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

Abstract

Electron-electron interactions are intrinsically long ranged, but many models of strongly interacting electrons only take short-ranged interactions into account. Here, we present results of atomistic calculations including both long-ranged and short-ranged electron-electron interactions for the magnetic phase diagram of twisted bilayer graphene and demonstrate that qualitatively different results are obtained when long-ranged interactions are neglected. In particular, we use Hartree theory augmented with Hubbard interactions and calculate the interacting spin susceptibility at a range of doping levels and twist angles near the first magic angle to identify the dominant magnetic instabilities. At the magic angle, mostly antiferromagnetic order is found, while ferromagnetism dominates at other twist angles. Moreover, long-ranged interactions significantly increase the twist angle window in which strong correlation phenomena can be expected. These findings are in good agreement with available experimental data.

Flat bands, electron interactions and magnetic order in magic-angle mono-trilayer graphene

“…In the upper layers the magnetization has peaks in the AABC regions which are separated by a node. A similar state has been found in tBLG [65,105]. Finally, Figs.…”

“…Moreover, in Ref. 105, it was shown that U = 4 eV for tBLG yields good agreement with the available experimental data. For additional details about the method, see Sec.…”

“…As a consequence of screening, the range of the exchange interaction is significantly reduced and we therefore an atomic Hubbard interaction for electrons in the carbon p z -orbitals [64-68, 83, 105] and calculate the interacting spin susceptibility using the random-phase approximation (RPA) as function of doping, twist angle and value of the Hubbard U parameter. From these results, we identify the critical value of the Hubbard parameter U c at which the susceptibility diverges [65,105]. If U c is smaller than the physical value of the Hubbard parameter, we expect the system to undergo a phase transition into a magnetically ordered state whose spatial structure is determined by the leading eigenvector of the spin response function.…”

Electrostatic interactions in twisted bilayer graphene

“…These results suggest that the valleys remain decoupled. Interactions at the atomic scale, will favor a phase in which the two sublattices have equal occupation, over the phase where all the charge resides in the same sublattice [50][51][52][53]. Finally, the zeroth point energy of excitations above the Hartree-Fock solutions discussed here can also favor specific combinations of wavefunctions of the type shown in Eq.…”

Magnetism of magic-angle twisted bilayer graphene

“…However, other factors may also be relevant in an experiment such as strain when the bilayer is deposited on a substrate. In the same spirit, Coulomb interactions should actually be long-range [60], at least for free-standing bilayers, since atomically thin layers cannot screen the Coulomb repulsion between electrons. Still, screening will depend on the actual substrate and may thus depend on the exact experimental conditions.…”