic pressure, and explained with an analytical model, suggesting that this phenomenon remains robust across disparate material systems.

Topological phases in two-dimensional materials: a review

Topological phases with insulating bulk and gapless surface or edge modes have attracted intensive attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this review, we mainly focus on recent progress in the engineering of topologically nontrivial phases (such as [Formula: see text] topological insulators, quantum anomalous Hall effects, quantum valley Hall effects etc) in two-dimensional systems, including quantum wells, atomic crystal layers of elements from group III to group VII, and the transition metal compounds.

Spin generation via bulk spin current in three-dimensional topological insulators

To date, spin generation in three-dimensional topological insulators is primarily modelled as a single-surface phenomenon, attributed to the momentum-spin locking on each individual surface. In this article, we propose a mechanism of spin generation where the role of the insulating yet topologically non-trivial bulk becomes explicit: an external electric field creates a transverse pure spin current through the bulk of a three-dimensional topological insulator, which transports spins between the top and bottom surfaces. Under sufficiently high surface disorder, the spin relaxation time can be extended via the Dyakonov–Perel mechanism. Consequently, both the spin generation efficiency and surface conductivity are largely enhanced. Numerical simulation confirms that this spin generation mechanism originates from the unique topological connection of the top and bottom surfaces and is absent in other two-dimensional systems such as graphene, even though they possess a similar Dirac cone-type dispersion.

Future spintronic devices may exploit topological insulators, bulk-insulating materials possessing conductive surface states with orthogonally-locked electronic spin and momentum. Here, the authors propose a mechanism by which bulk spin currents drive surface spin accumulation in such a material.

Light-Induced Exciton Spin Hall Effect in van der Waals Heterostructures

We propose a light-induced spin Hall effect for interlayer exciton gas in monolayer MoSe2-WSe2 van der Waals heterostructure. By applying two infrared, spatially varying laser beams coupled to the exciton internal states, a spin-dependent gauge potential on the exciton center-of-mass motion is induced. This gauge potential deflects excitons in different spin states towards opposite directions, leading to a finite spin current but vanishing mass current. In the Hall bar geometry, the spin-dependent deflection gives rise to spin-dependent chiral edge states with spin-velocity locking. The spin current and chiral edge states of the excitons can be detected by spatially resolved photoluminescence spectroscopy.

Odd-parity magnetoresistance in pyrochlore iridate thin films with broken time-reversal symmetry

A new class of materials termed topological insulators have been intensively investigated due to their unique Dirac surface state carrying dissipationless edge spin currents. Recently, it has been theoretically proposed that the three dimensional analogue of this type of band structure, the Weyl Semimetal phase, is materialized in pyrochlore oxides with strong spin-orbit coupling, accompanied by all-in-all-out spin ordering. Here, we report on the fabrication and magnetotransport of Eu₂Ir₂O₇ single crystalline thin films. We reveal that one of the two degenerate all-in-all-out domain structures, which are connected by time-reversal operation, can be selectively formed by the polarity of the cooling magnetic field. Once formed, the domain is robust against an oppositely polarised magnetic field, as evidenced by an unusual odd field dependent term in the magnetoresistance and an anomalous term in the Hall resistance. Our findings pave the way for exploring the predicted novel quantum transport phenomenon at the surfaces/interfaces or magnetic domain walls of pyrochlore iridates.

Strain-induced metal-semimetal transition of BeB2 monolayer

The Dirac point and cones make some two-dimensional materials (e.g., graphene, silicone and graphyne) exhibit ballistic charge transport and enormously high carrier mobilities.

Inducing a Lifshitz transition by extrinsic doping of surface bands in the topological crystalline insulator Pb1-xSnxSe

The narrow gap semiconductor Pb1-xSnxSe was investigated for topologically protected surface states in its rocksalt structural phase for x=0.45, 0.23, 0.15, and 0. Angle-resolved photoelectron spectroscopy of intrinsically p-doped samples showed a clear indication of two Dirac cones, eccentric about the time-reversal invariant point X¯ of the surface Brillouin zone for all but the x=0 sample. Adsorption of alkalies gradually filled the surface bands with electrons, driving the x>0 topological crystalline insulator systems through Lifshitz transitions, and from a holelike to electronlike Fermi surface. The electron-doped bands in x>0 samples exhibited the full configuration of the Dirac cones, also confirming electron-hole symmetry of the surface bands.

Ferromagnetism and topological surface states of manganese doped Bi2Te3: insights from density-functional calculations

Based on first-principles calculations, the electronic, magnetic, and topological characters of manganese (Mn) doped topological insulator Bi2Te3 were investigated. The Mn substitutionally doped Bi2Te3, where Mn atoms tend to be uniformly distributed, was shown to be p-type ferromagnetic, arising from hole-mediated Ruderman-Kittel-Kasuya-Yosida interaction. Mn doping leads to an intrinsic band splitting at Γ point, which is substantially different from that of nonmagnetic dopant. The topological surface state of Bi2Te3 is indeed gapped by Mn doping; however, the bulk conductance limits the appearance of an insulating state. Moreover, the n-type doping behavior of Bi2Te3 is derived from Mn entering into the van der Waals gap of Bi2Te3.

Anisotropy of spin relaxation and transverse transport in metals

Using first-principles methods we explore the anisotropy of the spin relaxation and transverse transport properties in bulk metals with respect to the real-space direction of the spin-quantization axis in paramagnets or of the spontaneous magnetization in ferromagnets. Owing to the presence of the spin-orbit coupling the orbital and spin character of the Bloch states depends sensitively on the orientation of the spins relative to the crystal axes. This leads to drastic changes in quantities which rely on interband mixing induced by the spin-orbit interaction. The anisotropy is particularly striking for quantities which exhibit spiky and irregular distributions in the Brillouin zone, such as the spin-mixing parameter or the Berry curvature of the electronic states. We demonstrate this for three cases: (i) the Elliott-Yafet spin-relaxation mechanism in paramagnets with structural inversion symmetry; (ii) the intrinsic anomalous Hall effect in ferromagnets; and (iii) the spin Hall effect in paramagnets. We discuss the consequences of the pronounced anisotropic behavior displayed by these properties for spin-polarized transport applications.

Realization of spin gapless semiconductors: the Heusler compound Mn2CoAl

Recent studies have reported an interesting class of semiconductor materials that bridge the gap between semiconductors and half-metallic ferromagnets. These materials, called spin gapless semiconductors, exhibit a band gap in one of the spin channels and a zero band gap in the other and thus allow for tunable spin transport. Here, we report the first experimental verification of the spin gapless magnetic semiconductor Mn(2)CoAl, an inverse Heusler compound with a Curie temperature of 720 K and a magnetic moment of 2 μ(B). Below 300 K, the compound exhibits nearly temperature-independent conductivity, very low, temperature-independent carrier concentration, and a vanishing Seebeck coefficient. The anomalous Hall effect is comparatively low, which is explained by the symmetry properties of the Berry curvature. Mn(2) CoAl is not only suitable material for room temperature semiconductor spintronics, the robust spin polarization of the spin gapless semiconductors makes it very promising material for spintronics in general.

Insulating behavior in ultrathin bismuth selenide field effect transistors

Ultrathin (approximately three quintuple layer) field-effect transistors (FETs) of topological insulator Bi(2)Se(3) are prepared by mechanical exfoliation on 300 nm SiO(2)/Si susbtrates. Temperature- and gate-voltage-dependent conductance measurements show that ultrathin Bi(2)Se(3) FETs are n-type and have a clear OFF state at negative gate voltage, with activated temperature-dependent conductance and energy barriers up to 250 meV.

Observation of intrinsic inverse spin Hall effect

We report observation of intrinsic inverse spin Hall effect in undoped GaAs multiple quantum wells with a sample temperature of 10 K. A transient ballistic pure spin current is injected by a pair of laser pulses through quantum interference. By time resolving the dynamics of the pure spin current, the momentum relaxation time is deduced, which sets the lower limit of the scattering time between electrons and holes. The transverse charge current generated by the pure spin current via the inverse spin Hall effect is simultaneously resolved. We find that the charge current is generated well before the first electron-hole scattering event. Generation of the transverse current in the scattering-free ballistic transport regime provides unambiguous evidence for the intrinsic inverse spin Hall effect.

Non-Abelian topological order in s-wave superfluids of ultracold fermionic atoms

It is proposed that in s-wave superfluids of cold fermionic atoms with laser-field-generated effective spin-orbit interactions, a topological phase with gapless edge states and Majorana fermion quasiparticles obeying non-Abelian statistics is realized in the case with a large Zeeman magnetic field. Our scenario provides a promising approach to the realization of quantum computation based on the manipulation of non-Abelian anyons via an s-wave Feshbach resonance.

Tunneling between edge states in a quantum spin Hall system

We analyze a quantum spin Hall device with a point contact connecting two of its edges. The contact supports a net spin tunneling current that can be probed experimentally via a two-terminal resistance measurement. We find that the low-bias tunneling current and the differential conductance exhibit scaling with voltage and temperature that depend nonlinearly on the strength of the electron-electron interaction.

Mott insulators in the strong spin-orbit coupling limit: from Heisenberg to a quantum compass and Kitaev models

We study the magnetic interactions in Mott-Hubbard systems with partially filled t_{2g} levels and with strong spin-orbit coupling. The latter entangles the spin and orbital spaces, and leads to a rich variety of the low energy Hamiltonians that extrapolate from the Heisenberg to a quantum compass model depending on the lattice geometry. This gives way to "engineer" in such Mott insulators an exactly solvable spin model by Kitaev relevant for quantum computation. We, finally, explain "weak" ferromagnetism, with an anomalously large ferromagnetic moment, in Sr2IrO4.

Giant intrinsic spin and orbital hall effects in Sr2MO4 (M=Ru, Rh, Mo)

We investigate the intrinsic spin Hall conductivity (SHC) and the d-orbital Hall conductivity (OHC) in metallic d-electron systems, by focusing on the t2g-orbital tight-binding model for Sr2MO4 (M=Ru, Rh, Mo). The conductivities obtained are one or 2 orders of magnitude larger than predicted values for p-type semiconductors with approximately 5% hole doping. The origin of these giant Hall effects is the "effective Aharonov-Bohm phase" that is induced by the d-atomic angular momentum in connection with the spin-orbit interaction and the interorbital hopping integrals. The huge SHC and OHC generated by this mechanism are expected to be ubiquitous in multiorbital transition metal compounds, which opens the possibility of realizing spintronics as well as "orbitronics" devices.

Intrinsic spin Hall effect in platinum: first-principles calculations

Spin Hall effect (SHE) is studied with first-principles relativistic band calculations for platinum, which is one of the most important materials for metallic SHE and spintronics. We find that intrinsic spin Hall conductivity (SHC) is as large as approximately 2000(variant Planck's over 2 pi/e)(Omega cm)(-1) at low temperature and decreases down to approximately 200(variant Planck's over 2 pi/e)(Omega cm)(-1) at room temperature. It is due to the resonant contribution from the spin-orbit splitting of the doubly degenerated d bands at high-symmetry L and X points near the Fermi level. By modeling these near degeneracies by an effective Hamiltonian, we show that SHC has a peak near the Fermi energy and that the vertex correction due to impurity scattering vanishes. We therefore argue that the large SHE observed experimentally in platinum is of intrinsic nature.

Quantum Spin Hall Insulator State in HgTe Quantum Wells

Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nanometers, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d > 6.3 nanometers), the nominally insulating regime showed a plateau of residual conductance close to 2e(2)/h, where e is the electron charge and h is Planck's constant. The residual conductance was independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance was destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nanometers, was also independently determined from the magnetic field-induced insulator-to-metal transition. These observations provide experimental evidence of the quantum spin Hall effect.

Generalized Stern-Gerlach effect for chiral molecules

The Stern-Gerlach effect is well known as spin-dependent splitting of a beam of atoms with magnetic moments by a magnetic-field gradient. Here, we show that an induced gauge potential may lead to a similar effect for chiral molecules. In the presence of three inhomogeneous light fields, the center of mass of a three-level chiral molecule is subject to an optically induced gauge potential, and the internal dynamics of the molecule can be described as an adiabatic evolution in the reduced pseudospin subspace of the two lowest energy levels. We demonstrate numerically that such an induced gauge potential can lead to observable pseudospin-dependent and chirality-dependent generalized Stern-Gerlach effects for mixed left- and right-handed chiral molecules under realistic conditions.

Current and strain-induced spin polarization in InGaN/GaN superlattices

The lateral current-induced spin polarization in InGaN/GaN superlattices (SLs) without an applied magnetic field is reported. The fact that the sign of the nonequilibrium spin changes as the current reverses and is opposite for the two edges provides a clear signature for the spin Hall effect. In addition, it is discovered that the spin Hall effect can be strongly manipulated by the internal strains. A theoretical work has also been developed to understand the observed strain-induced spin polarization. Our result paves an alternative way for the generation of spin polarized current.

Localization in a quantum spin Hall system

The localization problem of electronic states in a two-dimensional quantum spin Hall system (that is, a symplectic ensemble with topological term) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent nu for the divergence of the localization length is estimated as nu congruent with 1.6, which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. Our analysis strongly suggests a different universality class related to the topology of the pertinent system.

Optically induced spin-Hall effect in atoms

We propose an optical means to realize the spin-Hall effect (SHE) in a neutral atomic system by coupling the internal spin states of atoms to radiation. The interaction between the external optical fields and the atoms creates effective magnetic fields that act in opposite directions on "electrically" neutral atoms with opposite spin polarizations. This effect leads to a Landau level structure for each spin orientation in direct analogy with the familiar SHE in semiconductors. The conservation and topological properties of the spin current, and the creation of a pure spin current are discussed.

Quantum spin Hall effect and topological phase transition in HgTe quantum wells

We show that the quantum spin Hall (QSH) effect, a state of matter with topological properties distinct from those of conventional insulators, can be realized in mercury telluride-cadmium telluride semiconductor quantum wells. When the thickness of the quantum well is varied, the electronic state changes from a normal to an "inverted" type at a critical thickness d(c). We show that this transition is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. We also discuss methods for experimental detection of the QSH effect.

Quantum spin Hall effect and enhanced magnetic response by spin-orbit coupling

We show that the spin-Hall conductivity in insulators is related to a magnetic susceptibility representing the strength of the spin-orbit coupling. We use this relationship as a guiding principle to search real materials showing quantum spin-Hall effect. As a result, we theoretically predict that two-dimensional bismuth will show the quantum spin-Hall effect, both by calculating the helical edge states, and by showing the nontriviality of the Z2 topological number, and propose possible experiments.

Helical liquid and the edge of quantum spin Hall systems

The edge states of the recently proposed quantum spin Hall systems constitute a new symmetry class of one-dimensional liquids dubbed the "helical liquid," where the spin orientation is determined by the direction of electron motion. We prove a no-go theorem which states that a helical liquid with an odd number of components cannot be constructed in a purely 1D lattice system. In a helical liquid with an odd number of components, a uniform gap in the ground state can appear when the time-reversal symmetry is spontaneously broken by interactions. On the other hand, a correlated two-particle backscattering term by an impurity can become relevant while keeping the time-reversal invariance.

Spin Hall effect in doped semiconductor structures

In this Letter we present a microscopic theory of the extrinsic spin Hall effect based on the diagrammatic perturbation theory. Side-jump and skew-scattering contributions are explicitly taken into account to calculate the spin Hall conductivity, and we show that their effects scale as sigma(xy)SJ/sigma(xy)SS approximately (h/tau)/epsilonF, with tau being the transport relaxation time. Motivated by recent experimental work we apply our theory to n- and p-doped 3D and 2D GaAs structures, obtaining sigma(s)/sigma(c) approximately 10(-3)-10(-4), where sigma(s(c)) is the spin Hall (charge) conductivity, which is in reasonable agreement with the recent experimental results of Kato et al. [Science 306, 1910 (2004)] in n-doped 3D GaAs system.

Quantum spin Hall effect in graphene

We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are nonchiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed.

Sign changes of intrinsic spin Hall effect in semiconductors and simple metals: first-principles calculations

First-principles calculations are applied to study spin Hall effect in semiconductors and simple metals. We found that intrinsic spin Hall conductivity (ISHC) in realistic materials shows rich sign changes, which may be used to distinguish the effect from the extrinsic one. The calculated ISHC in n-doped GaAs can be well compared with experiment, and it differs from the sign obtained from the extrinsic effect. On the other hand, the ISHC in W and Au, which shows opposite sign, respectively, is robust and not sensitive to the disorder.

Z2 topological order and the quantum spin Hall effect

The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel Z2 topological invariant, which distinguishes it from an ordinary insulator. The Z2 classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the Z2 order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multiband and interacting systems.