Fractional quantum Hall effect in the absence of Landau levels

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…

• NS
  National Science Foundation

  Awards: 0958596, NSFPHY05-51164, DMR-0958596
• UD
  U.S. Department of Energy

  Awards: FG02-06ER46305, DE-FG02-, DE-FG02-06ER46305, DE-FG02
• NN
  National Natural Science Foundation of China

  Awards: 10874066, 11074110
• DA
  Defense Advanced Research Projects Agency
• MU
  Multidisciplinary University Research Initiative
• DO
  Division of Materials Research
• BE
  Basic Energy Sciences

  Awards: DE-FG02-06ER46305, DE-FG02
• AF
  Air Force Office of Scientific Research
• AR
  Army Research Office