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 those of 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.

Figure 1

Average DOS in the 0D chiral system with fluctuating imbalance. Dashed lines show quasiclassical result (6). At low energies, DOS vanishes linearly, cf. Eq. (7).

Figure 2

Schematic average DOS in the 2D chiral metal with vacancies. Black line shows the result of Eq. (13) in the limit $\mathrm{\Delta }=0$. Weak imbalance results in the linear decay of DOS at exponentially low energies (14). Strong imbalance leads to the gap with exponentially small subgap tail (19).