Manipulating topological-insulator properties using quantum confinement

Abstract

Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators are insulating in the bulk but have conductive surface or edge states. Topological materials show various unusual physical properties and are surmised to enable the creation of exotic Majorana-fermion quasiparticles. How the signatures of topological behavior evolve when the system size is reduced is interesting from both a fundamental and an application-oriented point of view, as such understanding may form the basis for tailoring systems to be in specific topological phases. This work considers the specific case of quantum-well confinement defining two-dimensional layers. Based on the effective-Hamiltonian description of bulk topological insulators, and using a harmonic-oscillator potential as an example for a softer-than-hard-wall confinement, we have studied the interplay of band inversion and size quantization. Our model system provides a useful platform for systematic study of the transition between the normal and topological phases, including the development of band inversion and the formation of massless-Dirac-fermion surface states. The effects of bare size quantization, two-dimensional-subband mixing, and electron-hole asymmetry are disentangled and their respective physical consequences elucidated.

15 pages, 5 figures, IoP article style. Interactive simulations referenced in the article are available at https://www.dropbox.com/sh/ouq3e8p25m9kzvm/AAAgHZjdL8P0VWH_JzcH3rVRa?dl=0 . v2: added references & final paragraph in Conclusions. To appear in NJP

References in corpus (16)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• Wilson Fermions and Axion Electrodynamics in Optical Lattices
• Topological Insulators and Metals in Atomic Optical Lattices
• Magneto-optics of massive Dirac fermions in bulk Bi2Se3
• Spontaneous breakdown of topological protection in two dimensions
• Effects of Smooth Boundaries on Topological Edge Modes in Optical Lattices
• Finite-size energy gap in weak and strong topological insulators
• Edge states reconstruction from strong correlations in quantum spin Hall insulators
• Relativistic k.p Hamiltonians for centrosymmetric topological insulators from ab initio wave functions
• Finite-size and composition-driven topological phase transition in (Bi${}_{1-x}$In${}_x$)${}_2$Se${}_3$ thin films
• Quantum spin Hall insulators in centrosymmetric thin films composed from topologically trivial BiTeI trilayers

Cited by in corpus (7)

• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Volkov-Pankratov states in topological heterojunctions
• Progress in epitaxial thin-film Na3Bi as a topological electronic material
• Spherical topological-insulator nanoparticles: Quantum size effects and optical transitions
• Finite-size effects in cylindrical topological insulators
• Dirac electrons in quantum rings
• Exact Solutions of D-dimensional Klein-Gordon Oscillator with Snyder-de Sitter Algebra