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

TL;DR

This paper proposes that insulating states in twisted bilayer graphene near magic angles are due to Wigner crystallization rather than Mott insulators, based on energy calculations and threshold criteria.

Contribution

It introduces a model showing Wigner crystallization explains insulating behavior in TBLG at certain fillings, challenging the Mott insulator explanation.

Findings

Wigner crystal states are predicted at ν=2 and 3, but not at ν=1.

The Mott criterion does not match experimental densities.

Transition thresholds for Wigner crystallization are identified.

Abstract

We devise a model to explain why twisted bi-layer graphene (TBLG) exhibits insulating behavior when $\nu=2,3$ charges occupy a unit moir\'e cell, a feature attributed to Mottness, but not for $\nu=1$, 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 $10^4$ higher than in the experiments and (ii) a transition to a series of Wigner crystalline states exists as a function of $\nu$. We find, for $\nu=1$, $r_s$ fails to cross the threshold ($r_s = 37$) for the triangular lattice and metallic transport ensues. However, for $\nu=2$ and $\nu=3$, the thresholds, $r_s=22$, and $r_s=17$, respectively are satisfied for a transition to Wigner crystals (WCs) with a honeycomb ($\nu=2$) and kagome ($\nu=3$) structure. We believe, such crystalline states form the correct starting point for analyzing superconductivity.