STRUCTURING THE SET OF INCOMPRESSIBLE QUANTUM HALL FLUIDS

Details STRUCTURING THE SET OF INCOMPRESSIBLE QUANTUM HALL FLUIDS STRUCTURING THE SET OF INCOMPRESSIBLE QUANTUM HALL FLUIDS

1995-05-31

arxiv.org/abs/cond-mat/9505156v1

Physics

Condensed Matter

40 pages, LaTeX, 1 figure included; (for some possible macro issues, see the remarks about ``ways of producing the symbols for

Scientific paper

10.1016/0550-3213(95)00426-S

A classification of incompressible quantum Hall fluids in terms of integral lattices and arithmetical invariants thereof is proposed. This classification enables us to characterize the plateau values of the Hall conductivity $\sH$ in the interval $\,(0,1]\,$ (in units where $\,e^2/h=1$) corresponding to ``stable'' incompressible quantum Hall fluids. A bijection, called shift map, between classes of stable incompressible quantum Hall fluids corresponding to plateaux of $\sH$ in the intervals $\,[1/(2\mini p+1),1/(2\mini p-1)\mini)\,$ and $\,[1/(2\mini q+1),1/(2\mini q-1)\mini)$, respectively, is constructed, with $\,p,q=1,2,3, (\ldots),\ p\neq q$. Our theoretical results are carefully compared to experimental data, and various predictions and experimental implications of our theory are discussed.

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