JCJC - Jeunes chercheuses & jeunes chercheurs

SU(4) fractional quantum Hall effect – SU(4) FQHE

Submission summary

Quantum Hall physics - the study of two-dimensional (2D) electrons in a strong magnetic field - has provided a stream of exotic and unexpected phenomena over the last 25 years. Most saliently, the integral and fractional quantum Hall effects (IQHE and FQHE, Nobel Prizes in 1995 and 1998) have joined superconductivity and superfluidity as members of the exclusive club of macroscopic quantum phenomena. During the last year, multicomponent quantum Hall systems have attracted growing attention. These internal degrees of freedom can go beyond the usual SU(2) spin, leading to possible new quantum phases. We propose an in-depth study of the SU(4) fractional quantum Hall effect motivated by 2D electron gases both in bilayer systems with spin and in graphene. The collaboration of this project unites the major streams of theoretical physics, namely state-of-the-art numerical physics (Nicolas Regnault), analytical methods in condensed-matter (Mark Goerbig, Christophe Mora) and mathematical physics (Vincent Pasquier). The actors, who are located in three different laboratories of the Paris Region, have made significant contributions to the field of quantum Hall physics. The current collaboration between Nicolas Regnault and Mark Goerbig has already led to a (yet unpublished) preprint of preliminary results that is the 'backbone' of the present project on the SU(4) fractional quantum Hall physics. Our scientific project covers different topics related to the SU(4) fractional quantum Hall effect. A complete numerical topography of the quantum states will aim to discriminate which states should be relevant in the thermodynamical limit. Different types of ferromagnetism may arise in such systems. A complete classification of these ferromagnetic states and a description of topological skyrmion-like excitations is one of our goals. Apart from these ferromagnetic properties, we will investigate fractionally-charged quasiparticle excitations. First, we will generalise the point of view developed by Haldane in the case of the Laughlin and Pfaffian states to describe these excitations. Relation between this description and the Calogero-Sutherland integrable model will be addressed. Second, a composite-fermion approach will be developed based on the generalised Halperin wavefunctions to describe flux quantum attachment. In both cases, analytical results will be compared to numerical calculations to valid the different approaches. Although the project is clearly a theoretical one, three of the participants work in laboratories which are constituted mainly of experimentalists. Specifically for the present project, a close interaction with Christian Glattli and his group (Laboratoire Pierre Aigrain - CEA SPEC), who are investigating a possible fractional quantum Hall effect in graphene, is envisioned and will be a strong motivation to look at the experimental consequences and realizations.

Project coordination

Nicolas REGNAULT (Organisme de recherche)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

Help of the ANR 141,424 euros
Beginning and duration of the scientific project: - 36 Months

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