Generalized Kubo Formulas for the Transport Properties of Incommensurate 2D Atomic Heterostructures

Abstract

We give an exact formulation for the transport coefficients of incommensurate two-dimensional atomic multilayer systems in the tight-binding approximation. This formulation is based upon the C* algebra framework introduced by Bellissard and collaborators to study aperiodic solids (disordered crystals, quasicrystals, and amorphous materials), notably in the presence of magnetic fields (quantum Hall effect). We also present numerical approximations and test our methods on a one-dimensional incommensurate bilayer system.

References in corpus (4)

• The Kernel Polynomial Method
• Twistronics: Manipulating the Electronic Properties of Two-dimensional Layered Structures through their Twist Angle
• Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene
• Electronic Structure Theory of Weakly Interacting Bilayers

Cited by in corpus (21)

• Relaxation and Domain Formation in Incommensurate 2D Heterostructures
• Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene
• Moiré of Moiré: Modeling Mechanical Relaxation in Incommensurate Trilayer van der Waals Heterostructures
• Roadmap on Nonlocality in Photonic Materials and Metamaterials
• Linear response of twisted bilayer graphene: continuum vs. tight-binding models
• Energy minimization of 2D incommensurate heterostructures
• Topological Gaps by Twisting
• Disordered Crystals from First Principles I: Quantifying the Configuration Space
• Bistritzer-MacDonald dynamics in twisted bilayer graphene
• Low-energy moiré phonons in twisted bilayer van der Waals heterostructures
• Plane Wave Methods for Quantum Eigenvalue Problems of Incommensurate Systems
• Intrinsically-multilayer moiré heterostructures
• Disordered Crystals from First Principles II: Transport Coefficients
• Efficient Computation of Kubo Conductivity for Incommensurate 2D Heterostructures
• Chebyshev Polynomial Method to Landauer-Büttiker Formula of Quantum Transport in Nanostructures
• Moiré band theory for M-valley twisted transition metal dichalcogenides
• Quantization of Conductance in Quasi-Periodic Quantum Wires
• Energy Spectrum Theory of Incommensurate Systems
• Electronic Observables for Relaxed Bilayer 2D Heterostructures in Momentum Space
• Modeling and Computation of Kubo Conductivity for 2D Incommensurate Bilayers
• Incommensurate Heterostructures in Momentum Space