2011/07/31 by M. O. Goerbig · 1 citation
Materials Science · Physics and Astronomy · #Composite fermion #Fractional quantum Hall effect #Graphene research and applications #Homogeneous #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum anomalous Hall effect #Quantum spin Hall effect #Spin (aerodynamics) #Spin Hall effect #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1140/epjb/e2011-20857-6
published as Eur. Phys. J. B 85(1), 15 (2012) · 8 pages, 3 figure; published version with labels in Figs. 2 and 3 corrected
openalex publication_date 2012/01/01 · arxiv created 2012/01/18 · arxiv updated 2012/01/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.