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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 , 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
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