From fractional Chern insulators to a fractional quantum spin hall effect
Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS UMR
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Received in final form: 20 October 2011
Published online: 11 January 2012
We investigate the algebraic structure of flat energy bands a partial filling of which may give rise to a fractional quantum anomalous Hall effect (or a fractional Chern insulator) and a fractional quantum spin Hall effect. Both effects arise in the case of a sufficiently flat energy band as well as a roughly flat and homogeneous Berry curvature, such that the global Chern number, which is a topological invariant, may be associated with a local non-commutative geometry. This geometry is similar to the more familiar situation of the fractional quantum Hall effect in two-dimensional electron systems in a strong magnetic field.
Key words: Mesoscopic and Nanoscale Systems
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2012