Book•
Spin-orbit Coupling Effects in Two-Dimensional Electron and Hole Systems
10 Oct 2003-
TL;DR: The Extended Kane Model has been used to model the band structure of Semiconductors as mentioned in this paper, and it has been shown that the Extended Kane model can be used to explain spin-orbit coupling effects.
Abstract: Introduction.- Band Structure of Semiconductors.- The Extended Kane Model.- Electron and Hole States in Quasi 2D Systems.- Origin of Spin-Orbit Coupling Effects.- Inversion Asymmetry Induced Spin Splitting.- Anisotropic Zeeman Splitting in Quasi 2D Systems.- Landau Levels and Cyclotron Resonance.- Anomalous Magneto-Oscillations.- Conclusions.- Notation and Symbols.- Quasi Degenerate Perturbation Theory.- The Extended Kane Model: Tables.- Band Structure Parameters.
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TL;DR: Topological superconductors are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors and are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry.
Abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.
11,092 citations
Cites background from "Spin-orbit Coupling Effects in Two-..."
...Starting from the four low-lying states|P1+z , ↑ (↓)〉 and |P2−z , ↑ (↓)〉 at the Γ point, such a Hamiltonian can be constructed by the theory of invari- ants (Winkler, 2003) at a finite wavevectork....
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TL;DR: In this article, first-principles electronic structure calculations of the layered, stoichiometric crystals Sb2Te3, Bi2Se3, SbSe3 and BiSe3 were performed.
Abstract: Topological insulators are new states of quantum matter in which surface states residing in the bulk insulating gap of such systems are protected by time-reversal symmetry. The study of such states was originally inspired by the robustness to scattering of conducting edge states in quantum Hall systems. Recently, such analogies have resulted in the discovery of topologically protected states in two-dimensional and three-dimensional band insulators with large spin–orbit coupling. So far, the only known three-dimensional topological insulator is BixSb1−x, which is an alloy with complex surface states. Here, we present the results of first-principles electronic structure calculations of the layered, stoichiometric crystals Sb2Te3, Sb2Se3, Bi2Te3 and Bi2Se3. Our calculations predict that Sb2Te3, Bi2Te3 and Bi2Se3 are topological insulators, whereas Sb2Se3 is not. These topological insulators have robust and simple surface states consisting of a single Dirac cone at the Γ point. In addition, we predict that Bi2Se3 has a topologically non-trivial energy gap of 0.3 eV, which is larger than the energy scale of room temperature. We further present a simple and unified continuum model that captures the salient topological features of this class of materials. First-principles calculations predict that Bi2Se3, Bi2Te3 and Sb2Te3 are topological insulators—three-dimensional semiconductors with unusual surface states generated by spin–orbit coupling—whose surface states are described by a single gapless Dirac cone. The calculations further predict that Bi2Se3 has a non-trivial energy gap larger than the energy scale kBT at room temperature.
4,982 citations
TL;DR: In this paper, a detailed review of the role of the Berry phase effect in various solid state applications is presented. And a requantization method that converts a semiclassical theory to an effective quantum theory is demonstrated.
Abstract: Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.
3,344 citations
TL;DR: In this article, a review of recent advances in the condensed matter search for Majorana fermions is presented, which has led many in the field to believe that this quest may soon bear fruit.
Abstract: The 1937 theoretical discovery of Majorana fermions-whose defining property is that they are their own anti-particles-has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review paper highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic 'topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to 'engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions-the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.
2,156 citations
TL;DR: Bychkov and Rashba as discussed by the authors introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors, which has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductor devices.
Abstract: In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade has been particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topological classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.
1,533 citations
References
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TL;DR: The most interesting developments in semiconductor physics that have occurred in the last few years and that are anticipated in the next few years appear to lie in the realm between physics and chemistry as mentioned in this paper.
Abstract: Many of the most interesting developments in semiconductor physics that have occurred in the last few years and that are anticipated in the next few years appear to lie in the realm between physics and chemistry. In this article I have tried to show how this realm can be treated accurately and realistically within the framework of theory.
883 citations
Book•
02 Feb 1978865 citations
TL;DR: Smith's classic book Semiconductors was published in 1978 as mentioned in this paper, which was an event of practical significance, since before then students of the subject were forced to draw their knowledge from a variety of published papers and reviews and there was no complete treatment of semiconductors as a class.
Abstract: R A Smith 1978 London: Cambridge University Press xvii + 523 pp price £27.50 (£8.95 paperback) It is difficult to believe that 20 years have passed since R A Smith's classic book Semiconductors was published. The publication was an event of practical significance, since before then students of the subject were forced to draw their knowledge from a variety of published papers and reviews – there was no complete treatment of semiconductors as a class.
166 citations
"Spin-orbit Coupling Effects in Two-..." refers background or methods in this paper
...53As [1,8,6] InP [1,9,6] CdTe [1,9,6] ZnSe [1,9,6]...
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...GaAs [1,5,6] AlAs [1,6] InSb [7,1,6] InAs [1,8,6] AlSb [1,6]...
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...Furthermore, it is essentially equivalent to the Foldy–Wouthuysen transformation [5] used in the context of relativistic quantum mechanics and to the Schrieffer–Wolff transformation [6] used in the context of the Anderson and Kondo models....
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01 Jan 1984
TL;DR: In this paper, the motion of two-dimensional carriers in quantum wells and superlattices is discussed, with emphasis on subband dispersion parallel to the interfaces and on quantization in a perpendicular magnetic field.
Abstract: The motion of two-dimensional carriers in quantum wells and superlattices is discussed, with emphasis on subband dispersion parallel to the interfaces and on quantization in a perpendicular magnetic field. For coupled bands (valence bands, coupled s-p bands in narrow-gap semiconductors, etc.) striking non-parabolicities of the subband dispersion and non-linearities of the Landau levels versus magnetic field occur. Results for GaAs-GaAlAs and InAs-GaSb systems are compared to analytical solutions for simple models and to experiments.
21 citations
"Spin-orbit Coupling Effects in Two-..." refers result in this paper
...3 we present the calculated absorption spectra for 2D hole systems in strained Ge–SixGe1−x QWs [39] which are in good agreement with the experimental data of Engelhardt et al....
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