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

Bikash Padhi; Chandan Setty; Philip W. Phillips

doi:10.1021/acs.nanolett.8b02033

paper

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

arXiv:1804.01101 · doi:10.1021/acs.nanolett.8b02033

Abstract

We devise a model to explain why twisted bi-layer graphene (TBLG) exhibits insulating behavior when $ν = 2, 3$ charges occupy a unit moiré cell, a feature attributed to Mottness, but not for $ν = 1$ , clearly inconsistent with Mott insulation. We compute $r_{s} = E_{U} / E_{K}$ , where $E_{U}$ and $E_{K}$ are the potential and kinetic energies, respectively, and show that (i) the Mott criterion lies at a density $1 0^{4}$ higher than in the experiments and (ii) a transition to a series of Wigner crystalline states exists as a function of $ν$ . We find, for $ν = 1$ , $r_{s}$ fails to cross the threshold ( $r_{s} = 37$ ) for the triangular lattice and metallic transport ensues. However, for $ν = 2$ and $ν = 3$ , the thresholds, $r_{s} = 22$ , and $r_{s} = 17$ , respectively are satisfied for a transition to Wigner crystals (WCs) with a honeycomb ( $ν = 2$ ) and kagome ( $ν = 3$ ) structure. We believe, such crystalline states form the correct starting point for analyzing superconductivity.

Version accepted in Nano Letters

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

Abstract

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