凝聚态物理学进展-2019

1、Chern Insulator (break Time reversal symmetry)Instructor: Cheng-Cheng Liu (刘铖铖) School of physics in BITSolid-State book: A material with bands fully filled or without Fermi surface. (only for band insulators).Kohn: A material for which all electronic phenomena are local, i.e. insensitive to boundar

2、y conditions.(for band insulators, Mott insulator, Anderson insulators, etc.)Kohn, Phys. Rev. 133 A 171 (1964)What is an insulator?From normal to topological insulator整数量子霍尔效应See movieGauss-Bonnet-Chern公式TKNN (Chern number) & Hall conductance Berry Phase量子反常霍尔效应(QAH)Haldane ModelTopological invarian

3、ts-Chern number in T-symmetry breaking systemChern number must be an integer, equals the number of monopoles inside the torus.It is a reflection of the fact that a smooth gauge choice is NOT possible over the entire BZ.Chern InsulatorThe Hall conductance equals the Chern number and is an integer onl

4、y if the base manifold (the BZ) is compact. In the continuum, the momentum runs over a pact manifold (the infinite Euclidean plane),and this does not apply.Zero mode in Dirac equation and surface state in topological insulator0m0-m00m0-m0-m0-m0Some Comments on the edge statesThe edge mode of the qua

5、ntum anomalous Hall effect is very special, since it only propagates along one direction. Such type of edge mode is called chiral edge state. It can also be understood as a kind of fractionalization. As shown in Fig. (a), the normal 1D system always has two branches, one left mover and one right mov

6、er. When we consider a quantum anomalous Hall insulator with two edges, we will see that the two branches are spatically separated into two opposite edges, therefore it can be viewed as a fractionalization of the normal 1D system. Also due to the spatial separation of the two branches, they can not be scattered into each other by any local perturbation, such as disorder. When the electron in the edge mode encounter an impurity, it will go around the impurity instead of the backs