Quantum phenomena in topological materials

In 1980, the integer quantum Hall effect in two-dimensional(2D) systems was discovered under high magnetic field [1],which opened a door to the novel phase of matter. The concept of topology was then introduced into condensed matter physics to distinguish the intriguing phenomenon of quantum Hall effect by non-zero Chern number(C) [2]. The topological scenario suggests a new type of phase where the phase transition does not need symmetry breaking. In 2005,