Hyperbolic lattices with mass disorder: Phases and phase transitions

Abstract

Nearest-neighbor (NN) tight-binding models (TBMs) on plaquette-centered $\{ 10,3\}$ (Schläfli symbol), $\{ 8,3\}$, and $\{ 8,4\}$ hyperbolic lattices on a Poincaré disk with open boundary conditions display a vanishing, a finite, and a diverging density of states (DOS) near zero energy (band center), respectively, yielding a Dirac liquid, a Fermi liquid, and a flat band. Emergent bipartite nature of these lattices within the framework of NN-TBMs, allows us to scrutinize the impact of mass disorder on the electronic states and DOS therein. From extensive numerical calculations of the average and typical DOS using the kernel polynomial method, we show that hyperbolic Dirac liquid remains stable against weak mass disorder, undergoing a semimetal-to-metal quantum phase transition at moderate disorder, followed by an Anderson metal-to-insulator transition at even stronger disorder. The remaining two systems display only the latter transition. Critical exponents near all these transitions are found to be close to the ones mediated by on-site potential disorder.