Dolan, Brian P.
Duality in the Quantum Hall Effect - the Role
of Electron Spin.
Physical Review B, 62.
At low temperatures the phase diagram for the quantum Hall effect has a
powerful symmetry arising from the Law of Corresponding States. This symmetry
gives rise to an infinite order discrete group which is a generalisation of
Kramers-Wannier duality for the two dimensional Ising model. The duality
group, which is a subgroup of the modular group, is analysed and it is argued
that there is a quantitative difference between a situation in which the spin
splitting of electron energy levels is comparable to the cyclotron energy and
one in which the spin splitting is much less than the cyclotron energy. In the
former case the group of symmetries is larger than in the latter case. These
duality symmetries are used to constrain the scaling functions of the theory
and, under an assumption of complex meromorphicity, a unique functional
form is obtained for the crossover of the conductivities between Hall states
as a function of the external magnetic field. This analytic form is shown to
give good agreement with experimental data.
The analysis requires a consideration of the way in which longitudinal
resistivities are extracted from the experimentally measured longitudinal resistances
and a novel method is proposed for determining the correct normalisation
for the former.
||Preprint version of original published article available at DOI: 10.1103/PhysRevB.62.10278 (American Physical Society)
||Duality; Quantum Hall Effect; Electron Spin;
||Faculty of Science and Engineering > Mathematical Physics
Dr. Brian Dolan
||16 Nov 2011 16:47
|Journal or Publication Title:
||Physical Review B
||American Physical Society
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