One-dimensional topological insulator: a model for studying finite-size effects in topological insulator thin films

Abstract

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.

14 pages, total 6 panels in 4 captioned figures

References in corpus (5)

• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Finite-size energy gap in weak and strong topological insulators

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• Comparative study of Weyl semimetal, topological and Chern insulators: thin-film point of view
• Characterizing the weak topological properties: Berry phase point of view
• Coexistence of Strong and Weak Majorana Zero Modes in Anisotropic XY Spin Chain with Second-Neighbor Interaction
• Manipulating topological-insulator properties using quantum confinement
• Hinge Modes and Surface States in Second-Order Topological Three-Dimensional Quantum Hall Systems induced by Charge Density Modulation
• Effective model for massless Dirac electrons on a surface of weak topological insulators
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
• Emergent topology in thin films of nodal line semimetals
• Non-unique connection between bulk topological invariants and surface physics