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.

References in corpus (27)

• Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride
• Tunable Phase Boundaries and Ultra-Strong Coupling Superconductivity in Mirror Symmetric Magic-Angle Trilayer Graphene
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Single Layer Behavior and Its Breakdown in Twisted Graphene Layers
• Continuum Model of the Twisted Bilayer
• Lattice relaxation and energy band modulation in twisted bilayer graphenes
• Electric field tunable unconventional superconductivity in alternating twist magic-angle trilayer graphene
• Origin of band gaps in graphene on hexagonal boron nitride
• Electrical switching of magnetic order in an orbital Chern insulator
• Electrically tunable correlated and topological states in twisted monolayer-bilayer graphene
• Strain fields in twisted bilayer graphene
• $\Gamma$-Valley Transition-Metal-Dichalcogenide Moirè Bands
• Continuum models for twisted bilayer graphene: the effects of lattice deformation and hopping parameter
• Tunable van Hove Singularities and Correlated States in Twisted Trilayer Graphene
• Spontaneous Strains and Gap in Graphene on Boron Nitride
• Electronic structure of spontaneously strained graphene on hexagonal Boron Nitride
• General continuum model for twisted bilayer graphene and arbitrary smooth deformations
• Pseudo-magnetic fields, particle-hole asymmetry, and microscopic effective continuum Hamitonians of twisted bilayer graphene
• Continuum effective Hamiltonian for graphene bilayers for an arbitrary smooth lattice deformation from microscopic theories
• Mixing of surface and bulk electronic states at a graphite-hexagonal boron nitride interface
• Mixed-dimensional moiré systems of graphitic thin films with a twisted interface
• Full Slonczewski-Weiss-McClure parametrization of few-layer twistronic graphene
• Topological Flat Bands in Graphene Super-moiré Lattices
• Moiré patterns in graphene -- rhenium disulfide vertical heterostructures
• Revealing flat bands and hybridization gaps in a twisted bilayer graphene device with microARPES
• Moiré Superstructures in Marginally-Twisted NbSe${}_2$ Bilayers
• Dislocations in twistronic heterostructures

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