Dimensional crossover of transport characteristics in topological insulator nanofilms

Abstract

We show how the two-dimensional (2D) topological insulator evolves, by stacking, into a strong or weak topological insulator with different topological indices, proposing a new conjecture that goes beyond an intuitive picture of the crossover from quantum spin Hall to the weak topological insulator. Studying the conductance under different boundary conditions, we demonstrate the existence of two conduction regimes in which conduction happens through either surface- or edge-conduction channels. We show that the two conduction regimes are complementary and exclusive. Conductance maps in the presence and absence of disorder are introduced, together with 2D ${\mathbb{Z}}_2$-index maps, describing the dimensional crossover of the conductance from the 2D to the 3D limit. Stacking layers is an effective way to invert the gap, an alternative to controlling the strength of spin-orbit coupling. The emerging quantum spin Hall insulator phase is not restricted to the case of odd numbers of layers.

14 pages, 8 figures, published version

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• Magnetic-field-induced topological phase transition in Fe-doped (Bi,Sb)${}_2$Se${}_3$ heterostructures
• Helicity-protected domain-wall magnetoresistance in ferromagnetic Weyl semimetal
• Application of Convolutional Neural Network to Quantum Percolation in Topological Insulators
• Comparative study of Weyl semimetal, topological and Chern insulators: thin-film point of view
• Emerging topological bound states in Haldane model zigzag nanoribbons
• Manipulating topological-insulator properties using quantum confinement
• Multi-terminal Conductance at the Surface of a Weyl Semimetal
• Ballistic transport in disordered Dirac and Weyl semimetals
• Ferromagnetic-electrodes-induced Hall effect in topological Dirac semimetals
• Origin of Robust ${\mathbb{Z}}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion
• Finite-size scaling analysis of the conductivity of Dirac electrons on a surface of disordered topological insulators
• Weak topological insulators with step edges: Subband engineering and its effect on electron transport
• Dimensional crossover of class D real-space topological invariants
• Non-unique connection between bulk topological invariants and surface physics