Theoretical Study on Correlation Effects in Topological Matter - Hiroki Isobe Gebunden

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 ho w 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.