Theoretical Study on Correlation Effects in Topological Matter

  • Hiroki Isobe

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Hiroki Isobe
    Pages 1-31
  3. Hiroki Isobe
    Pages 63-81
  4. Hiroki Isobe
    Pages 131-133
  5. Back Matter
    Pages 135-136

About this book


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 Zgroup by using the bosonization technique and a geometrical consideration.


Topological insulators and electron correlations Renormalization group analysis Hund’s rule for two-atom systems Quantum critical phenomena topological phase transitions Topological crystalline insulators Electron interactions in Dirac and Weyl semimetals Dirac fermions in organic conductors

Authors and affiliations

  • Hiroki Isobe
    • 1
  1. 1.Massachusetts Institute of Technology CambridgeUSA

Bibliographic information