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Jainendra K Jain

Publications and source records attributed to Jainendra K Jain.

9 recordsLinked to original sources
PubMed2006

Understanding the 5/2 fractional quantum Hall effect without the Pfaffian wave function.

It is demonstrated that an understanding of the 5/2 fractional quantum Hall effect can be achieved within the composite fermion theory without appealing to the Pfaffian wave function. The residual interaction between composite fermions plays a crucial role in establishing incompressibility at this filling factor. This approach has the advantage of being amenable to systematic perturbative improvements, and produces ground as well as excited states. It, however, does not relate to non-Abelian statistics in any obvious manner.

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PubMed2006

Resonant tunneling in the fractional quantum Hall effect: superperiods and braiding statistics.

We study theoretically resonant tunneling of composite fermions through their quasibound states around a fractional quantum Hall island, and find a rich set of possible transitions of the island state as a function of the magnetic field or the backgate voltage. These have possible relevance to a recent experimental study, and reveal many subtleties involved in deducing fractional braiding statistics.

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PubMed2005

Reconstructing the electron in a fractionalized quantum fluid.

The low-energy physics of the fractional Hall liquid is described in terms of quasiparticles that are qualitatively distinct from electrons. We show, however, that a long-lived electronlike quasiparticle also exists in the excitation spectrum: the state obtained by the application of an electron creation operator to a fractional quantum Hall ground state has a nonzero overlap with a complex, high energy bound state containing an odd number of composite-fermion quasiparticles. The electron annihilation operator similarly couples to a bound complex of composite-fermion holes. We predict that these bound states can be observed through a conductance resonance in experiments involving a tunneling of an external electron into the fractional quantum Hall liquid. A comment is made on the origin of the breakdown of the Fermi liquid paradigm in the fractional Hall liquid.

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PubMed2005

Microscopic verification of topological electron-vortex binding in the lowest Landau-level crystal state.

When two-dimensional electrons are subjected to a very strong magnetic field, they are believed to form a triangular crystal. By a direct comparison with the exact wave function, we demonstrate that this crystal is not a simple Hartree-Fock crystal of electrons but an inherently quantum mechanical crystal characterized by a nonperturbative binding of quantized vortices to electrons. It is suggested that this has qualitative consequences for experiment.

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PubMed2004

Flavor altering excitations of composite fermions.

Past theoretical studies have considered excitations of a given flavor of composite fermions across composite-fermion quasi-Landau levels. We show that in addition there exists a ladder of flavor changing excitations in which composite fermions are partially dissociated by a removal of some or all of their vortices, and suggest that these are relevant to the intriguing experimental discovery of Hirjibehedin et al. [Phys. Rev. Lett. 91, 186802 (2003)] of coexisting excitation modes of composite fermions of different flavors in the filling factor range 1/3 > nu > or = 1/5.

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PubMed2003

Fractional statistics in the fractional quantum Hall effect.

A microscopic confirmation of the fractional statistics of the quasiparticles in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at nu=1/3 and nu=2/5 by evaluating the Berry phase for a closed loop encircling another composite-fermion quasiparticle. A careful consideration of subtle perturbations in the trajectory due to the presence of an additional quasiparticle is crucial for obtaining the correct value of the statistics. The conditions for the applicability of the fractional statistics concept are discussed.

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PubMed2003

Two-dimensional electron system in high magnetic fields: Wigner crystal versus composite-fermion liquid.

The two-dimensional system of electrons in a high magnetic field offers an opportunity to investigate a phase transition from a quantum liquid into a Wigner solid. Recent experiments have revealed an incipient composite fermion liquid in a parameter range where theory and many experiments had previously suggested the Wigner crystal phase, thus calling into question our current understanding. This Letter shows how very small quantitative corrections (<1%) in the energy due to the weak interaction between composite fermions can cause a fundamental change in the nature of the ground state, thus providing insight into the puzzling experimental results.

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PubMed2002

Relevance of inter-composite-fermion interaction to the edge Tomonaga-Luttinger liquid.

It is shown that Wen's effective theory correctly describes the Tomonaga-Luttinger liquid at the edge of a system of noninteracting composite fermions. However, the weak residual interaction between composite fermions is found to be a relevant perturbation. The filling factor dependence of the Tomonaga-Luttinger parameter is estimated for interacting composite fermions in a microscopic approach and satisfactory agreement with experiment is achieved. It is suggested that the electron field operator may not have a simple representation in the effective one-dimensional theory.

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