From Fractional Chern Insulators to a Fractional Quantum Spin Hall Effect

Details From Fractional Chern Insulators to a Fractional Quantum Spin Hall Effect From Fractional Chern Insulators to a Fractional Quantum Spin Hall Effect

2011-07-11

arxiv.org/abs/1107.1986v3

Eur. Phys. J. B 85(1), 15 (2012)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

8 pages, 3 figure; published version with labels in Figs. 2 and 3 corrected

Scientific paper

10.1140/epjb/e2011-20857-6

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.

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