Constrained random phase approximation of the effective Coulomb interaction in lattice models of twisted bilayer graphene
Abstract
Recent experiments on twisted bilayer graphene show the urgent need for establishing a lowenergy lattice model for the system. We use the constrained random phase approximation to study the interaction parameters of such models, taking into account screening from the moiré bands left outside the model space. Based on an atomicscale tightbinding model, we numerically compute the polarization function and study its behavior for different twist angles. We discuss an approximation scheme which allows us to compute the screened interaction, in spite of the very large number of atoms in the unit cell. We find that the polarization has three different momentum regimes. For small momenta, the polarization is quadratic, leading to a linear dielectric function expected for a twodimensional dielectric material. For large momenta, the polarization becomes independent of the twist angle and approaches that of uncoupled graphene layers. In the intermediatemomentum regime, the dependence on the twist angle is strong. Close to the largest magic angle the dielectric function peaks at a momentum of 1 /(4 nm) , attaining values of 1825, depending on the exact model, meaning very strong screening at intermediate distances. We also calculate the effective screened Coulomb interaction in real space and give estimates for the onsite and extended interaction terms for the recently developed hexagonallattice model. For freestanding twisted bilayer graphene, the effective interaction decays slower than 1 /r at intermediate distances r , while it remains essentially unscreened at large enough r .
 Publication:

Physical Review B
 Pub Date:
 July 2020
 DOI:
 10.1103/PhysRevB.102.035154
 arXiv:
 arXiv:1909.09556
 Bibcode:
 2020PhRvB.102c5154V
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 Phys. Rev. B 102, 035154 (2020)