Hybrid-functional electronic structure of multilayer graphene

Abstract

Multilayer graphene with rhombohedral and Bernal stacking is supposed to be metallic, as predicted by density functional theory calculations using semilocal functionals. However, recent angular resolved photoemission and transport data have questioned this point of view. In particular, rhombohedral flakes are suggested to be magnetic insulators, a view supported also by hybrid-functional calculations. Bernal flakes composed of an even number of layers are insulating (for N 6), while those composed of an odd number of layers are pseudogapped (for N 7). Here, by systematically benchmarking with plane-waves codes, we develop very accurate all-electron Gaussian basis sets for graphene multilayers, allowing a precise description of the electronic structure in the 100 meV energy range from the Fermi energy at the hybrid-functional level. We find, in agreement with our previous calculations, that rhombohedral stacked multilayers are gapped and magnetic. However, the valence band curvature and the details of the electronic structure at the ∼10 meV scale show a dependence on the basis set. A substantially extended basis set is needed to describe the long-range interlayer interactions and, consequently, to correctly reproduce the effective mass of the valence band top at the K point. In the case of Bernal stacking, we show that exact exchange gaps the flakes composed by four layers and opens pseudogaps for N = 3, 6, 7, 8. However, the gap or pseudogap size and its behavior as a function of thickness are not compatible with experimental data. Moreover, hybrid functionals lead to a metallic solution for five layers and a magnetic ground state for five, six, and eight layers. Magnetism is very weak with practically no effect on the electronic structure and the magnetic moments are mostly concentrated in the central layers. Our hybridfunctional calculations on trilayer Bernal graphene are in excellent agreement with GW results. For thicker multilayers, our calculations are a benchmark for many-body theoretical modeling of the low energy electronic structure.

Gate-induced half-metals in Bernal stacked graphene multilayer

“…When the electron-electron interaction is considered, our calculation suggests that the onsite Coulomb repulsion can induce a gapped SDW-like ground state with antiferromagnetic spin order. It is in good agreement with the recent DFT calculation 51 . The corresponding spin structure is shown in Fig.…”

“…More importantly, a recent first principle calculations suggest that the correlated ground states of the BGMs also can host an antiferromagnetic spin order 51 , similar as the LAF states in the RGMs. Therefore, a natural question is that if the BGMs can be induced into a half metallic ferromagnetic state via applying electric field and doping.…”

Clarifying the apparent flattening of the graphene band near the van Hove singularity

“…Therefore, the presence of such DOS singularity is the source for strong electronic instabilities able to open a gap near E F , possibly developing a new symmetry breaking ground state. Those instabilities can drive the system to develop magnetic orders [2][3][4][5][6][7][8][9], superconducting states [1,5,[10][11][12][13], or charge density wave phases [5].…”

“…The strategies to get DOS singularity are many, and graphene holds an enormous potential in this field. It emerges from graphene moiré physics at magic angles in connection with a flat band originating from Dirac band hybridization in a bilayer system, as in twisted graphene bilayers [1,[13][14][15] or in epitaxial multilayer graphene [6,9,[16][17][18][19][20]. In addition, a DOS singularity is already present in the band structure of graphene at a saddle point in the unoccupied energy region far from the Dirac point (neutrality), known as the van Hove singularity (VHS) [21].…”

Can the "shadow" of graphene band clarify its flatness?

“…The strategies to get DOS singularity are many, and graphene holds enormous potential in this field. It emerges from graphene Moiré physics at magic angles in connection with a flat band originated by Dirac bands hybridization in bilayer system, as in twisted graphene bilayers [1,[13][14][15] or in epitaxial multilayer graphene [6,9,[16][17][18][19][20]. In addition, a DOS singularity is already present in the band structure of graphene at a saddle point in the unoccupied energy region far from the Dirac point (neutrality), known as van Hove singularity (VHS) [21].…”