Stacking order, interaction, and weak surface magnetism in layered graphene sheets

Abstract

Recent transport experiments have demonstrated that the rhombohedral stacking trilayer graphene is an insulator with an intrinsic gap of 6meV and the Bernal stacking trilayer one is a metal. We propose a Hubbard model with a moderate U for layered graphene sheets, and show that the model well explains the experiments of the stacking dependent energy gap. The on-site Coulomb repulsion drives the metallic phase of the non-interacting system to a weak surface antiferromagnetic insulator for the rhombohedral stacking layers, but does not alter the metallic phase for the Bernal stacking layers.

Flat band electrons and interactions in rhombohedral trilayer graphene

“…The calculated coefficients of the onsite Coulomb repulsion have values of 2-5 eV with an estimated effective dielectric constant = 2 in graphene systems, which are consistent with the parameter range in a mean-field analysis 18 for the experimentally observed energy gap. 41,42 We also note that the long-range interaction terms of up to the fifth nearest neighbors (rows 1-3) have a magnitude comparable to the on-site terms, indicating that the effective interaction range could be much longer than the usual screened interaction treatments with up to nearest or next-to-nearest neighbors.…”

“…44 At low temperature, the ferromagnetic order among two-dimensional cell spins could be detectable using a magnetic scanning probe microscopy technique, such as magnetic force microscopy and spin-polarized scanning tunneling microscopy. 48 We note that this in-plane ferromagnetic order is also suggested by several theoretical models [18][19][20][21][22] in the distinct system where the Fermi level is near the charge neutrality point and the correlation between both flat bands is involved.…”

“…The first term is the ordinary onsite Hubbard term used in some mean-field studies of multilayer graphene systems. 17,18 The second term captures the diagonal portion of the Coulomb interaction at long range, which favors certain charge order, such as a two-dimensional Wigner crystal. The absence of a dispersion in a low-density system implies that this term can be relevant and must be kept in accurate models.…”

“…Our interaction model extends beyond the mean-field 18 and renormalization group 19,20 studies, where a screened interaction with either the onsite Hubbard term or a short-ranged interaction term is considered. Our study is also different from those with ab initio calculations 21 and Hartree-Fock approximations, 22 which rely on a certain local approximation to treat the nonlocal interaction and spin exchange terms.…”

Antiferromagnetic and topological states in silicene: A mean field study

“…Considering pseudospin (i.e., which layer), valley, and real electron spin degrees of freedom, various broken-symmetry phases have been predicted or considered. [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] Among these phases, the antiferromagnetic (AFM) state [31,[36][37][38][39] is considered to be the most possible one, due to its consistency with the later observations including their response to a perpendicular electric field [18,23] and tilted magnetic field. [22] Noticing the striking similarity between BLG and silicene, the electronelectron interaction might induce magnetism for silicene, and the competition between the magnetic state and topological state may lead to new physics, which is worthwhile to be carefully studied.…”