Fractional quantum Hall effect in the absence of Landau levels

Abstract

It is well known that the topological phenomena with fractional excitations, the fractional quantum Hall effect, will emerge when electrons move in Landau levels. Here we show the theoretical discovery of the fractional quantum Hall effect in the absence of Landau levels in an interacting fermion model. The non-interacting part of our Hamiltonian is the recently proposed topologically non-trivial flat-band model on a checkerboard lattice. In the presence of nearest-neighbouring repulsion, we find that at 1/3 filling, the Fermi-liquid state is unstable towards the fractional quantum Hall effect. At 1/5 filling, however, a next-nearest-neighbouring repulsion is needed for the occurrence of the 1/5 fractional quantum Hall effect when nearest-neighbouring repulsion is not too strong. We demonstrate the characteristic features of these novel states and determine the corresponding phase diagram.

Exotic electronic states in the world of flat bands: From theory to material

“…The proposed topological FB is just like a counterpart of the LL, characterized by a Chern number equal to 1 [12]. It has been further shown by numerical simulations that such FBs support QH-like states, exhibiting not only the integer QH effects, but also the fractional QH (FQH) effects [20][21][22]. More importantly, considering the energy scales in lattices, the FQH effects -such as fractionalization and entanglement -can be realized in a much higher temperature in the FB than in the LL [18], charting a revolutionary route towards quantum computation [23].…”

Symmetry-protected fractional Chern insulators and fractional topological insulators

“…In the numerical simulations of FCI phases 12,13 , only the m-fold topological degeneracy of ν = 1/m FCI is observed on torus. This indicates that the FCI wavefunctions respect the full lattice symmetry, since otherwise there should be extra degeneracies due to lattice symmetry breaking.…”

“…They are characterized by different PSGs in the bulk. These states can all serve as candidate states for the FCI state found in numerical simulations 12,13,15 . Which state is realized in the simulated model 12,13,15 would be determined by energetics.…”

“…These states can all serve as candidate states for the FCI state found in numerical simulations 12,13,15 . Which state is realized in the simulated model 12,13,15 would be determined by energetics. Because our proposed wavefunctions has the form of a Slater determinant and can be effectively implemented by variational Monte Carlo approach, the energetics of the proposed states can be studied by future numerical investigation.…”

“…However, it takes more than two decades for people to show that similar statement is true even for FQHE. Recently results from a series of model studies [10][11][12][13][14][15][16][17][18] , including convincing evidences from exact diagonalizations [12][13][14][15][16][17] , indicate that fractional quantum hall states exist in the ground states of interacting lattice models, in the absence of an external magnetic field. It is found that the ground state is likely to respect the full lattice symmetry.…”