Weak localization and universal conductance fluctuations in large area twisted bilayer graphene

TL;DR

This work investigates diffusive magnetotransport in large-area, heavily p-doped twisted bilayer graphene across twist angles spanning Dirac-like to near the van Hove singularity. The authors employ macroscopic TBG devices and HLN analysis to reveal weak localization, extracting the phase coherence length $L_\phi$ and intervalley scattering length $L_\u0011iv$, with dephasing governed by electron-electron interactions and intervalley scattering driven by point defects. They also report universal conductance fluctuations in the 9° sample near the vHs, demonstrating mesoscopic quantum interference in a moiré system. The results show that scalable fabrication of large-area TBG enables observation of quantum interference phenomena and point toward future high-quality samples to explore richer regimes such as weak anti-localization in large-angle, valley-preserved contexts.

Abstract

We study diffusive magnetotransport in highly p-doped large area twisted bilayer graphene samples as a function of twist angle, crossing from 1° (below), to 20° (above) the van Hove singularity with 7° and 9° samples near the van Hove singularity. We report weak localization in twisted bilayer graphene for the first time. All samples exhibit weak localization, from which we extract the phase coherence length and intervalley scattering lengths, and from that determine that dephasing is caused by electron-electron scattering and intervalley scattering is caused by point defects. We observe signatures of universal conductance fluctuations in the 9° sample, which has high mobility and is near the van Hove singularity. Further improvements in sample quality and applications to large area moire materials will open new avenues to observe quantum interference effects.

Figures (4)

• Figure 1: Crossing the van Hove singularity in doped twisted bilayer graphene: the $1^\circ$ sample (green) is deep in the multiband regime, the $7^\circ$ (purple) and $9^\circ$ (blue) samples are near the van Hove singularity, and the $20^\circ$ (orange) sample is deep in the Dirac regime. The twist angle uncertainty is estimated to be $1.5^\circ$. (a) Sample twist and chemical potential plotted with regimes in red and blue with the phase boundary determined from the first van Hove singularity of a tight-binding model. (b) Hall effect measurements at $20~\mathrm{K}$ (colored), linear fits (dotted), and extracted hole densities in $10^{13} /\mathrm{cm}^{2}$. (c) Density of states and chemical potential from fitting hole densities to the tight-binding model density of states.
• Figure 2: Weak localization in twisted bilayer graphene. (a) Twist-angle and temperature dependent magnetoconductivity (MC) plotted against dimensionless magnetic field $\mu_h B$. Note the pronounced weak-localization peak around zero field. The $20^\circ$ sample has low mobility and low MC which is multiplied by 10 to plot on the same axes as the other samples. (b) Quantum contribution to the MC obtained by subtracting the classical Drude term from the total MC; data are fitted (dotted black lines) by the Hikami-Larkin-Nagaoka (HLN) formula for quantum contribution to the MC. (c) Phase coherence length from the HLN fit; power law scaling between $-0.5$ and $-1$ indicates electron-electron scattering is the main mechanism for phase decoherence. (d) Intervalley scattering length from the HLN fit; the roughly temperature independent length suggests that intervalley scattering is caused by point defects in the lattice.
• Figure 3: Universal conductance fluctuations in the $9^\circ$ twisted bilayer graphene sample. (a) Total magnetoconductivity (MC) for two separate runs on the same sample. (b) Quantum MC obtained by subtracting classical Drude MC. (c) The magnitude of fluctuations is on the scale of the universal conductance $(e^2/h)^2$ and falls off with the phase coherence length $L_\phi$.
• Figure 4: Raw magnetoresistance data. The color bar scale is the same as in the main text, where dark blue is 2 K and dark red is 110 K. Note that the difference between $9^\circ$ Run A and Run B is less than 0.5% and is not visible until the classical magnetoresistance is subtracted as we do in the main text.