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Magic-angle semimetals with chiral symmetry

Yang-Zhi Chou, Yixing Fu, Justin H. Wilson, E. J. König, and J. H. Pixley
Phys. Rev. B 101, 235121 – Published 4 June 2020

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 (DOS) and subdiffusive 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 DOS 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.

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  • Received 18 November 2019
  • Accepted 26 March 2020

DOI:https://doi.org/10.1103/PhysRevB.101.235121

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Yang-Zhi Chou1,2,*, Yixing Fu3, Justin H. Wilson3, E. J. König3, and J. H. Pixley3

  • 1Condensed Matter Theory Center and the Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
  • 2Department of Physics and Center for Theory of Quantum Matter, University of Colorado Boulder, Boulder, Colorado 80309, USA
  • 3Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA

  • *yzchou@umd.edu

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Issue

Vol. 101, Iss. 23 — 15 June 2020

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