Hartree theory calculations of quasiparticle properties in twisted bilayer graphene

Abstract

A detailed understanding of interacting electrons in twisted bilayer graphene (tBLG) near the magic angle is required to gain insights into the physical origin of the observed broken symmetry phases. Here, we present extensive atomistic Hartree theory calculations of the electronic properties of tBLG in the (semi-)metallic phase as function of doping and twist angle. Specifically, we calculate quasiparticle properties, such as the band structure, density of states (DOS) and local density of states (LDOS), which are directly accessible in photoemission and tunnelling spectroscopy experiments. We find that quasiparticle properties change significantly upon doping—an effect which is not captured by tight-binding theory. In particular, we observe that the partially occupied bands flatten significantly which enhances the density of states at the Fermi level. We predict a clear signature of this band flattening in the LDOS in the AB/BA regions of tBLG which can be tested in scanning tunneling experiments. We also study the dependence of quasiparticle properties on the dielectric environment of tBLG and discover that these properties are surprisingly robust as a consequence of the strong internal screening. Finally, we present a simple analytical expression for the Hartree potential which enables the determination of quasiparticle properties without the need for self-consistent calculations.

Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene

“…Figure 5 shows that the extra electron fill the flat states and align the Dirac point with the Fermi energy. Small modifications in the electronic band structure as a result of new electrostatic contributions is observed, similarly to other twisted multilayer systems [68][69][70][71].…”

Importance of long-ranged electron-electron interactions for the magnetic phase diagram of twisted bilayer graphene

“…where n j denotes the occupancy of the p z orbital on atom j and n is the average occupancy [48]. Also, W i j denotes the screened Coulomb interaction between electrons at τ i and τ j [49]. In principle, V (τ i ) must be determined self-consistently, but it has been shown [46,47,49] that the resulting potential is accurately described by…”

“…It is well known, however, that long-ranged interactions play an important role in tBLG. Using Hartree theory, several groups [46][47][48][49][50] demonstrated that long-ranged interactions result in significant changes of the electronic structure which depend sensitively on doping and twist angle. In particular, Hartree interactions result in a flattening of the doped bands (in addition to the band flattening induced by twisting) [26][27][28][29].…”

Correlation-driven topological phases in magic-angle twisted bilayer graphene

“…4a,c,e). This signals that the shape of dispersive pockets within the flat bands do not change significantly as flatter parts of the bands are deformed due to interactions 30,31 . Taken together, these observations put strict restrictions on the overall band structure of the MATBG and provide guidence for further theoretical modeling.…”

“…Some of the early observations in MATBG remain poorly understood-e.g., the appearance of four-fold degenerate LLs around charge neutrality 1 instead of eight-fold as expected from the presence of eight degenerate Dirac cones of the two stacked monolayers, and anomalously large bandwidth (∼ 40 meV) of the flat band [19][20][21][22] deviating from the 5 − 10 meV widths expected from continuum models 10 . This is largely due to difficulties in band structure calculations that incorporate all relevant effects such as electronic correlations [30][31][32] , strain 33 , and atomic reconstruction 34 . In particular, several mechanisms were proposed to explain the origin of four-fold LLs formed at charge neutrality 33,35,36 but to date there is no general consensus.…”