Origin of Magic Angles in Twisted Bilayer Graphene
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 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.
- Authors:
-
- Harvard Univ., Cambridge, MA (United States)
- Publication Date:
- Research Org.:
- Harvard Univ., Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1610984
- Alternate Identifier(s):
- OSTI ID: 1513050
- Grant/Contract Number:
- SC0007870; de-sc0007870
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 122; Journal Issue: 10; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Physics; Bilayers; Electronic structure; Graphene; Superconductors; Superlattices
Citation Formats
Tarnopolsky, Grigory, Kruchkov, Alex Jura, and Vishwanath, Ashvin. Origin of Magic Angles in Twisted Bilayer Graphene. United States: N. p., 2019.
Web. doi:10.1103/physrevlett.122.106405.
Tarnopolsky, Grigory, Kruchkov, Alex Jura, & Vishwanath, Ashvin. Origin of Magic Angles in Twisted Bilayer Graphene. United States. https://doi.org/10.1103/physrevlett.122.106405
Tarnopolsky, Grigory, Kruchkov, Alex Jura, and Vishwanath, Ashvin. Fri .
"Origin of Magic Angles in Twisted Bilayer Graphene". United States. https://doi.org/10.1103/physrevlett.122.106405. https://www.osti.gov/servlets/purl/1610984.
@article{osti_1610984,
title = {Origin of Magic Angles in Twisted Bilayer Graphene},
author = {Tarnopolsky, Grigory and Kruchkov, Alex Jura and Vishwanath, Ashvin},
abstractNote = {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.},
doi = {10.1103/physrevlett.122.106405},
journal = {Physical Review Letters},
number = 10,
volume = 122,
place = {United States},
year = {Fri Mar 15 00:00:00 EDT 2019},
month = {Fri Mar 15 00:00:00 EDT 2019}
}
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