Evolution of individual quantum Hall edge states in the presence of disorder

Employing the Bloch eigenmode matching approach, we numerically study the evolution of individual quantum Hall edge states with respect to disorder. As shown by the two-parameter renormalization group flow of the Hall and Thouless conductances, quantum Hall edge states with high Chern number n are completely different from that of n=1 case. Two categories of individual edge modes are evaluated in a quantum Hall system with high Chern number. Edge states from the lowest Landau level have similar eigenfunctions which are well localized at the system edge and independent of the Fermi energy. On the other hand, at fixed Fermi energy, the edge state from higher Landau levels has larger expansion, which leads to less stable quantum Hall states at high Fermi energies. By presenting the local current density distribution, the influence of disorder on eigenmode-resolved edge states is vividly demonstrated.