Analytical Model for Atomic Relaxation in Twisted Moiré Materials

Abstract

By virtue of being atomically thin, the electronic properties of heterostructures built from two-dimensional materials are strongly influenced by atomic relaxation. The atomic layers behave as flexible membranes rather than rigid crystals. Here we develop an analytical theory of lattice relaxation in twisted moiré materials. We obtain analytical results for the lattice displacements and corresponding pseudo gauge fields, as a function of twist angle. We benchmark our results for twisted bilayer graphene and twisted WSe${}_2$ bilayers using large-scale molecular dynamics simulations. Our \textit{single-parameter} theory is valid in graphene bilayers for twist angles $\theta \gtrsim 0.7^{\circ }$, and in twisted WSe${}_2$ for $\theta \gtrsim 1.6^{\circ }$. We also investigate how relaxation alters the electronic structure in twisted bilayer graphene, providing a simple extension to the continuum model to account for lattice relaxation.

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Cited by in corpus (15)

• Measuring Phonon Dispersion and Electron-Phason Coupling in Twisted Bilayer Graphene with a Cryogenic Quantum Twisting Microscope
• Visualizing the microscopic origins of topology in twisted molybdenum ditelluride
• Moiré optical phonons dancing with heavy electrons in magic-angle twisted bilayer graphene
• Analytical solution for the relaxed atomic configuration of twisted bilayer graphene including heterostrain
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Geometrical properties of strained and twisted moiré heterostructures
• Twisted bilayer graphene from first-principles: structural and electronic properties
• Wavefunction textures in twisted bilayer graphene from first principles
• Theory for Lattice Relaxation in Marginal Twist Moirés
• Charged moiré phonons in twisted bilayer graphene
• Superconducting order parameter in aperiodic binary systems
• Buckling and flat bands in twisted bilayer graphene
• Relaxation and Its Effects on Electronic Structure in Twisted Systems: An Analytical Perspective
• Randomly twisted bilayer graphene -- the cascade transitions
• Straintronics and twistronics in bilayer graphene