Fig. 4: Hartree-Fock interacting phase diagrams. | Nature Communications

Fig. 4: Hartree-Fock interacting phase diagrams.

From: Topological minibands and interaction driven quantum anomalous Hall state in topological insulator based moiré heterostructures

Fig. 4

a The energy difference per particle Ei − En at 1/4 filling of the four-band model with both CB1 and CB2 for the case ϕ = 0, α = 1, V0/E0 = 0. Here Ei and En is the interacting ground state energy and non-interacting metallic state energy, respectively. The orange (black) line is for the \({C}_{2}{{{{{{{\mathcal{T}}}}}}}}\) symmetry breaking (preserving) density matrix. The interacting ground states in the regime A, B, C correspond to a metallic phase, an insulating phase with C = ± 1, and an insulating phase with C = 0, respectively. b Ei − En for the case with ϕ = 0, α = 0, V0/E0 = 1.2. c, d The spectra (orange) of the Hartree-Fock mean-field Hamiltonian for the Coulomb interaction strength in regime B and C of (a). C is the Chern number of each band. e The spectra (orange) of the mean-field Hamiltonian for the Coulomb interaction strength in regime B of (b). In (c–e), the blues lines are single-particle spectra.

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