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Published on: January 21, 2016
Fractional quantum Hall effect in the absence of Landau levels
D N Sheng1, Zheng-Cheng Gu, Kai Sun
1Department of Physics and Astronomy, California State University, Northridge, California 91330, USA. shengli@nju.edu.cn
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.
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