Origin of Magic Angles in Twisted Bilayer Graphene

Tarnopolsky, Grigory; Kruchkov, Alex Jura; Vishwanath, Ashvin

doi:10.1103/physrevlett.122.106405

Title: Origin of Magic Angles in Twisted Bilayer Graphene

Journal Article · Fri Mar 15 00:00:00 EDT 2019 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.122.106405· OSTI ID:1610984

Tarnopolsky, Grigory ^[1]; Kruchkov, Alex Jura ^[1]; Vishwanath, Ashvin ^[1]

Harvard Univ., Cambridge, MA (United States)

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 α ~ 1/θ, the magic angles recur with a remarkable periodicity of Δα ≃ 3/2. 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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Research Organization:: Harvard Univ., Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0007870; de-sc0007870

OSTI ID:: 1610984

Alternate ID(s):: OSTI ID: 1513050

Journal Information:: Physical Review Letters, Vol. 122, Issue 10; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 299 works

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Title: Origin of Magic Angles in Twisted Bilayer Graphene

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