Global phase diagram of two-dimensional dirty hyperbolic Dirac liquids

TL;DR

This paper investigates the stability and phase transitions of two-dimensional hyperbolic Dirac fermions under disorder, revealing a phase diagram with ballistic, metallic, and insulating phases driven by disorder strength.

Contribution

It provides the first detailed phase diagram of disordered hyperbolic Dirac liquids, showing how background curvature influences localization and metallic behavior.

Findings

Ballistic Dirac quasiparticles are stable against weak disorder.

A continuous transition from a Dirac semimetal to a metal occurs at moderate disorder.

At strong disorder, the system becomes an Anderson insulator with vanishing typical DOS.

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 (Schl\"afli symbol) with more than $10^8$ and $10^5$ sites, respectively, with open boundary conditions. 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.