Electronic Structure Theory of Strained Two-Dimensional Materials with Hexagonal Symmetry

TL;DR

This paper develops detailed tight-binding models for strained two-dimensional hexagonal materials like graphene and transition metal dichalcogenides, incorporating strain effects beyond simple pair-wise interactions, to aid electronic device design and quantum physics exploration.

Contribution

It introduces ab initio derived, symmetry-respecting tight-binding Hamiltonians for strained hexagonal 2D materials, including strain effects beyond the central force approximation.

Findings

Models include strain effects respecting hexagonal symmetry.

Provides coefficients for symmetry-allowed terms in low-energy Hamiltonians.

Framework for coupling electrons to phonons, spins, and electromagnetic fields.

Abstract

We derive electronic tight-binding Hamiltonians for strained graphene, hexagonal boron nitride and transition metal dichalcogenides based on Wannier transformation of {\it ab initio} density functional theory calculations. Our microscopic models include strain effects to leading order that respect the hexagonal crystal symmetry and local crystal configuration, and are beyond the central force approximation which assumes only pair-wise distance dependence. Based on these models, we also derive and analyze the effective low-energy Hamiltonians. Our {\it ab initio} approaches complement the symmetry group representation construction for such effective low-energy Hamiltonians and provide the values of the coefficients for each symmetry-allowed term. These models are relevant for the design of electronic device applications, since they provide the framework for describing the coupling of electrons to other degrees of freedom including phonons, spin and the electromagnetic field. The models can also serve as the basis for exploring the physics of many-body systems of interesting quantum phases.