Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation.
basic_science · Level V
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- Record sourced from PubMed, PMID 30185049.
- Also identified by DOI 10.1021/acs.nanolett.8b02033.
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Abstract
We devise a model to explain why twisted bilayer graphene exhibits insulating behavior when ν = 2 or 3 charges occupy a unit moiré cell, a feature attributed to Mottness per previous work but not for ν = 1, clearly inconsistent with Mott insulation. We compute r<sub>s</sub> = E<sub>U</sub>/ E<sub>K</sub>, where E<sub>U</sub> and E<sub>K</sub> 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 10<sup>4</sup> and (ii) a transition to a series of Wigner crystalline states exists as a function of ν. We find that, for ν = 1, r<sub>s</sub> fails to cross the threshold ( r<sub>s</sub> = 37) for the triangular lattice, and metallic transport ensues. However, for ν = 2 and ν = 3, the thresholds r<sub>s</sub> = 22 and r<sub>s</sub> = 17, respectively, are satisfied for a transition to Wigner crystals (WCs) with a honeycomb (ν = 2) and a kagome (ν = 3) structure. We posit that such crystalline states form the correct starting point for analyzing superconductivity.