Reshaping Of Dirac Cones In Topological Insulators And Graphene
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Reshaping of Dirac Cones in Topological Insulators and Graphene
Author: Álvaro Díaz Fernández
language: en
Publisher: Springer Nature
Release Date: 2020-12-09
Dirac cones are ubiquitous to non-trivial quantum matter and are expected to boost and reshape the field of modern electronics. Particularly relevant examples where these cones arise are topological insulators and graphene. From a fundamental perspective, this thesis proposes schemes towards modifying basic properties of these cones in the aforementioned materials. The thesis begins with a brief historical introduction which is followed by an extensive chapter that endows the reader with the basic tools of symmetry and topology needed to understand the remaining text. The subsequent four chapters are devoted to the reshaping of Dirac cones by external fields and delta doping. At all times, the ideas discussed in the second chapter are always a guiding principle to understand the phenomena discussed in those four chapters. As a result, the thesis is cohesive and represents a major advance in our understanding of the physics of Dirac materials.
Theoretical Study on Correlation Effects in Topological Matter
This thesis elucidates electron correlation effects in topological matter whose electronic states hold nontrivial topological properties robust against small perturbations. In addition to a comprehensive introduction to topological matter, this thesis provides a new perspective on correlated topological matter. The book comprises three subjects, in which electron correlations in different forms are considered. The first focuses on Coulomb interactions for massless Dirac fermions. Using a perturbative approach, the author reveals emergent Lorentz invariance in a low-energy limit and discusses how to probe the Lorentz invariance experimentally. The second subject aims to show a principle for synthesizing topological insulators with common, light elements. The interplay between the spin–orbit interaction and electron correlation is considered, and Hund's rule and electron filling are consequently found to play a key role for a strong spin–orbit interaction important for topological insulators. The last subject is classification of topological crystalline insulators in the presence of electron correlation. Unlike non-interacting topological insulators, such two- and three-dimensional correlated insulators with mirror symmetry are demonstrated to be characterized, respectively, by the Z4 and Z8 group by using the bosonization technique and a geometrical consideration.
Reshaping of Dirac Cones in topological insulators and Graphene
La mecánica cuántica alcanzó su máximo esplendor a principios del siglo XX de la mano de grandes científicos como Schrödinger, Heisenberg, Dirac, Pauli y muchos otros. Los conceptos que estos físicos introdujeron fueron increíblemente revolucionarios, incluso uno podría aventurar a decir que superaron a la relatividad de Einstein. Hoy en día pudiera parecer que únicamente explotamos las consecuencias de la mecánica cuántica para construir transistores o diodos emisores de luz, dispositivos que, por otra parte, han cambiado por completo el mundo en el que vivimos. En lo que respecta a la física teórica, uno podría pensar que lo único que queda por hacer es encender la maquinaria matemática y esperar a obtener resultados, sin nuevos conceptos que descubrir. Sin embargo, nada más lejos de la realidad. Tenemos la suerte de vivir en lo que los expertos denominan la segunda revolución cuántica...