This is a numerical study of quasiparticle localization in symmetry class $BD$ (realized, for example, in chiral $p$-wave superconductors), by means of a staggered-fermion lattice model for two-dimensional Dirac fermions with a random mass. For sufficiently weak disorder, the system size dependence of the average (thermal) conductivity $\sigma$ is well described by an effective mass $M_{\text{eff}}$, dependent on the first two moments of the random mass $M\left(\mathit{r}\right)$. The effective mass vanishes linearly when the average mass $\overline{M}\to 0$, reproducing the known insulator-insulator phase boundary with a scale invariant dimensionless conductivity ${\sigma }_c=1/\pi$ and critical exponent $\nu =1$. For strong disorder a transition to a metallic phase appears, with larger ${\sigma }_c$ but the same $\nu$. The intersection of the metal-insulator and insulator-insulator phase boundaries is identified as a repulsive tricritical point.

• Received 10 April 2010

DOI:https://doi.org/10.1103/PhysRevB.81.214203