Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation

Bikash Padhi, Chandan Setty, Philip W. Phillips

Research output: Contribution to journalArticlepeer-review

Abstract

We devise a model to explain why twisted bilayer graphene exhibits insulating behavior when Î = 2 or 3 charges occupy a unit moiré cell, a feature attributed to Mottness per previous work but not for Î = 1, clearly inconsistent with Mott insulation. We compute rs = EU/EK, where EU and EK are the potential and kinetic energies, respectively, and show that (i) the Mott criterion lies at a density larger than experimental values by a factor of 104 and (ii) a transition to a series of Wigner crystalline states exists as a function of Î. We find that, for Î = 1, rs fails to cross the threshold (rs = 37) for the triangular lattice, and metallic transport ensues. However, for Î = 2 and Î = 3, the thresholds rs = 22 and rs = 17, respectively, are satisfied for a transition to Wigner crystals (WCs) with a honeycomb (Î = 2) and a kagome (Î = 3) structure. We posit that such crystalline states form the correct starting point for analyzing superconductivity.

Original languageEnglish (US)
Pages (from-to)6175-6180
Number of pages6
JournalNano letters
Volume18
Issue number10
DOIs
StatePublished - Oct 10 2018

Keywords

  • Bilayer graphene
  • Mott insulator
  • Wigner crystal
  • magic angle
  • superconductivity

ASJC Scopus subject areas

  • Bioengineering
  • Chemistry(all)
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanical Engineering

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