Strain-induced 4-fold Degeneracy Splitting in Twisted Bilayer Graphene Enables Quantum Correlation Studies

Twisted bilayer graphene, a material celebrated for its potential in superconductivity and correlated electron physics, exhibits remarkably sensitive behaviour under even slight distortions, and researchers are now revealing how these distortions fundamentally alter its properties. Lorenzo Crippa, Gautam Rai, and colleagues from the University of Hamburg, alongside collaborators including Jonah Herzog-Arbeitman and B. Andrei Bernevig from Princeton University, investigate the impact of strain and lattice relaxation on the material’s electronic structure. Their work demonstrates that these subtle changes split the material’s key energy bands and break fundamental symmetries, leading to a much better understanding of experimental observations, including scanning tunneling microscopy data and entropy measurements. This research successfully explains previously puzzling features in the material’s behaviour and provides a pathway to controlling and optimising its correlated electron properties for future technological applications.

DMFT-QMC Calculations of Correlated Electrons

Researchers employed a sophisticated technique combining Dynamical Mean-Field Theory and Quantum Monte Carlo to accurately model strongly interacting electrons in twisted bilayer graphene and similar materials. The study focuses on calculating entropy, analyzing the spectral function, and determining the chemical potential, all crucial for understanding the material’s electronic properties, accompanied by a rigorous error analysis to ensure reliability. The entropy, a measure of disorder, is calculated by examining how the chemical potential changes with temperature, with careful consideration given to potential errors. The spectral function, describing the probability of adding or removing an electron with a specific energy, was analyzed at key points within the material’s electronic structure to identify features like flat bands and compare findings with experimental data.

Determining the chemical potential, which dictates the number of electrons in the system, is achieved through an iterative process within the DMFT-QMC framework, with meticulous propagation of uncertainties from all sources. This detailed calculation of entropy provides insights into the thermodynamic properties of the system and the number of available electronic states, contributing to a deeper understanding of correlated electron behavior. This work demonstrates the power of advanced computational techniques in unraveling the complex behavior of correlated electron systems, with comparison to experimental data confirming the validity of the theoretical model.

Lattice Effects on Twisted Bilayer Graphene Bands

This study investigates how subtle changes in the material’s structure, specifically heterostrain and lattice relaxation, affect the electronic properties of magic-angle twisted bilayer graphene. Researchers applied theoretical modelling to a topological heavy fermion model, successfully reproducing several experimentally observed features, and discovered that heterostrain splits the eight-fold degenerate flat bands into two four-fold degenerate subsets, directly impacting the system’s electronic structure. Furthermore, lattice relaxation breaks the inherent particle-hole symmetry of the unperturbed model, significantly altering the behavior of electrons. To account for these structural effects, the team incorporated first-order perturbation theory into the heavy fermion model, utilizing data from detailed ab initio calculations, resulting in a modified Hamiltonian that includes corrections representing strain and non-local tunneling terms.

Specifically, the introduction of orbital-dependent chemical potential terms shifted the energy levels of different electrons relative to each other, inducing a splitting of approximately 7 meV in the flat-band manifold with applied uniaxial strain. The resulting interacting problem was solved using charge self-consistent dynamical mean-field theory, assuming a screened interaction and performing an all-order treatment of local interactions. Calculations performed at temperatures above 11. 6K closely reproduce experimental data obtained through scanning tunneling microscopy and quantum twisting microscopy, including cascade transitions and charge sector freezing, providing a comprehensive understanding of correlated electron behavior.

Heterostrain and Relaxation Tune Graphene’s Flat Bands

This work presents a detailed theoretical study of magic-angle twisted bilayer graphene, incorporating the effects of both heterostrain and lattice relaxation on correlated electron physics. Researchers applied dynamical mean-field theory to a topological heavy fermion model, successfully reproducing several experimentally observed features, and discovered that heterostrain splits the eight-fold degenerate flat bands into two four-fold degenerate subsets, directly impacting the system’s electronic structure. Furthermore, lattice relaxation breaks the particle-hole symmetry inherent in the unperturbed model, significantly altering the behavior of electrons. Experiments reveal a filling-independent maximum in the spectral density, consistently appearing at approximately 10 meV away from zero bias, mirroring results obtained through scanning tunneling microscopy and quantum twisting microscopy.

Measurements also demonstrate an overall reduction in both the size and degeneracy of local moments as temperature decreases, aligning with entropy measurements and confirming a transition from an eight-fold to a four-fold degenerate local moment state. The absence of particle-hole symmetry leads to a stronger suppression of local moments on the hole-doped side compared to the electron-doped side, ultimately influencing the stability and existence of correlated phases at different doping levels. The study confirms that fine-level structures present in experimental data can now be accurately reproduced and understood through this theoretical framework. Specifically, lattice relaxation causes the upper flat band to become more dispersive than the lower flat bands, a crucial detail for accurately modeling the system’s behavior, providing a comprehensive understanding of the interplay between lattice symmetries, electronic correlations, and the resulting low-temperature phases.

Strain Controls Correlated Electron Physics

This research demonstrates how subtle structural effects, specifically heterostrain and lattice relaxation, profoundly influence the correlated electron physics of magic-angle twisted bilayer materials. By applying theoretical modelling to a topological heavy fermion model, scientists have successfully explained several experimentally observed features, including a filling-independent maximum in the spectral density and the reduction in local moment size with decreasing temperature, aligning with both scanning tunneling microscopy and entropy measurements. The team’s work reveals that strain splits the flat bands into subsets, with only one becoming active depending on whether the material is electron or hole-doped, and this mechanism accounts for persistent features observed in experiments. Furthermore, the study clarifies the role of lattice relaxation in breaking particle-hole symmetry, leading to a stronger suppression of local moments on the hole-doped side compared to the electron-doped side. This asymmetry explains differences in the stability of correlated phases depending on doping, and accurately reproduces the observed variations in charge compressibility, a feature previously missing from theoretical models. These findings establish a clear link between structural details and electronic behaviour, offering a pathway towards controlling and optimizing the properties of these complex materials, highlighting the importance of considering subtle structural effects when investigating the fascinating physics of twisted bilayer graphene.