Charge order and Mott insulating ground states in small-angle twisted bilayer graphene

Abstract

In this work, we determine states of electronic order of small-angle twisted bilayer graphene. Ground states are determined for weak and strong couplings which are representatives for varying distances of the twist-angle from its magic value. In the weak-coupling regime, charge density waves emerge which break translational and C 3-rotational symmetry. In the strong coupling-regime, we find rotational and translational symmetry breaking Mott insulating states for all commensurate moiré band fillings. Depending on the local occupation of superlattice sites hosting up to four electrons, global spin-(ferromagnetic) and valley symmetries are also broken which may give rise to a reduced Landau level degeneracy as observed in experiments for commensurate band fillings. The formation of those particular electron orders is traced back to the important role of characteristic non-local interactions which connect all localized states belonging to one hexagon formed by the AB- and BA-stacked regions of the superlattice.

Transport through quantum anomalous Hall bilayers with lattice mismatch

“…For example, a graphene bilayer, even regularly stacked as a periodic lattice, has possessed electronic structures and transport properties significantly different from those of a monolayer one [14]. By twisting bilayers into generic non-commensurate or quasi-periodic lattices, more nontrivial physics emerge, including strong correlation, superconductivity and nontrivial topology [15][16][17][18][19].…”

Time-reversal symmetry breaking versus chiral symmetry breaking in twisted bilayer graphene

“…In this Rapid Communication, we study the effects of the Coulomb interaction at the CNP of TBG near the magic angle, with the aim of discerning whether dynamical symmetry breaking takes place under different screening conditions. We adopt a tight-binding approach to make a real-space description of the system, and we resort to a Hartree-Fock approximation in order to assess the effects of the Coulomb interaction [36,38,[52][53][54][55]. This approach allows us to treat the on-site Hubbard and long-range Coulomb interaction on the same footing.…”