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Topological flat moir\'e bands with nearly ideal quantum geometry have been identified in homobilayer transition metal dichalcogenide moir\'e superlattices, and are thought to be crucial for understanding the fractional Chern insulating…
The rapid advances in the study of fractional Chern insulators (FCIs) raise a fundamental question: while initially discovered in flat Chern bands motivated by their topological equivalence to Landau levels, is single- particle band…
The quantum geometry of Bloch wavefunctions,encoded in the Berry curvature and quantum metric, is believed to be a decisive ingredient in stabilizing fractional quantum anomalous Hall (FQAH) effect(i.e., fractional Chern insulator, FCI, at…
Electrons in topological flat bands can form novel topological states driven by the correlation effects. The penta-layer rhombohedral graphene/hBN moire superlattice has been shown to host fractional quantum anomalous Hall effect (FQAHE) at…
We re-examine the nature of the ground states of bilayer graphene at odd integer filling factors within a simplified model of nearly degenerate $n=0$ and $n=1$ Landau levels. Previous Hartree-Fock studies have found that ferroelectric…
We theoretically examine entanglement in fractional quantum hall states, explicitly taking into account and emphasizing the quasi-two-dimensional nature of experimental quantum Hall systems. In particular, we study the entanglement entropy…
Electrostatically defined quantum dots (QDs) in Bernal stacked bilayer graphene (BLG) are a promising quantum information platform because of their long spin decoherence times, high sample quality, and tunability. Importantly, the shape of…
Band crossing points, such as Weyl and Dirac points, play a crucial role in the topological classification of materials and guide the exploration of exotic topological phases. The Berry dipole, a three-dimensional band crossing point beyond…
We investigate integer and half-integer filling states (uniform and unidimensional stripe states respectively) for graphene using the Hartree-Fock approximation. For fixed filling factor, the ratio between the scales of the Coulomb…
Analytical calculations based on a Landau Level (LL) picture are reported for a many-electron system moving in an interface (with a finite-width Quantum Well (QW)) and in the presence of an external perpendicular magnetic field. They lead…
Certain lattices with specific geometries have one or more spectral bands that are strictly flat, i.e. the electron energy is independent of the momentum. This can occur robustly irrespective of the specific couplings between the lattices…
While the ground state phase diagram of the correlated flat-band systems have been intensively investigated, the dynamic and thermodynamic properties of such lattice models are less explored, but it is the latter which is most relevant to…
We study the formation and properties of perfectly-flat zero energy bands in a multi-layer graphene systems in the chiral limit. Employing the degrees of freedoms of the multi-layer system, such as relative twist-angle and relative shifts,…
Strong interactions in Landau flat bands are known to stabilize correlated states that do not form in other types of flat bands. We report hallmarks of topological protection at the Landau level filling factor v=7/11 in a two-dimensional…
We study the influence of the quantum geometry on the magnetic responses of quadratic band crossing semimetals. More explicitly, we examine the Landau levels, quantum Hall effect, and magnetic susceptibility of a general two-band…
Since the discovery of the Fractional Quantum Hall Effect in 1982 there has been considerable theoretical discussion on the possibility of fractional quantization of conductance in the absence of Landau levels formed by a quantizing…
In crystalline solids the interactions of charge and spin can result in a variety of emergent quantum ground states, especially in partially filled, topological flat bands such as Landau levels or in 'magic-angle' bilayer graphene. Much…
We present a detailed microscopic investigation of fractional quantum Hall states with gapped boundaries in a coupled bilayer lattice model featuring holes whose counterpropagating chiral edge states are hybridized and gapped out. We focus…
Here we show that the Pfaffian state proposed for the $\frac52$ fractional quantum Hall states in conventional two-dimensional electron systems can be readily realized in a bilayer graphene at one of the Landau levels. The properties and…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…