Hermitian scattering behavior for the non-Hermitian scattering center

We study the scattering problem for the non-Hermitian scattering center, which consists of two Hermitian clusters with anti-Hermitian couplings between them. Counterintuitively, it is shown that it acts as a Hermitian scattering center, satisfying $|r| ^{2}+|t| ^{2}=1$, i.e., the Dirac probability current is conserved, when one of two clusters is embedded in the waveguides. This conclusion can be applied to an arbitrary parity-symmetric real Hermitian graph with additional PT-symmetric potentials, which is more feasible in experiment. Exactly solvable model is presented to illustrate the theory. Bethe ansatz solution indicates that the transmission spectrum of such a cluster displays peculiar feature arising from the non-Hermiticity of the scattering center.Comment: 6 pages, 2 figure

The effects of disorder and interactions on the Anderson transition in doped Graphene

We undertake an exact numerical study of the effects of disorder on the Anderson localization of electronic states in graphene. Analyzing the scaling behaviors of inverse participation ratio and geometrically averaged density of states, we find that Anderson metal-insulator transition can be introduced by the presence of quenched random disorder. In contrast with the conventional picture of localization, four mobility edges can be observed for the honeycomb lattice with specific disorder strength and impurity concentration. Considering the screening effects of interactions on disorder potentials, the experimental findings of the scale enlarges of puddles can be explained by reviewing the effects of both interactions and disorder.Comment: 7 pages, 7 figure