Density of states in a two-dimensional chiral metal with vacancies
  We study quantum interference effects in a two-dimensional chiral metal (bipartite lattice) with vacancies. We demonstrate that randomly distributed vacancies constitute a peculiar type of chiral disorder leading to strong modifications of critical properties at zero energy as compared to conventional chiral metals. In particular, the average density of states diverges as $\rho \propto E^{-1} |\ln E|^{-3/2}$ and the correlation length $L_c \propto \sqrt{|\ln E|}$ in the limit $E \to 0$. When the average density of vacancies is different in the two sublattices, a finite concentration of zero modes emerges and a gap in the quasiclassical density of states opens around zero energy. Interference effects smear this gap resulting in exponentially small tails at low energies. 
P. M. Ostrovsky, I. V. Protopopov, E. J. K\"onig, I. V. Gornyi, A. D.   Mirlin, M. A. Skvortsov
cond-mat.mes-hall