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Origin of Magic Angles in Twisted Bilayer Graphene

Grigory Tarnopolsky, Alex Jura Kruchkov, and Ashvin Vishwanath
Phys. Rev. Lett. 122, 106405 – Published 15 March 2019

Abstract

Twisted bilayer graphene (TBG) was recently shown to host superconductivity when tuned to special “magic angles” at which isolated and relatively flat bands appear. However, until now the origin of the magic angles and their irregular pattern have remained a mystery. Here we report on a fundamental continuum model for TBG which features not just the vanishing of the Fermi velocity, but also the perfect flattening of the entire lowest band. When parametrized in terms of α1/θ, the magic angles recur with a remarkable periodicity of Δα3/2. We show analytically that the exactly flat band wave functions can be constructed from the doubly periodic functions composed of ratios of theta functions—reminiscent of quantum Hall wave functions on the torus. We further report on the unusual robustness of the experimentally relevant first magic angle, address its properties analytically, and discuss how lattice relaxation effects help justify our model parameters.

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  • Received 24 November 2018
  • Corrected 16 May 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.106405

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Corrections

16 May 2019

Correction: The author contribution statement has been removed at the request of the authors.

Authors & Affiliations

Grigory Tarnopolsky, Alex Jura Kruchkov*, and Ashvin Vishwanath

  • Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

  • *akruchkov@g.harvard.edu

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Issue

Vol. 122, Iss. 10 — 15 March 2019

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