After more than three decades, the fractional quantum Hall effect still poses challenges to contemporary physics. Recent experiments point toward a fractal scenario for the Hall resistivity as a function of the magnetic field. Here, we consider the so-called thin-torus limit of the Hamiltonian describing interacting electrons in a strong magnetic field, restricted to the lowest Landau level, and we show that it can be mapped onto a one-dimensional lattice gas with repulsive interactions, with the magnetic field playing the role of the chemical potential. The statistical mechanics of such models leads us to interpret the sequence of Hall plateaux as a fractal phase diagram whose landscape shows a qualitative agreement with experiments.

Devil's Staircase Phase Diagram of the Fractional Quantum Hall Effect in the Thin-Torus Limit / P. Rotondo, L.G. Molinari, P. Ratti, M. Gherardi. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - 116:25(2016 Jun 24), pp. 256803.1-256803.5. [10.1103/PhysRevLett.116.256803]

Devil's Staircase Phase Diagram of the Fractional Quantum Hall Effect in the Thin-Torus Limit

P. Rotondo;L.G. Molinari;M. Gherardi
2016-06-24

Abstract

After more than three decades, the fractional quantum Hall effect still poses challenges to contemporary physics. Recent experiments point toward a fractal scenario for the Hall resistivity as a function of the magnetic field. Here, we consider the so-called thin-torus limit of the Hamiltonian describing interacting electrons in a strong magnetic field, restricted to the lowest Landau level, and we show that it can be mapped onto a one-dimensional lattice gas with repulsive interactions, with the magnetic field playing the role of the chemical potential. The statistical mechanics of such models leads us to interpret the sequence of Hall plateaux as a fractal phase diagram whose landscape shows a qualitative agreement with experiments.
quantum Hall effect; FQHE; devil's staircase
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
PHYSICAL REVIEW LETTERS
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/435956
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