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Register a new userThin films of a three-dimensional topological insulator in a strong magnetic field: a microscopic study
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The response of thin films of Bi$_2$Se$_3$ to a strong perpendicular magnetic field is investigated by performing magnetic bandstructure calculations for a realistic multi-band tight-binding model. Several crucial features of Landau quantization in a realistic three-dimensional topological insulator are revealed. The $n=0$ Landau level is absent in ultra-thin films, in agreement with experiment. In films with a crossover thickness of five quintuple layers, there is a signature of the $n=0$ level, whose overall trend as a function of magnetic field matches the established low-energy effective-model result. Importantly, we find a field-dependent splitting and a strong spin-polarization of the $n=0$ level which can be measured experimentally at reasonable field strengths. Our calculations show mixing between the surface and bulk Landau levels which causes the character of levels to evolve with magnetic field.
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We report on a study of an ultrathin topological insulator film with hybridization between the top and bottom surfaces, placed in a quantizing perpendicular magnetic field. We calculate the full Landau level spectrum of the film as a function of the applied magnetic field and the magnitude of the hybridization matrix element, taking into account both the orbital and the Zeeman spin splitting effects of the field. For an undoped film, we find a quantum phase transition between a state with a zero Hall conductivity and a state with a quantized Hall conductivity equal to $e^2/h$, as a function of the magnitude of the applied field. The transition is driven by the competition between the Zeeman and the hybridization energies.
As a model for describing finite-size effects in topological insulator thin films, we study a one-dimensional (1D) effective model of a topological insulator (TI). Using this effective 1D model, we reveal the precise correspondence between the spatial profile of the surface wave function, and the dependence of the finite-size energy gap on the thickness (Lx) of the film. We solve the boundary problem both in the semi-infinite and slab geometries to show that the Lx-dependence of the size gap is a direct measure of the amplitude of the surface wave function at the depth of x=Lx+1 [here, the boundary condition is chosen such that the wave function vanishes at x=0]. Depending on the parameters, the edge state function shows either a damped oscillation (in the TI-oscillatory region of FIG. 2, or becomes overdamped (ibid., in the TI-overdamped phase). In the original 3D bulk TI, an asymmetry in the spectrum of valence and conduction bands is omnipresent. Here, we demonstrate by tuning this asymmetry one can drive a crossover from the TI-oscillatory to the TI-overdamped phase.
We report that the finite thickness of three-dimensional topological insulator (TI) thin films produces an observable magnetoresistance (MR) in phase coherent transport in parallel magnetic fields. The MR data of Bi2Se3 and (Bi,Sb)2Te3 thin films are compared with existing theoretical models of parallel field magnetotransport. We conclude that the TI thin films bring parallel field transport into a unique regime in which the coupling of surface states to bulk and to opposite surfaces is indispensable for understanding the observed MR. The {beta} parameter extracted from parallel field MR can in principle provide a figure of merit for searching TI compounds with more insulating bulk than existing materials.
We use the bulk Hamiltonian for a three-dimensional topological insulator such as $rm Bi_2 Se_3$ to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based on a lattice discretization of the bulk Hamiltonian. We find that the application of a potential along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering across the edge is studied as a function of the edge potential. We show that a magnetic field in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states.
Low energy excitation of surface states of a three-dimensional topological insulator (3DTI) can be described by Dirac fermions. By using a tight-binding model, the transport properties of the surface states in a uniform magnetic field is investigated. It is found that chiral surface states parallel to the magnetic field are responsible to the quantized Hall (QH) conductance $(2n+1)frac{e^2}{h}$ multiplied by the number of Dirac cones. Due to the two-dimension (2D) nature of the surface states, the robustness of the QH conductance against impurity scattering is determined by the oddness and evenness of the Dirac cone number. An experimental setup for transport measurement is proposed.
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