SciPost Phys. Core 3, 015 (2020) ·
published 9 December 2020

· pdf
Strong interactions between electrons occupying bands of opposite (or like) topological quantum numbers (Chern$=\pm1$), and with flat dispersion, are studied by using lowest Landau level (LLL) wavefunctions. More precisely, we determine the ground states for two scenarios at halffilling: (i) LLL's with opposite sign of magnetic field, and therefore opposite Chern number; and (ii) LLL's with the same magnetic field. In the first scenario  which we argue to be a toy model inspired by the chirally symmetric continuum model for twisted bilayer graphene  the opposite Chern LLL's are Kramer pairs, and thus there exists timereversal symmetry ($\mathbb{Z}_2$). Turning on repulsive interactions drives the system to spontaneously break timereversal symmetry  a quantum anomalous Hall state described by one particle per LLL orbital, either all positive Chern $++\cdots+>$ or all negative $\cdots>$. If instead, interactions are taken between electrons of likeChern number, the ground state is an $SU(2)$ ferromagnet, with total spin pointing along an arbitrary direction, as with the $\nu=1$ spin$\frac{1}{2}$ quantum Hall ferromagnet. The ground states and some of their excitations for both of these scenarios are argued analytically, and further complimented by density matrix renormalization group (DMRG) and exact diagonalization.