Global phase diagram of two-dimensional dirty hyperbolic Dirac liquids

Abstract

Within the framework of the canonical nearest-neighbor tight-binding model for spinless fermions, a family of two-dimensional bipartite hyperbolic lattices hosts massless Diraclike excitations near half-filling with the iconic vanishing density of states (DOS) near zero energy. We show that a collection of such ballistic quasiparticles remains stable against sufficiently weak pointlike charge impurities, a feature captured by the vanishing average [${\rho }_a(0)$] and typical [${\rho }_t(0)$] DOS at zero energy, computed by employing the kernel polynomial method in sufficiently large $\{10,3\}$ hyperbolic lattices (Schläfli symbol) with open boundary condition containing more than $10^8$ and $10^6$ sites, respectively. However, at moderate disorder the system enters a metallic state via a continuous quantum phase transition where both ${\rho }_a(0)$ and ${\rho }_t(0)$ become finite. With increasing strength of disorder, ultimately an Anderson insulator sets in, where only ${\rho }_t(0)\to 0$. The resulting phase diagram for dirty Dirac fermions living on a hyperbolic space solely stems from the background negative spatial curvature, as confirmed from the vanishing ${\rho }_t(0)$ for arbitrarily weak disorder on honeycomb lattices, fostering relativistic fermions on a flatland, as the thermodynamic limit is approached.

6 Pages and 3 Figures: Supplemental Material as ancillary file