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.
Highlights
Topological insulators [1,2,3] (TIs) have emerged as a new materials class that provides a testing ground for exploring ground-breaking new ideas [4, 5] about the properties of condensed matter
The interplay between topological properties and quantum confinement has been studied as a way to disentangle various phenomena typically associated with topological materials in a controlled fashion [23]
We have used the effective-model description of bulk-Topological insulators [1–3] (TIs) band structures to investigate the effect of a soft, harmonic-oscillator-type, quantum confinement on physical properties that epitomize topological phases
Summary
Topological insulators [1,2,3] (TIs) have emerged as a new materials class that provides a testing ground for exploring ground-breaking new ideas [4, 5] about the properties of condensed matter. We utilize an effective-model description of quantum wells made from TI materials to map changes in the size of the fundamental gap, the degree of band inversion, and the hybridization of surface states in a detailed way. Further motivation to investigate influences of the confinement strength on 3D-TI properties is provided by the observation that 2D TIs (realized in HgTe quantum wells or simulated by cold atoms, respectively) subjected to soft confinement experience a proliferation of edge modes that modifies topological properties [12, 13, 26, 27]. Signatures of topological behavior in the subband dispersions (section 3) and in bound-state properties such as the band-inversion-related pseudospin and the surface-state hybridization (section 4) are identified, with respect to their observability in real (electron-holeasymmetric) systems. Some more mathematical details about the methods used for calculating 3D-TI-layer subband dispersions and eigenstates are given in the appendix
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