Angle-Dependent {\it Ab initio} Low-Energy Hamiltonians for a Relaxed Twisted Bilayer Graphene Heterostructure
arXiv:1908.00058
The paper develops efficient, angle‑dependent low‑energy Hamiltonians for relaxed twisted bilayer graphene by combining continuum elasticity, DFT‑based Wannier tight‑binding, and projection near the Dirac points, extracting intra‑layer pseudo‑gauge fields and inter‑layer coupling terms across a range of twist angles.
Abstract
We present efficient angle-dependent low-energy Hamiltonians to describe the properties of the twisted bilayer graphene (tBLG) heterostructure, based on {\it ab initio} calculations of mechanical relxation and electronic structure. The angle-dependent relaxed atomic geometry is determined by continuum elasticity theory, which induces both in-plane and out-of-plane deformations in the stacked graphene layers. The electronic properties corresponding to the deformed geometry are derived from a Wannier transformation to local interactions obtained from Density Functional Theory calculations. With these {\it ab initio} tight-binding Hamiltonians of the relaxed heterostructure, the low-energy effective theories are derived from the projections near Dirac cones at K valleys. For twist angles ranging from 0.7$^\circ$ to 4$^\circ$, we extract both the intra-layer pseudo-gauge fields and the inter-layer coupling terms in the low-energy Hamiltonians, which extend the conventional low-energy continuum models. We further include the momentum dependent inter-layer scattering terms which give rise to the particle-hole asymmetric features of the electronic structure. Our model Hamiltonians can serve as a starting point for formulating physically meaningful, accurate interacting electron theories.
12 pages, 6 figures, scripts available at https://github.com/stcarr/kp_tblg