The importance and promise that topological materials hold has been recently underscored by the award of the Nobel Prize in Physics in 2016 ``for theoretical discoveries of topological phase transitions and topological phases of matter." This dissertation explores the novel qualities and useful topologically protected surface states of topological insulators and semimetals.
Topological materials have protected qualities which are not removed by weak perturbations. The manifestations of these qualities in topological insulators are spin-momentum-locked surface states, and in Weyl and Dirac semimetals they are unconventional open surface states (Fermi arcs) with anomalous electrical transport properties. There is great promise in utilizing the topologically protected surface states in electronics of the future, including spintronics, quantum computers, and highly sensitive devices. Physicists and chemists are also interested in the fundamental physics and exotic fermions exhibited in topological materials and in heterostructures including them.
Chapter 1 provides an introduction to the concepts and methods of topological band theory. Chapter 2 investigates the spin and spin-orbital texture and electronic structures of the surface states at side surfaces of a topological insulator, Bi2Se3, by using slab models within density functional theory. Two representative, experimentally achieved surfaces are examined, and it is shown that careful consideration of the crystal symmetry is necessary to understand the physics of the surface state Dirac cones at these surfaces. This advances the existing literature by properly taking into account surface relaxation and symmetry beyond what is contained in effective bulk model Hamiltonians.
Chapter 3 examines the Fermi arcs of a topological Dirac semimetal (DSM) in the presence of asymmetric charge transfer, of the kind which would be present in heterostructures. Asymmetric charge transfer allows one to accurately identify the projections of Dirac nodes despite the existence of a band gap and to engineer the properties of the Fermi arcs, including spin texture. Chapter 4 investigates the effect of an external magnetic field applied to a DSM. The breaking of time reversal symmetry splits the Dirac nodes into topologically charged Weyl nodes which exhibit Fermi arcs as well as conventionally-closed surface states as one varies the chemical potential. / Ph. D. / The importance and promise that topological materials hold has been recently underscored by the award of the Nobel Prize in Physics in 2016 “for theoretical discoveries of topological phase transitions and topological phases of matter.” This dissertation explores the novel qualities and useful topologically protected surface states of topological insulators and semimetals.
Topological materials have protected qualities which are not removed by weak perturbations to the system. The manifestations of these qualities in topological insulators are spin-momentum-locked surface states which can be used to develop spin-polarized currents in electronics. Further, these states have linear dispersion at a special momentum point, called the Dirac cone. Conventionally these surface states form closed loops in momentum space. But in two other species of topological materials, Weyl and Dirac semimetals, the surface states form open arcs (called Fermi arcs) and these cause anomalous electrical transport properties including Hall conductivity and Nernst effect. Weyl and Dirac semimetals also have special momentum points (nodes) at which the bulk conduction and valence bands touch with linear dispersion. There is great promise in utilizing the topologically protected surface states in the electronics of the future, including spintronics, quantum computers, and highly sensitive devices. Physicists and chemists are also interested in the fundamental physics and exotic fermions exhibited in topological materials and in heterostructures including them.
Chapter 1 provides an introduction to the concepts and methods of topological band theory. Chapter 2 investigates the spin and spin-orbital texture and electronic structures of the surface states of a topological insulator, Bi₂Se₃, at its side surfaces (beyond the familiar cleaving surface). We use slab models within density functional theory (DFT) to investigate two representative, experimentally achieved surfaces, and it is shown that careful consideration of the threefold rotational crystal symmetry is necessary to understand the physics of the surface state Dirac cones at these surfaces. The differing atomic orbital and cationic/anionic characters of the topological states are examined. This advances the existing literature by properly taking into account how the atoms at the surface relax at the interface with the vacuum and the full symmetry beyond what is contained in effective bulk model Hamiltonians.
Chapter 3 examines the Fermi arcs of a topological Dirac semimetal (DSM) in the presence of asymmetric charge transfer at only one surface, of the kind which would be present in heterostructures comprised of DSMs and topologically-trivial materials. We use a thin slab model within DFT to calculate the electronic structure of the DSM. Asymmetric charge transfer allows one to accurately identify the projections of the linearly dispersing Dirac nodes despite the existence of a bulk band gap and to engineer the properties of the surface Fermi arcs, including their spin texture. Chapter 4 investigates the effect of an external magnetic field applied to a DSM. The breaking of time reversal symmetry splits the Dirac nodes into topologically charged Weyl nodes which exhibit Fermi arcs as well as conventionally-closed surface states as one varies the chemical potential. The topological charge of the Weyl nodes is what makes them, and their Fermi arcs, robust against weak perturbations such as strain. Meticulously determining the topological index, or Chern number, of Fermi surface sheets demonstrates the bulk-boundary correspondence between the Weyl nodes and their Fermi arcs, and provides evidence for the existence of multiple-charge double Weyl nodes which, until now, have only been discussed sparingly in the literature on topological DSMs.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/82959 |
| Date | 30 April 2018 |
| Creators | Villanova, John William |
| Contributors | Physics, Park, Kyungwha, Tao, Chenggang, Economou, Sophia E., Heremans, Jean J. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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