Pressure-Induced Metal-Insulator Transition in Twisted Bi-layer Graphene

TL;DR

This paper investigates how hydrostatic pressure induces a metal-insulator transition in twisted bilayer graphene, revealing a Wigner crystal phase and predicting a dome-shaped pressure dependence of insulating states.

Contribution

It demonstrates that pressure tuning can induce Wigner crystallization in TBLG, providing a new understanding of insulating states beyond Mott physics and predicting a pressure-dependent phase diagram.

Findings

Insulating states at quarter, two, and three charges per supercell are enhanced under pressure.

The ratio of potential to kinetic energy crosses the Wigner crystallization threshold within a specific pressure window.

The pressure window for Wigner states has a dome shape, peaking around 1.5 GPa.

Abstract

Recent experiments [arXiv: 1808.07865] on twisted bilayer graphene (TBLG) show that under hydrostatic pressure, an insulating state at quarter-filling of the moir\'e superlattice (i.e., one charge per supercell) emerges, in sharp contrast with the previous ambient pressure measurements of Cao et al. where the quarter--filling state (QFS) is a metal [Nature 556, 43 & 80 (2018)]. In fact, the insulating state at the other commensurate fillings of two and three charges per supercell is also enhanced under applied pressure. Based on realistic computations of the band structure for TBLG which show that the bandwidth first shrinks and then expands with increasing hydrostatic pressure, we compute the ratio of the potential to the kinetic energy, $r_s$. We find an experimentally relevant window of pressure for which $r_s$ crosses the threshold for a triangular Wigner crystal, thereby corroborating our previous work [Nano Lett. (2018)] that the insulating states in TBLG are due to Wigner rather than Mott physics. A key prediction of this work is that the window for the onset of the hierarchy of Wigner states that obtains at commensurate fillings is dome-shaped as a function of the applied pressure, which can be probed experimentally. Theoretically, we find a peak for crystallization around $1.5$ GPa relative to the experimental optimal pressure of $1.33$ GPa for the observation of the insulating states. Consequently, TBLG provides a new platform for the exploration of Wigner physics and its relationship with superconductivity.