Disorder-induced Majorana metal in interacting non-Abelian anyon systems

We demonstrate that a thermal metal of Majorana fermions forms in a two-dimensional system of interacting non-Abelian (Ising) anyons in the presence of moderate disorder. This bulk metallic phase arises in the $\nu =5/2$ quantum Hall state when disorder pins the anyonic quasiparticles. More generally, it naturally occurs for various proposed systems supporting Majorana fermion zero modes when disorder induces the random pinning of a finite density of vortices. This includes all two-dimensional topological superconductors in so-called symmetry class D. A distinct experimental signature of the thermal metal phase is the presence of bulk heat transport down to zero temperature.

Figure 1

Going from Ising anyons (left) to Majoranas (right).

Figure 2

Phase diagram of sign-disordered triangular lattice hopping problem in the $(p,\mu )$ plane. The thermal metal phase at $\mu =0$ extends from $p_c\approx 0.15\pm 0.05$ to $1-p_c$, estimated from the soft onset of wave-function multifractality and the log divergence of the density of states at numerically accessible system sizes.

Figure 3

Finite-size scaling collapse of the disorder averaged Chern number $\overline{\nu }$ at $\mu =-0.1$ with $p_c\approx 0.225$ and $\nu \approx 5\pm 1$.

Figure 4

Disorder averaged density of states $\rho \left(E\right)$ near $E=0$ at $p=1/2$ collected from $N=2–3\times {10}^4$ samples per size $L$.

Figure 5

Left: The inverse participation ratios of the wave function for disorder strength $p=0.5$ averaged over $N=2\times {10}^3$ samples per size $L$ in an energy window $E<{10}^{-3}$. Right: The multifractal exponents characterizing the decay of the inverse participation ratios.