Current carrying states in the disordered quantum anomalous Hall effect

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. 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. 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.     

4,5-二苯基-2-取代基-1-磺酰基咪唑的合成

用多种磺酰氯或磺酸酐与4,5-二苯基-2-取代-1-磺酰基咪唑负离子反应, 合成了10个未见文献报道的1-磺酰基咪唑类化合物. 所有化合物均经1H NMR和13C NMR确证.