Atomistic Hartree theory of twisted double bilayer graphene near the magic angle

Abstract

Twisted double bilayer graphene (tDBLG) is a moiré material that has recently generated significant interest because of the observation of correlated phases near the magic angle. We carry out atomistic Hartree theory calculations to study the role of electron-electron interactions in the normal state. In contrast to twisted bilayer graphene (tBLG), we find that such interactions do not result in significant doping-dependent deformations of the electronic band structure. However, interactions play an important role for the electronic structure in the presence of a perpendicular electric field as they screen the external field. Finally, we analyze the contribution of the Hartree potential to the crystal field, i.e. the onsite energy difference between the inner and outer layers. We find that the onsite energy obtained from Hartree theory has the same sign, but a smaller magnitude compared to previous studies who determined the onsite energy by fitting tight-binding results to ab initio density-functional theory (DFT) band structures. To understand this quantitative difference, we analyze the ab initio Kohn-Sham potential obtained from DFT and find that a subtle interplay of electron-electron and electron-ion interactions determines the magnitude of the onsite potential.

Moiré modulation of charge density waves

“…) dr, (7) where g is the coupling constant between the CDWs [74]. Such a term is motivated from the electrostatic interactions between the two layers in a mean-field approximation (since a cosine charge density of one layer gives rise to a cosine electrostatic potential on the other layer [67,75]); a more rigorous approach would explicitly derive this interaction, and take into account screening and exchange, as done for graphene layers in [76].…”

Short Versus Long Range Exchange Interactions in Twisted Bilayer Graphene

“…[ 66,67 ] Moreover, these atomistic approaches can also include long‐ranged interactions, such as self‐consistent Hartree interactions. [ 68–73 ]…”

“…[66,67] Moreover, these atomistic approaches can also include long-ranged interactions, such as self-consistent Hartree interactions. [68][69][70][71][72][73] A significant limiting factor of self-consistent atomistic approaches for broken symmetry phases is their computational cost. [71,74,75] Some examples of such calculations exist in the literature, [71][72][73]76] but modeling of the full phase diagram -as function of twist angle and doping level, amongst other experimental variables -has not yet been achieved.…”