Topological Insulator Slab Research Articles

Effect of surface states on scattering from a slab made of topological insulator material with rough interface

ABSTRACTUsing the perturbation theory (PT), reflected field both in specular and non specular directions from a slab made of topological insulator (TI) material with rough interface is studied. The specular reflections are described by zeroth order terms of the perturbation series while non specular reflections are associated with higher order terms. To describe the surface states on the TI, γ-model characterized by the surface admittance is utilized. It is observed that the co-polarized specular reflection increases for large values of surface admittance which results in vanishing transmission. The main objective is to pronounce distinctions between the results for a dielectric slab and TI slab. It is observed that the co polarized diffraction efficiency of the sinusoidal grating is enhanced for p-polarization as the surface admittance increases. Moreover, the scattering behavior of the TI slab with Gaussian rough interface as a function of surface admittance differs significantly from that of the dielectric slab.

Topological phase transition at the interface of a topological with a conventional insulator

We study the topological states which appear at the interface between a topological insulator (TI) and a conventional insulator (CI) using effective Hamiltonians which accurately describe the band structure of the Bi2Se3 family. Due to the hybridization between the TI and the CI states, the band-gap that appears in the interface Dirac cone decreases and ultimately vanishes by tuning the interface-hopping amplitude or by selecting a CI of appropriate band effective mass. More importantly, we find that a topologically trivial TI slab can be made non-trivial and vice-versa by tuning of such an interface-hopping amplitude or by tuning the CI band effective-mass; namely, a topological phase transition can be induced in such heterostructures indicated by the presence or absence of gapless linear edge modes. We discuss the relevance and realization of our results and conclusions in future experiments.

Van der Waals torque and force between anisotropic topological insulator slabs

We investigate the character of the van der Waals (vdW) torque and force between two coplanar and dielectrically anisotropic topological insulator (TI) slabs separated by a vacuum gap in the non-retardation regime, where the optic axes of the slabs are each perpendicular to the normal direction to the slab-gap interface and also generally differently oriented from each other. We find that in addition to the magnetoelectric coupling strength, the anisotropy can also influence the sign of the vdW force, viz., a repulsive vdW force can become attractive if the anistropy is increased sufficiently. In addition, the vdW force oscillates as a function of the angular difference between the optic axes of the TI slabs, being most repulsive/least attractive (least repulsive/most attractive) for angular differences that are integer (half-integer) multiples of $\pi$. Our third finding is that the vdW torque for TI slabs is generally weaker than that for ordinary dielectric slabs. Our work provides the first instance in which the vector potential appears in a calculation of the vdW interaction for which the limit is non-retarded or static.

有限厚度拓扑绝缘体平板附近原子的自发辐射特性

有限厚度拓扑绝缘体平板附近原子的自发辐射特性

Identification of trivial and nontrivial insulators: Enhanced lateral shift in topological insulator-based cavity

We theoretically exploit the parallel and perpendicular lateral shifts of topological insulator slab by using stationary-phase approach. Compared with ordinary insulators, the perpendicular lateral shift of topological insulator exhibits unusual features, which provides a promising approach to differentiate these two phases. Furthermore, it is found that the perpendicular lateral shift of topological insulator is a surface-sensitive parameter and can be used to extract its surface characteristics. Additionally, a topological insulator-based cavity structure is proposed to remarkably enhance the lateral shift due to the localized defect mode, which enables better observation of the lateral shift in the experiment.

Induced spectral gap and pairing correlations from superconducting proximity effect

We theoretically consider superconducting proximity effect, using the Bogoliubov-de Gennes theory, in heterostructure sandwich-type geometries involving a normal s-wave superconductor and a non-superconducting material with the proximity effect being driven by Cooper pairs tunneling from the superconducting slab to the non-superconducting slab. Applications of the superconducting proximity effect may rely on an induced spectral gap or induced pairing correlations without any spectral gap. We clarify that in a non-superconducting material the induced spectral gap and pairing correlations are independent physical quantities arising from the proximity effect. This is a crucial issue in proposals to create topological superconductivity through the proximity effect. Heterostructures of 3D topological insulator (TI) slabs on conventional s-wave superconductor (SC) substrates provide a platform, with proximity-induced topological superconductivity expected to be observed on the "naked" top surface of a thin TI slab. We theoretically study the induced superconducting gap on this naked surface. In addition, we compare against the induced spectral gap in heterostructures of SC with a normal metal or a semiconductor with strong spin orbit coupling and a Zeeman splitting potential (another platform for topological superconductivity). We find that for any model for the non-SC metal (including metallic TI) the induced spectral gap on the naked surface decays as $L^{-3}$ as the thickness ($L$) of the non-SC slab is increased in contrast to the slower $1/L$ decay of the pairing correlations. Our distinction between proximity-induced spectral gap (with its faster spatial decay) and pairing correlation (with its slower spatial decay) has important implications for the currently active search for topological superconductivity and Majorana fermions in various superconducting heterostructures.

Carrier transport in Bi2Se3 topological insulator slab

Electron transport in Bi2Se3 topological insulator slabs is investigated in the thermal activation regime (>50K) both in the absence (ballistic) and presence of weak and strong acoustic phonon scattering using the non-equilibrium Green function approach. Resistance of the slab is simulated as a function of temperature for a range of slab thicknesses and effective doping in order to gain a handle on how various factors interact and compete to determine the overall resistance of the slab. If the Bi2Se3 slab is biased at the Dirac point, resistance is found to display an insulating trend even for strong electron–phonon coupling strength. However, when the Fermi-level lies close to the bulk conduction band (heavy electron doping), phonon scattering can dominate and result in a metallic behavior, although the insulating trend is retained in the limit of ballistic transport. Depending on values of the operating parameters, the temperature dependence of the slab is found to exhibit a remarkably complex behavior, which ranges from insulating to metallic, and includes cases where the resistance exhibits a local maximum, much like the contradictory behaviors seen experimentally in various experiments.

Quantum anomalous Hall effect and a nontrivial spin-texture in ultra-thin films of magnetic topological insulators

We study the evolution of quantum anomalous Hall (QAH) effect for a Z2 topological insulator (TI) thin films in a proximity induced magnetic phase by a realistic layered k·p model with interlayer coupling. We examine three different magnetic configurations in which ferromagnetic (FM) layer(s) is added either from one side (FM-TI), from both sides (FM-TI-FM), or homogeneously distributed (magnetically doped) in a TI slab. We map out the thickness-dependent topological phase diagram under various experimental conditions. The critical magnetic exchange energy for the emergence of QAH effect in the latter two cases decreases monotonically with increasing number of quintuple layers (QLs), while it becomes surprisingly independent of the film thickness in the former case. The gap size of the emergent QAH insulator depends on the non-magnetic “parent” gap of the TI thin film and is tuned by the FM exchange energy, opening a versatile possibility to achieve room-temperature QAH insulator in various topological nanomaterials. Finally, we find that the emergent spin-texture in the QAH effect is very unconventional, non-“hedgehog” type; and it exhibits a chiral out-of-plane spin-flip texture within the same valence band which is reminiscent of dynamical “skyrmion” pattern, except our results are in the momentum space.

Effect of band-alignment operation on carrier transport in Bi2Se3 topological insulator.

Band-alignment induced current modulation in Bi2Se3 three-dimensional topological insulator slab has been investigated by quantum transport simulations for three different device designs, one for purely lateral transport and other two with vertical transport. Non-Equilibrium Green Function formalism has been deployed to understand the transport mechanism in band-alignment devices to appraise the possibility of a 3D-TI based resonant device. A resonance condition is observed when the Dirac-points (bands) are aligned. This results in the maximum current at resonance for the design with only lateral transport. However, current ratio between resonant and non-resonant condition is found to be relatively small and strong temperature dependence is also noticed. The other two designs with vertical transport have degraded transfer characteristics, although from state-of-art literature they are expected to manifest nearly an ideal resonance peak. The physical insights for these observations have been posited along with the suggestions for attaining close to an ideal operation for the first design, which we also suggest for the pursuit in the future for spintronic oscillators and analog multipliers based on band-alignment induced resonance.

Optical properties of magnetically doped ultrathin topological insulator slabs

Starting from a three dimensional Hamiltonian, we study the optical properties of ultra-thin topological insulator slabs for which the coupling between Dirac fermions on opposite surfaces results in two degenerated gapped hyperbolic bands. The gap is a threshold for the optical absorption and translates in a peak in the imaginary part of the optical conductivity. An exchange field applied perpendicular to the slab splits the degenerated hyperbolic bands and a double step structure come out in the optical absorption, whereas a double peak structure appears in the imaginary part of the longitudinal optical conductivity. The exchange field breaks time-reversal symmetry and for exchange fields larger than the surfaces coupling gap, the zero frequency Hall conductivity is quantized to $e^2/h$. This result implies large values of the Kerr and Faraday rotation angles. In ultra-thin slabs, the absence of light multiple scattering and bulk conductivity, makes the Kerr and Faradays angles to remain rather large in a wide range of frequencies.

Giant topological magnetoelectric and optical Hall effects for a topological insulator as a defect in photonic crystals

A system with a topological insulator slab sandwiched by two one-dimensional photonic crystals as a defect is investigated. A giant topological magnetoelectric effect is proposed which is characterized by two resonant peaks with half-unit transmissions and rich polarization behaviors in the photonic band gap. We also predict a giant optical Hall effect in our system, in which the transverse shift of the transmitted light could be 1000 times larger than the wavelength. These effects are purely from the $\ensuremath{\Theta}$-domain walls at the topological insulator interfaces and could be observed easily.

Casimir force between topological insulator slabs

The Casimir force between two finite-thick topological insulator slabs and its dependence on the gap size between the slabs are investigated in detail. Two typical substrate materials including semi-infinite vacuum and silicon are used in the study, in which the Casimir force can always change from attractive to repulsive when the gap size decreases. The gap width at transition is a function of the slab thickness and also depends strongly on the electric permittivity and topological magnetoelectric polarizability of the slabs. In particular, in the absence of a substrate, this width increases with decreasing slab thickness and for thin slabs with large internal and external topological magnetoelectric polarizability the Casimir force is always repulsive where the surface topological magnetoelectric effect of the slabs plays a dominant role. In the presence of a semi-infinite silicon substrate, however, the attractive role of the silicon substrate becomes increasingly important, and thus the transition gap decreases with decreasing thickness of the slab. The characteristic features of the Casimir force may be detected experimentally through exploring its gradient with a certain dynamical method.

Interaction and disorder effects in three-dimensional topological insulator thin films

A theory of combined interference and interaction effects on the diffusive transport properties of 3D topological insulator surface states is developed. We focus on a slab geometry (characteristic for most experiments) and show that interactions between the top and bottom surfaces are important at not too high temperatures. We treat the general case of different surfaces (different carrier densities, uncorrelated disorder, arbitrary dielectric environment, etc.). In order to access the low-energy behavior of the system we renormalize the interacting diffusive sigma model in the one loop approximation. It is shown that intersurface interaction is relevant in the renormalization group (RG) sense and the case of decoupled surfaces is therefore unstable. An analysis of the emerging RG flow yields a rather rich behavior. We discuss realistic experimental scenarios and predict a characteristic non-monotonic temperature dependence of the conductivity. In the infrared (low-temperature) limit, the systems flows into a metallic fixed point. At this point, even initially different surfaces have the same transport properties. Investigating topological effects, we present a local expression of the $\mathbb Z_2$ theta term in the sigma model by first deriving the Wess-Zumino-Witten theory for class DIII by means of non-abelian bosonization and then breaking the symmetry down to AII. This allows us to study a response of the system to an external electromagnetic field. Further, we discuss the difference between the system of Dirac fermions on the top and bottom surfaces of a topological insulator slab and its non-topological counterpart in a double-well structure with strong spin-orbit interaction.

Thermal coherence properties of topological insulator slabs in time-reversal symmetry breaking fields

We first develop a general Green's-function method for the slab geometry, which can handle quite complex conversions between the different polarized radiation modes. Then by using the method, we study the near field thermal coherence properties of a slab of ${Z}_{2}$ topological insulator (TI) with a finite thickness. Under a strong enough external magnetic field, the gapless helical Dirac fermions on the TI surfaces can acquire an energy gap larger than the photon energy of the radiation field at the Dirac point. This gapped surface states can couple strongly with the waveguide modes in the bulk of the TI slab, which thus induces an electromagnetic resonance. Exactly due to the resonance, the coherence properties of the thermal radiation field can be modified dramatically. For ${Z}_{2}$ topological insulators, the parameter regime with the surface Hall conductivity half integer quantized is unique. We demonstrated that within the parameter regime, for a TI slab of a proper thickness, the thermal radiation energy density can be enhanced very much, and the coherence length of the thermal radiation field can be as long as twice that of SiC.

Superconductive proximity in a topological insulator slab and excitations bound to an axial vortex

We consider the proximity effect in a topological insulator (TI) sandwiched between two conventional superconductors by comparing $s$-wave spin singlet superconducting pairing correlations and odd-parity triplet pairing correlations with a zero spin component orthogonal to the slab (``polar'' phase). A superconducting gap opens in the Dirac dispersion of the surface states existing at the interfaces. An axial vortex is included, piercing the slab along the normal to the interfaces with the superconductors. It is known that, when proximity is $s$-wave, quasiparticles in the gap are Majorana bound states, localized at opposite interfaces. We report the full expression for the quantum field associated to the midgap neutral fermions, as derived in the two-orbital band model for the TI. When proximity involves odd-parity pairing, midgap modes are charged surface Andreev bound states, and they originate from interfacial circular states of definite chirality, centered at the vortex singularity and decaying in the TI film with oscillations. When the chemical potential is moved away from midgap, extended states along the vortex axis are also allowed. Their orbital structure depends on the symmetry of the bulk band from where the quasiparticle level splits off.

Anomalous Josephson Current via Majorana Bound States in Topological Insulators

We propose a setup involving Majorana bound states (MBS) hosted by a vortex on a superconducting surface of a 3D topological insulator (TI). We consider a narrow channel drilled across a TI slab with both sides covered by s-wave superconductor. In the presence of a vortex pinned to such a channel, it acts as a ballistic nanowire connecting the superconducting surfaces, with a pair of MBS localized in it. The energies of the MBS possess a 4π-periodic dependence on the superconductive phase difference φ between the surfaces. It results in the appearance of an anomalous term in the current-phase relation I(a)(φ) for the supercurrent flowing along the channel between the superconductive surfaces. We have calculated the shape of the 4π-periodic function I(a)(φ), as well as the dependence of its amplitude on temperature and system parameters.