Twisted Bilayer Graphene Exhibits Weak Localization and Universal Conductance Fluctuations at 7° and 9° Twist Angles

The unusual electronic properties of twisted bilayer graphene continue to reveal surprising behaviour, and a team led by Spenser Talkington and Debarghya Mallick, from the University of Pennsylvania and Oak Ridge National Laboratory respectively, now reports the first observation of weak localization within this material. Working with large-area samples and varying the twist angle, the researchers demonstrate that electrons within the graphene exhibit interference effects, allowing them to determine the factors limiting how far these electrons travel before losing coherence. This achievement, which also includes contributions from An-Hsi Chen, Benjamin F. Mead, Seong-Jun Yang, and Cheol-Joo Kim, provides crucial insight into the fundamental mechanisms governing electron behaviour in twisted bilayer graphene and opens exciting possibilities for exploiting these quantum effects in future devices. The team’s findings further reveal signatures of universal conductance fluctuations, indicating the high quality of their samples and paving the way for more detailed investigations of interference phenomena within this complex material.

Graphene’s Quantum Interference and Conductance Fluctuations

Researchers investigating large area twisted bilayer graphene have observed weak localisation and universal conductance fluctuations, quantum interference effects arising from electrons scattering off imperfections within the material. This study focuses on twisted bilayer graphene, where two graphene layers are stacked with a slight rotation, creating a unique electronic structure and potentially hosting correlated electron behaviour. By fabricating large samples and performing low temperature transport measurements, the team meticulously characterised electron behaviour, revealing these quantum phenomena. Scientists studied highly p-doped, large area twisted bilayer graphene samples, varying the twist angle from 1° to 20°, including samples near a specific energy point in the material’s band structure. The team reports the first observation of weak localisation in twisted bilayer graphene, a phenomenon present in all tested samples.

TBG Calculations, Data, and Magnetoresistance Measurements

This document provides supplementary information detailing the methods and data used in a study of twisted bilayer graphene. It offers a comprehensive overview of the theoretical modelling, computational details, and experimental data analysis, allowing for verification of the research findings and a deeper understanding of the underlying physics.

The document includes raw magnetoresistance data for samples with varying twist angles, enabling independent verification of the data processing and analysis. It also details a tight-binding model used to calculate the density of states in twisted bilayer graphene, specifying the parameters and computational methods employed. A table lists calculated energies associated with specific points in the material’s electronic structure for various twist angles, crucial for understanding its electronic and transport properties.

The tight-binding model utilises a Slater-Koster approach, considering interactions between carbon atoms through p and s orbitals. The model incorporates hopping terms that describe the interaction between these orbitals, and specific parameters define the strength of these interactions. The Dirac point, a key feature of graphene’s electronic structure, is calculated and adjusted within the model. Atomic positions are determined by rotating two honeycomb lattices, and a computational mesh is used to calculate the density of states. The chemical potential, representing the energy level of electrons, is determined by integrating the density of states, and uncertainties in the data are estimated based on variations in the twist angle.

Key concepts include twisted bilayer graphene, where two graphene layers are stacked with a relative twist angle, significantly altering its electronic properties. The tight-binding model is a computational method used to approximate the electronic structure of materials, and the density of states represents the number of available electronic states at a given energy. Van Hove singularities are points where the density of states diverges, leading to enhanced electronic and optical properties. The Hall effect is a phenomenon used to determine the carrier density and type in a material.

Weak Localization in Twisted Bilayer Graphene

This research demonstrates the first observation of weak localisation and universal conductance fluctuations within twisted bilayer graphene. By fabricating large-area samples with substantial p-doping, scientists observed these mesoscopic quantum coherence phenomena, previously seen in other graphene systems but challenging to detect in twisted bilayers. The team attributes the observed dephasing to electron-electron scattering and intervalley scattering caused by defects, providing insight into the mechanisms governing electron behaviour within the material.

The achievement overcomes limitations of previous studies, which were hampered by small sample sizes, insulating states, or insufficient doping. The developed fabrication technique, utilising a refined transfer process, is scalable and opens possibilities for future device applications and optical studies, including investigations of low-lying electronic excitations using terahertz spectroscopy. While the current work identifies defects as contributing to intervalley scattering, the authors acknowledge that further improvements in sample quality could allow for exploration of purely electronically-tuned physics and phenomena like weak anti-localisation in larger angle twisted bilayer graphene.