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A Pedagogic Review on Designing Model Topological Insulators

Das, Tanmoy (2016) A Pedagogic Review on Designing Model Topological Insulators. In: JOURNAL OF THE INDIAN INSTITUTE OF SCIENCE, 96 (2). pp. 77-105.

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Official URL: https://arxiv.org/abs/1604.07546

Abstract

Following the centuries old concept of the quantization of flux through a Gaussian curvature (Euler characteristic) and its successive dispersal into various condensed matter properties such as quantum Hall effect, and topological invariants, we can establish a simple and fairly universal understanding of various modern topological insulators (TIs). Formation of a periodic lattice (which is a non-trivial Gaussian curvature) of `cyclotron orbits' with applied magnetic field, or `chiral orbits' with fictitious `momentum space magnetic field' (Berry curvature) guarantees its flux quantization, and thus integer quantum Hall (IQH), and quantum spin-Hall (QSH) insulators, respectively, occur. The bulk-boundary correspondence associated with all classes of TIs dictates that some sort of pumping or polarization of a `quantity' at the boundary must be associated with the flux quantization or topological invariant in the bulk. Unlike charge or spin accumulations at the edge for IQH and QSH states, the time-reversal (TR) invariant Z(2) TI class pumps a mathematical quantity called `TR polarization' to the surface. This requires that the valence electron's wavefunction (say, psi(up arrow)(k)) switches to its TR conjugate (psi(dagger)(down arrow)(-k)) odd number of times in half of the Brillouin zone. These two universal features can be considered as `targets' to design and predict various TIs. For example, we demonstrate that when two adjacent atomic chains or layers are assembled with opposite spin-orbit coupling (SOC), serving as the TR partner to each other, the system naturally becomes a Z(2) TI. This review delivers a holistic overview on various concepts, computational schemes, and engineering principles of TIs.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the INDIAN INST SCIENCE, INDIAN INST SCIENCE, BANGALORE 560012, INDIA
Department/Centre: Division of Physical & Mathematical Sciences > Physics
Depositing User: Id for Latest eprints
Date Deposited: 23 Sep 2016 05:47
Last Modified: 23 Sep 2016 05:47
URI: http://eprints.iisc.ac.in/id/eprint/54345

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