Abstract
Altland and Zirnbauer's (AZ) classification is an approach to classify general random Hamiltonians of non-interacting fermionic systems with bulk energy gap in the presence or absence of time-reversal symmetry (TRS), particle-hole symmetry (PHS) and chiral symmetry (or sublattice symmetry (SLS)). Recently, it has become a useful table, like chemical periodic table, to classify topological insulators and topological superconductors.
In this seminar, basic knowledge of the AZ classification will be introduced at the beginning. Four well-known examples, namely, quantum anomalous Hall, quantum spin Hall and topological superconductors with and without TRS, which belong to four different symmetry classes, will be reviewed in details. Some discussions on how to construct models for AZ classification may be briefly presented.