SciPost Phys. 15, 081 (2023) ·
published 6 September 2023

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We derive BMlike continuum models for the bands of superlattice heterostructures formed out of Fechalcogenide monolayers: (I) a single monolayer experiencing an external periodic potential, and (II) twisted bilayers with longrange moire tunneling. A symmetry derivation for the interlayer moire tunnelling is provided for both the $\Gamma$ and $M$ highsymmetry points. In this paper, we focus on moire bands formed from holeband maxima centered on $\Gamma$, and show the possibility of moire bands with $C=0$ or ±1 topological quantum numbers without breaking timereversal symmetry. In the $C=0$ region for $\theta→0$ (and similarly in the limit of large superlattice period for I), the system becomes a square lattice of 2D harmonic oscillators. We fit our model to FeSe and argue that it is a viable platform for the simulation of the square Hubbard model with tunable interaction strength.
SciPost Phys. Core 3, 015 (2020) ·
published 9 December 2020

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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.
Dr Eugenio: "We thank the referee for recom..."
in Submissions  report on DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene