Abstract
We present a simple prescription to flatten isolated Bloch bands with a nonzero Chern number. We first show that approximate flattening of bands with a nonzero Chern number is possible by tuning ratios of nearest-neighbor and next-nearest-neighbor hoppings in the Haldane model and, similarly, in the chiral--flux square lattice model. Then we show that perfect flattening can be attained with further range hoppings that decrease exponentially with distance. Finally, we add interactions to the model and present exact diagonalization results for a small system at filling that support (i) the existence of a spectral gap, (ii) that the ground state is a topological state, and (iii) that the Hall conductance is quantized.
- Received 22 December 2010
DOI:https://doi.org/10.1103/PhysRevLett.106.236804
© 2011 American Physical Society
Viewpoint
Fractional quantum Hall effect without Landau levels
Published 6 June 2011
Researchers develop models that could exhibit a fractional quantum Hall effect in the absence of an external magnetic field.
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