Magic-Angle Semimetals with Chiral Symmetry

TL;DR

This paper introduces a two-dimensional chiral symmetric model with quasiperiodic hopping, revealing a rich phase diagram including a semimetal-to-metal transition, flat bands at the magic angle, and higher-order topological phases, with potential experimental realizations.

Contribution

It constructs and analyzes a novel quasiperiodic Dirac cone model exhibiting unique phase transitions and topological phases, linking quasiperiodic modulation to flat band formation and topological phenomena.

Findings

Identifies a semimetal-to-metal phase transition characterized by multifractal eigenstates.

Demonstrates the emergence of flat bands with renormalized bandwidth at the transition.

Provides evidence of diverging density of states and quantum-critical scaling in the model.

Abstract

We construct and solve a two-dimensional, chirally symmetric model of Dirac cones subjected to a quasiperiodic modulation. In real space, this is realized with a quasiperiodic hopping term. This hopping model, as we show, at the Dirac node energy has a rich phase diagram with a semimetal-to-metal phase transition at intermediate amplitude of the quasiperiodic modulation, and a transition to a phase with a diverging density of states and sub-diffusive transport when the quasiperiodic hopping is strongest. We further demonstrate that the semimetal-to-metal phase transition can be characterized by the multifractal structure of eigenstates in momentum space and can be considered as a unique "unfreezing" transition. This unfreezing transition in momentum space generates flat bands with a dramatically renormalized bandwidth in the metallic phase similar to the phenomena of the band structure of twisted bilayer graphene at the magic angle. We characterize the nature of this transition numerically as well as analytically in terms of the formation of a band of topological zero modes. For pure quasiperiodic hopping, we provide strong numerical evidence that the low-energy density of states develops a divergence and the eigenstates exhibit Chalker (quantum-critical) scaling despite the model not being random. At particular commensurate limits the model realizes higher-order topological insulating phases. We discuss how these systems can be realized in experiments on ultracold atoms and metamaterials.