Theoretical study on correlation effects in topological matter
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Bibliographic Information
Theoretical study on correlation effects in topological matter
（Springer theses : recognizing outstanding Ph. D. research）
Springer, c2017
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"Doctoral thesis accepted by the University of Tokyo, Tokyo, Japan"
Includes bibliographical references
Description and Table of Contents
Description
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.
Table of Contents
1 Introduction 1.1 Scope of the Thesis 1.2 Outline of the Thesis 1.3 Quantum Hall States 1.4 Topological Insulators 1.5 Weyl and Dirac Semimetals 1.6 -(BEDT-TTF)2I3 1.7 Topological Mott Insulators 1.8 Topological Crystalline Insulators 1.9 Classification of Topological States of Matter 2 Interacting Dirac Fermions in (3+1) Dimensions 2.1 Model 2.2 Renormalization Group Analysis 2.3 Density of States 2.4 Electromagnetic Properties 2.5 Spectral Function 2.6 Electric Conductivity 2.7 Energy Gap 2.8 Discussions and Summary 3 Tilted Dirac Cones in Two Dimensions 3.1 Model 3.2 Perturbative Renormalization Group Analysis 3.3 Spin Susceptibility 3.4 Discussions and Summary 4 Generalized Hund's Rule for Two-Atom Systems 4.1 Model 4.2 Results 4.3 Perturbative Calculation 4.4 Entanglement Entropy 4.5 Symmetry 4.6 Discussions and Summary 5 Interacting Topological Crystalline Insulators 5.1 Classification in Two Dimensions 5.2 Interacting TCIs in Three Dimensions 5.3 Discussions and Summary 6 Conclusions and Prospects
by "Nielsen BookData"
