Current Carrying States In The Disordered Quantum Anomalous Hall Effect

Robust transport in Quantum Hall effect originates from current of the edge states,and these states root in the Chern number carried by Landau levels.Therefore,Chern number is the symbol of the robust current,and the electronic states carrying a non-zero Chern number can be reckoned as current carrying states.In a quantum Hall effect,flat Landau levels may be broadened by disorder.However,it has been found that in the thermodynamic limit,all extended(or current carrying)states shrink to one single energy value within each Landau level.On the other hand,a quantum anomalous Hall effect consists of dispersive bands with finite widths.How will the distribution of current carrying states in quantum anomalous Hall effect be? In this thesis,we numerically investigate the picture of current carrying states in this case.With size scaling,the spectrum width of these states in each bulk band still shrinks to a single energy value in the thermodynamic limit,in a power law way.In other words,as long as the disorder exists in quantum anomalous Hall effect,the distribution of current carrying states is also infinitely narrow in the thermodynamic limit.According to our discovery,the value of scaling exponent is close to the result from the Quantum Hall effect when the disorder strength lives in the intermediate region.The magnitude of the scaling exponent at the intermediate disorder is close to that in the quantum Hall effects.The number of current carrying states obeys similar scaling rules,so that the density of states of current carrying states is finite.Other states in the bulk band are localized and may contribute to the formation of a topological Anderson insulator.