Effective mass and tricritical point for lattice fermions localized by a random mass

Abstract

This is a numerical study of quasiparticle localization in symmetry class \textit{BD} (realized, for example, in chiral \textit{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 $σ$ is well described by an effective mass $M_{\rm eff}$, dependent on the first two moments of the random mass $M(\bm{r})$. The effective mass vanishes linearly when the average mass $\bar{M}\to 0$, reproducing the known insulator-insulator phase boundary with a scale invariant dimensionless conductivity $σ_{c}=1/π$ and critical exponent $ν=1$. For strong disorder a transition to a metallic phase appears, with larger $σ_{c}$ but the same $ν$. The intersection of the metal-insulator and insulator-insulator phase boundaries is identified as a \textit{repulsive} tricritical point.

6 pages, 9 figures