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 language | English (US) |
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Pages (from-to) | 6175-6180 |
Number of pages | 6 |
Journal | Nano letters |
Volume | 18 |
Issue number | 10 |
DOIs | |
State | Published - Oct 10 2018 |
Keywords
- Bilayer graphene
- Mott insulator
- Wigner crystal
- magic angle
- superconductivity
ASJC Scopus subject areas
- Bioengineering
- General Chemistry
- General Materials Science
- Condensed Matter Physics
- Mechanical Engineering