Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class-D thermal quantum Hall effect

We investigate numerically the quasiparticle density of states $\ensuremath{\varrho}(E)$ for a two-dimensional, disordered superconductor in which both time-reversal and spin-rotation symmetries are broken. As a generic single-particle description of this class of systems (symmetry class D), we use the Cho-Fisher version of the network model. This has three phases: a thermal insulator, a thermal metal, and a quantized thermal Hall conductor. In the thermal metal, we find a logarithmic divergence in $\ensuremath{\varrho}(E)$ as $E\ensuremath{\rightarrow}0$, as predicted from sigma model calculations. Finite-size effects lead to superimposed oscillations, as expected from random-matrix theory. In the thermal insulator and quantized thermal Hall conductor, we find that $\ensuremath{\varrho}(E)$ is finite at $E=0$. At the plateau transition between these phases, $\ensuremath{\varrho}(E)$ decreases toward zero as $\ensuremath{\mid}E\ensuremath{\mid}$ is reduced, in line with the result $\ensuremath{\varrho}(E)\ensuremath{\sim}\ensuremath{\mid}E\ensuremath{\mid}\mathrm{ln}(1∕\ensuremath{\mid}E\ensuremath{\mid})$ derived from calculations for Dirac fermions with random mass.