Bulk Of Topological Insulator Research Articles

Voltage control of the quantum scattering time in InAs/GaSb/InAs trilayer quantum wells

We study the evolution of the quantum scattering time by gate voltage training in the topological insulator (TI) based on InAs/GaSb/InAs trilayer quantum wells. Depending on the minimal gate voltage applied during a gate voltage sweep cycle, the quantum scattering time can be improved by 50% from 0.08 ps to 0.12 ps albeit the transport scattering time is rather constant around 1.0 ps. The ratio of the quantum scattering time versus transport scattering time scales linearly with the charge carrier density and varies from 10 to 30, indicating Coulombic scattering as the dominant scattering mechanism. Our findings may enable to improve bulk and edge properties of TIs based on InAs/GaSb quantum well heterostructures solely by means of an electric field rather than temperature which opens the paths towards their application for macroscopic devices.

Particle–hole asymmetry and quantum confinement effects on the magneto-optical response of topological insulator thin-films

Intrinsically broken symmetries in the bulk of topological insulators (TIs) are manifested in their surface states. Despite particle–hole asymmetry in TIs, it has often been assumed that their surface states are characterized by a particle–hole symmetric Dirac energy dispersion. In this work, we demonstrate that the effect of particle–hole asymmetry is essential to correctly describe the energy spectrum and the magneto-optical response in TIs thin-films. In thin-films of TIs with a substantial degree of particle–hole symmetry breaking, such as Sb2Te3, the longitudinal optical conductivity displays absorption peaks arising from optical transitions between bulk and surface Landau levels for low photon energies. The transition energies between the bulk and surface Landau levels exhibit clearly discernable signatures from those between surface Landau levels due to their distinct magnetic field dependence. Bulk contributions to the magneto-optical conductivity in a TI thin-film are enhanced via one type of doping while being suppressed by the other. This asymmetric dependence on the type of doping aids in revealing the particle–hole asymmetry in TI thin-films.

Temperature dependence of spin—orbit torque-driven magnetization switching in in situ grown Bi2Te3/MnTe heterostructures

We report the temperature dependence of the spin–orbit torque (SOT) in the in situ grown Bi2Te3/MnTe heterostructures by molecular beam epitaxy. By appropriately designing the film stack, robust ferromagnetic order with high Curie temperature and strong perpendicular magnetic anisotropy is established in the MnTe layer. Meanwhile, the sharp hetero-interface warrants highly efficient spin current injection from the conductive topological insulator (TI) channel. Accordingly, SOT-driven magnetization switching is observed up to 90 K with the critical current density within the 106 A⋅cm−2 range. More importantly, the temperature-dependent harmonic measurement data can be divided into two categories, namely, the spin Hall effect of the TI bulk states gives rise to a relatively small spin Hall angle in the high-temperature region, whereas the spin-momentum locking nature of the interfacial Dirac fermions leads to the enhancement of the SOT strength once the topological surface states become the dominant conduction channel at deep cryogenic temperatures. Our results offer direct evidence of the underlying mechanism that determines the SOT efficiency and may set up a suitable platform to realize TI-based spin–orbit applications toward room temperature.

Ultrafast evolution of bulk, surface and surface resonance states in photoexcited hbox {Bi}_{2}hbox {Te}_{3}

We use circular dichroism (CD) in time- and angle-resolved photoemission spectroscopy (trARPES) to measure the femtosecond charge dynamics in the topological insulator (TI) hbox {Bi}_{2}hbox {Te}_{3}. We detect clear CD signatures from topological surface states (TSS) and surface resonance (SR) states. In time-resolved measurements, independently from the pump polarization or intensity, the CD shows a dynamics which provides access to the unexplored electronic evolution in unoccupied states of hbox {Bi}_{2}hbox {Te}_{3}. In particular, we are able to disentangle the unpolarized electron dynamics in the bulk states from the spin-textured TSS and SR states on the femtosecond timescale. Our study demonstrates that photoexcitation mainly involves the bulk states and is followed by sub-picosecond transport to the surface. This provides essential details on intra- and interband scattering in the relaxation process of TSS and SR states. Our results reveal the significant role of SRs in the subtle ultrafast interaction between bulk and surface states of TIs.

Spherical topological insulator nanoparticles: Quantum size effects and optical transitions

We have investigated the interplay between band inversion and size quantization in spherically shaped nanoparticles made from topological-insulator (TI) materials. A general theoretical framework is developed based on a versatile continuum-model description of the TI bulk band structure and the assumption of a hard-wall mass confinement. Analytical results are obtained for the wave functions of single-electron energy eigenstates and the matrix elements for optical transitions between them. As expected from spherical symmetry, quantized levels in TI nanoparticles can be labeled by quantum numbers $j$ and $m=-j, -j+1, \dots, j$ for total angular momentum and its projection on an arbitrary axis. The fact that TIs are narrow-gap materials, where the charge-carrier dynamics is described by a type of two-flavor Dirac model, requires $j$ to assume half-integer values and also causes a doubling of energy-level degeneracy where two different classes of states are distinguished by being parity eigenstates with eigenvalues $(-1)^{j\mp 1/2}$. The existence of energy eigenstates having the same $j$ but opposite parity enables optical transitions where $j$ is conserved, in addition to those adhering to the familiar selection rule where $j$ changes by $\pm 1$. All optical transitions satisfy the usual selection rule $\Delta m = 0, \pm 1$. We treat intra- and inter-band optical transitions on the same footing and establish ways for observing unusual quantum-size effects in TI nanoparticles, including oscillatory dependences of the band gap and of transition amplitudes on the nanoparticle radius. Our theory also provides a unified perspective on multi-band models for charge carriers in semiconductors and Dirac fermions from elementary-particle physics.

Observation of multichannel quantum coherent transport and electron-electron interaction in Bi2Te3 single crystal

The bulk of topological insulators is relatively unexplored, due to the excess contribution of conduction from native defects. Here, we investigate the bulk conduction in a Bi2Te3 crystal having a reduced number of defect states. Our results reveal the presence of three transport regimes which are dominated by thermal activation across the bulk band gap, defect state charge conduction, and quantum coherent transport. The low temperature conductance and magnetoconductance reveal the presence of multichannel two-dimensional quantum coherent transport in the bulk. The number of channels is of the order of quintuple layers, signifying each quintuple layer as a single transport channel. These transport channels exhibit a two-dimensional electron-electron interaction effect causing electron dephasing, whereas the conduction from defect states exhibits a three-dimensional electron-electron interaction effect.

Topological Insulator Film Growth by Molecular Beam Epitaxy: A Review

In this article, we will review recent progress in the growth of topological insulator (TI) thin films by molecular beam epitaxy (MBE). The materials we focus on are the V2-VI3 family of TIs. These materials are ideally bulk insulating with surface states housing Dirac excitations which are spin-momentum locked. These surface states are interesting for fundamental physics studies (such as the search for Majorana fermions) as well as applications in spintronics and other fields. However, the majority of TI films and bulk crystals exhibit significant bulk conductivity, which obscures these states. In addition, many TI films have a high defect density. This review will discuss progress in reducing the bulk conductivity while increasing the crystal quality. We will describe in detail how growth parameters, substrate choice, and growth technique influence the resulting TI film properties for binary and ternary TIs. We then give an overview of progress in the growth of TI heterostructures. We close by discussing the bright future for TI film growth by MBE.

Localization and interaction effects of epitaxial Bi2Se3 bulk states in two-dimensional limit

Quantum interference effects and electron-electron interactions are found to play an important role in two-dimensional (2D) bulk transport of topological insulator (TI) thin films, which were previously considered as 2D electron gas (2DEG) and explained on basis of Hikami-Larkin-Nagaoka formula and Lee-Ramakrishnan theory. The distinct massive Dirac-type band structure of the TI bulk state gives rise to quantum corrections to conductivity due to interference and interaction effects, which are quite different from that of a 2DEG. We interpret the experimental findings employing Lu-Shen theory particularly derived for the TI system in the 2D limit. The surface and the bulk conductions are identified based on slopes of logarithmic temperature-dependent conductivities with magnetic fields. The perpendicular field magnetoresistance is analyzed considering suppression of weak antilocalization/localization of the surface/bulk electrons by the applied field. We propose corresponding theoretical models to explain the parallel and tilted field magnetoresistance. The effect of the band structure is found to be crucial for an accurate explanation of the magnetotransport results in the TI thin film.

Spin Orbit Coupling Gap and Indirect Gap in Strain-Tuned Topological Insulator-Antimonene.

Recently, searching large-bulk band gap topological insulator (TI) is under intensive study. Through k·P theory and first-principles calculations analysis on antimonene, we find that α-phase antimonene can be tuned to a 2D TI under an in-plane anisotropic strain and the magnitude of direct bulk band gap (SOC gap) depends on the strength of spin-orbit coupling (SOC) which is strain-dependent. As the band inversion of this TI accompanies with an indirect band gap, the TI bulk band gap is the indirect band gap, not the SOC gap. SOC gap can be enhanced by increasing strain, whereas the indirect band gap can be closed by increasing strain, such that large bulk band gap are forbidden. With the k·P theory analysis on antimonene, we know how to avoid such an indirect band gap. In case of indirect band gap avoided, the SOC gap could become the bulk band gap of a TI which can be enhanced by strain. Thus our theoretical analysis can help searching large bulk band gap TI.

Spurious and realistic solutions for the quantum spin Hall edge states in InAs/GaSb/AlSb quantum wells

A solution of the 4 × 4 k · p Hamiltonian for the quantum spin Hall (QSH) edge states in ideal semiconductor topological insulator (TI) quantum wells (QWs) was recently demonstrated by the author using standard boundary conditions for the wave function and its derivative, in order to address unphysical behavior associated with open boundary conditions (Klipstein 2015 Phys. Rev. B 91 035310). For HgTe/CdTe QWs which have strong s-p hybridization, there are two non-degenerate solutions in each spin direction with a finite amplitude at the edge, one of which was shown to be spurious. For the case of weakly hybridized InAs/GaSb/AlSb QWs, the solutions near the zone center are degenerate, and the question is now settled of which solution is spurious. The physical solutions for the ideal QW are then used as the basis for a perturbation treatment of the edge state dispersions in realistic QWs, where interface, bulk and structural asymmetries are also present. Interactions are included with more remote states than considered previously, as required for a consistent treatment of the TI bulk states, where a large difference exists in the spin splittings of the conduction and valence band edges. The asymmetry perturbations induce only minor changes to the edge state dispersions, which no longer merge smoothly with the bulk band extrema.

Nonequilibrium spin texture within a thin layer below the surface of current-carrying topological insulatorBi2Se3: A first-principles quantum transport study

We predict that unpolarized charge current injected into a ballistic thin film of prototypical topological insulator (TI) Bi$_2$Se$_3$ will generate a {\it noncollinear spin texture} $\mathbf{S}(\mathbf{r})$ on its surface. Furthermore, the nonequilibrium spin texture will extend into $\simeq 2$ nm thick layer below the TI surfaces due to penetration of evanescent wavefunctions from the metallic surfaces into the bulk of TI. Averaging $\mathbf{S}(\mathbf{r})$ over few \AA{} along the longitudinal direction defined by the current flow reveals large component pointing in the transverse direction. In addition, we find an order of magnitude smaller out-of-plane component when the direction of injected current with respect to Bi and Se atoms probes the largest hexagonal warping of the Dirac-cone dispersion on TI surface. Our analysis is based on an extension of the nonequilibrium Green functions combined with density functional theory (NEGF+DFT) to situations involving noncollinear spins and spin-orbit coupling. We also demonstrate how DFT calculations with properly optimized local orbital basis set can precisely match putatively more accurate calculations with plane-wave basis set for the supercell of Bi$_2$Se$_3$.

Engineering Dirac electrons emergent on the surface of a topological insulator

The concept of the topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin–orbit coupled materials, some classes of nodal superconductors, superfluid 3He, etc. From a technological point of view, TIs are expected to serve as platforms for realizing dissipationless transport in a non-superconducting context. The TI exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context we contrast the cases of weak and strong TIs. We study the robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new research perspective in the field.

Spin-spin interaction in the bulk of topological insulators

We apply mean-field theory and Hirsch-Fye quantum Monte Carlo method to study the spin-spin interaction in the bulk of three-dimensional topological insulators. We find that the spin-spin interaction has three different components: the longitudinal, the transverse and the transverse Dzyaloshinskii-Moriya-like terms. When the Fermi energy is located in the bulk gap of topological insulators, the spin-spin interaction decays exponentially due to Bloembergen-Rowland interaction. The longitudinal correlation is antiferromagnetic and the transverse correlations are ferromagnetic. When the chemical potential is in the conduction or valence band, the spin-spin interaction follows power law decay, and isotropic ferromagnetic interaction dominates in short separation limit.

Anderson impurity in the bulk of topological insulators

When an Anderson impurity is immersed in the bulk of a topological insulator that has an ``inverted-Mexican-hat'' band dispersion, a Kondo resonant peak appears simultaneously with an in-gap bound state. The latter generates another spin state thereby screening the Kondo effect. Using a weak-coupling RG scheme, it is shown that the system exhibits complex crossover behavior between different symmetry configurations and may evolve into a self-screened Kondo or an $\mathrm{SO}(n)\phantom{\rule{0.28em}{0ex}}(n=3,4)$ low-energy fixed point. Experimental consequences of these scenarios are pointed out.

Weak localization effects as evidence for bulk quantization in Bi2Se3thin films

Strong spin-orbit coupling in topological insulators results in the ubiquitously observed weak antilocalization feature in their magnetoresistance. Here we present magnetoresistance measurements in ultra thin films of the topological insulator Bi_2Se_3, and show that in the 2D quantum limit, in which the topological insulator bulk becomes quantized, an additional negative magnetoresistance feature appears. Detailed analysis associates this feature with weak localization of the quantized bulk channels, providing thus evidence for this quantization. Examination of the dephasing fields at different temperatures indicates different scattering mechanism in the bulk vs the surface states.

Impurity scattering in the bulk of topological insulators

We study in this paper time-reversal $\ensuremath{\delta}$-impurity scattering effects in the bulk of topological insulators (TI) in two and three dimensions. Specifically we consider how impurity scattering strength is affected by the bulk band structure of topological insulators. An interesting band inversion effect associated with the change of the system from ordinary to topological insulator is pointed out. Experimental consequences of our findings are discussed.

Inverse quantum spin Hall effect generated by spin pumping from precessing magnetization into a graphene-based two-dimensional topological insulator

We present a multiterminal nanostructure for electrical probing of the quantum spin Hall effect (QSHE) in two-dimensional (2D) topological insulators (TIs). The device consists of a ferromagnetic (FM) island with precessing magnetization that pumps (in the absence of any bias voltage) pure spin current symmetrically into the left and right adjacent 2D TIs modeled as graphene nanoribbons with the intrinsic spin-orbit (SO) coupling. In the reference frame rotating with magnetization, the device is mapped onto a dc circuit with twice as many terminals whose effectively half-metallic ferromagnetic electrodes are biased by the frequency $\ensuremath{\hbar}\ensuremath{\omega}/e$ of the microwave radiation driving the magnetization precession at the ferromagnetic resonance conditions. The QSH regime of the six-terminal $\text{TI}|\text{FM}|\text{TI}$ nanodevice, attached to two longitudinal and four transverse normal metal electrodes, is characterized by the SO-coupling-induced energy gap, chiral spin-filtered edge states within finite length TI regions, and quantized spin Hall conductance when longitudinal bias voltage is applied, despite the presence of the FM island. The same unbiased device, but with precessing magnetization of the central FM island, blocks completely pumping of total spin and charge currents into the longitudinal electrodes while generating dc transverse charge Hall currents. Although these transverse charge currents are not quantized, their induction together with zero longitudinal charge current is a unique electrical response of TIs to pumped pure spin current that cannot be mimicked by SO coupled but topologically trivial systems. In the corresponding two-terminal inhomogeneous $\text{TI}|\text{FM}|\text{TI}$ nanostructures, we image spatial profiles of local spin and charge currents within TIs which illustrate transport confined to chiral spin-filtered edges states while revealing concomitantly the existence of interfacial spin and charge currents flowing around $\text{TI}\ensuremath{\mid}\text{FM}$ interfaces and penetrating into the bulk of TIs over some short distance.