Theoretical Study on Correlation Effects in Topological Matter

ISBN-13: 9789811099557 / Angielski / Miękka / 2018 / 136 str.

Hiroki Isobe

Spis treści

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

O autorze

Hiroki Isobe is a postdoctoral associate at the Massachusetts Institute of Technology. His work is concerned with the theory of condensed matter physics, and he particularly focuses on the effects of electron interactions in topological phases of matter. He is interested in interacting topological phases and exotic superconductivity. 

Hiroki Isobe received a Bachelor of Engineering from the Department of Applied Physics, The University of Tokyo in March 2011. Thereafter he joined the group led by Professor Naoto Nagaosa in the Department of Applied Physics, The University of Tokyo, receiving both a Master of Engineering and a Ph.D. in engineering from The University of Tokyo in March 2013 and in September 2015, respectively. In 2013, he received the Tanaka Shoji Prize from the Department of Applied Physics, The University of Tokyo for an outstanding Master’s thesis. He was also awarded a research fellowship by the Japan Society for the Promotion of Science (JSPS) in 2013, and was supported by JSPS during his doctoral course.

Blurb

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.