arXiv subjects

Jainendra K. Jain

Publications and source records attributed to Jainendra K. Jain.

At least 55 records · Page 3Linked to original sources

arXiv2007

Electron operator at the edge of the 1/3 fractional quantum Hall liquid

This study builds upon the work of Palacios and MacDonald (Phys. Rev. Lett. {\bf 76}, 118 (1996)), wherein they identify the bosonic excitations of Wen's approach for the edge of the 1/3 fractional quantum Hall state with certain operators introduced by Stone. Using a quantum Monte Carlo method, we extend to larger systems containing up to 40 electrons and obtain more accurate thermodynamic limits for various matrix elements for a short range interaction. The results are in agreement with those of Palacios and MacDonald for small systems, but offer further insight into the detailed approach to the thermodynamic limit. For the short range interaction, the results are consistent with the chiral Luttinger liquid predictions.We also study excitations using the Coulomb ground state for up to nine electrons to ascertain the effect of interactions on the results; in this case our tests of the chiral Luttinger liquid approach are inconclusive.

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arXiv2007

SU(4) composite fermions in graphene: New fractional quantum Hall states

Theoretical studies of the fractional quantum Hall effect (FQHE) in graphene have so far focused on the plausibility and stability of the previously known FQHE states for the interaction matrix elements appropriate for graphene. We consider FQHE for SU(4) symmetry, as appropriate for the situation when all four spin and valley Landau bands are degenerate, and predict new FQHE states that have no analog in GaAs. These result from an essential interplay between the two-fold spin and valley degeneracies at fractions of the form $ν=n/(2pn\pm 1)$, for $n\geq 3$. Conditions are outlined for the observation of these states and quantum phase transitions between them; the structure of these states and their excitations is also described.

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arXiv2006

Semiconductor quantum dots in high magnetic fields: The composite-fermion view

We review and extend the composite fermion theory for semiconductor quantum dots in high magnetic fields. The mean-field model of composite fermions is unsatisfactory for the qualitative physics at high angular momenta. Extensive numerical calculations demonstrate that the microscopic CF theory, which incorporates interactions between composite fermions, provides an excellent qualitative and quantitative account of the quantum dot ground state down to the largest angular momenta studied, and allows systematic improvements by inclusion of mixing between composite fermion Landau levels (called $Λ$ levels).

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arXiv2006

Fractional Quantum Hall Effect in Graphene

Unlike regular electron spin, the pseudospin degeneracy of Fermi points in graphene does not couple directly to magnetic field. Therefore, graphene provides a natural vehicle to observe the integral and fractional quantum Hall physics in an elusive limit analogous to zero Zeeman splitting in GaAs systems. This limit can exhibit new integral plateaus arising from interactions, large pseudoskyrmions, fractional sequences, even/odd numerator effects, composite-fermion pseudoskyrmions, and a pseudospin-singlet composite-fermion Fermi sea. The Dirac nature of the B=0 spectrum, which induces qualitative changes in the overall spectrum, has no bearing on the fractional quantum Hall effect in the $n=0$ Landau level of graphene. The second Landau level of graphene is predicted to show more robust fractional quantum Hall effect than the second Landau level of GaAs.

cond-mat.str-el↗

arXiv2006

Nature of excitations of the 5/2 fractional quantum Hall effect

It is shown, with the help of exact diagonalization studies on systems with up to sixteen electrons, in the presence of up to two delta function impurities, that the Pfaffian model is inadequate for the actual quasiholes and quasiparticles of the 5/2 fractional quantum Hall effect. Implications for non-Abelian statistics are discussed.

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arXiv2006

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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arXiv2006

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

We study theoretically resonant tunneling of composite fermions through their quasi-bound 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 considerations have possible relevance to a recent experimental study, and bring out many subtleties involved in deducing fractional braiding statistics.

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arXiv2005

Fractional Quantum Hall Effect in the Second Landau Level: the Importance of Inter-Composite-Fermion Interaction

Exact diagonalization of a two-dimensional electron gas in a strong magnetic field in the disk geometry shows that there exists a filling factor range in the second Landau level where the states significantly differ from those in the lowest Landau level. We show that the difference arises because the interaction between composite fermions is not negligible in higher Landau levels, as indicated by a substantial mixing between composite-fermion Landau-like levels, or lambda levels. We find that the exact ground state is well reproduced by composite fermion theory with lambda level mixing incorporated at the lowest level of approximation. Using the same variational approach in the spherical geometry we estimate the excitation gap at filling 1/3 in the second Landau level (which corresponds to 7/3 of experiment).

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arXiv2004

Reconstructing the electron in a fractionalized quantum fluid

The low energy physics of the fractional Hall liquid is described in terms quasiparticles that are qualitatively distinct from electrons. We show, however, that a long-lived electron-like 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 non-zero 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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arXiv2004

Composite-fermionization of bosons in rapidly rotating atomic traps

The non-perturbative effect of interaction can sometimes make interacting bosons behave as though they were free fermions. The system of neutral bosons in a rapidly rotating atomic trap is equivalent to charged bosons coupled to a magnetic field, which has opened up the possibility of fractional quantum Hall effect for bosons interacting with a short range interaction. Motivated by the composite fermion theory of the fractional Hall effect of electrons, we test the idea that the interacting bosons map into non-interacting spinless fermions carrying one vortex each, by comparing wave functions incorporating this physics with exact wave functions available for systems containing up to 12 bosons. We study here the analogy between interacting bosons at filling factors $ν=n/(n+1)$ with non-interacting fermions at $ν^*=n$ for the ground state as well as the low-energy excited states and find that it provides a good account of the behavior for small $n$, but interactions between fermions become increasingly important with $n$. At $ν=1$, which is obtained in the limit $n\rightarrow \infty$, the fermionization appears to overcompensate for the repulsive interaction between bosons, producing an {\em attractive} interactions between fermions, as evidenced by a pairing of fermions here.

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arXiv2004

Berry phases for composite fermions: effective magnetic field and fractional statistics

The quantum Hall superfluid is presently the only viable candidate for a realization of quasiparticles with fractional Berry phase statistics. For a simple vortex excitation, relevant for a subset of fractional Hall states considered by Laughlin, non-trivial Berry phase statistics were demonstrated many years ago by Arovas, Schrieffer, and Wilczek. The quasiparticles are in general more complicated, described accurately in terms of excited composite fermions. We use the method developed by Kjonsberg, Myrheim and Leinaas to compute the Berry phase for a single composite-fermion quasiparticle, and find that it agrees with the effective magnetic field concept for composite fermions. We then evaluate the "fractional statistics", related to the change in the Berry phase for a closed loop caused by the insertion of another composite-fermion quasiparticle in the interior. Our results support the general validity of fractional statistics in the quantum Hall superfluid, while also giving a quantitative account of corrections to it when the quasiparticle wave functions overlap. Many caveats, both practical and conceptual, are mentioned that will be relevant to an experimental measurement of the fractional statistics. A short report on some parts of this article has appeared previously.

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arXiv2004

Composite fermion theory of correlated electrons in semiconductor quantum dots in high magnetic fields

Interacting electrons in a semiconductor quantum dot at strong magnetic fields exhibit a rich set of states, including correlated quantum fluids and crystallites of various symmetries. We develop in this paper a perturbative scheme based on the correlated basis functions of the composite-fermion theory, that allows a systematic improvement of the wave functions and the energies for low-lying eigenstates. For a test of the method, we study systems for which exact results are known, and find that practically exact answers are obtained for the ground state wave function, ground state energy, excitation gap, and the pair correlation function. We show how the perturbative scheme helps resolve the subtle physics of competing orders in certain anomalous cases.

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arXiv2003

Nature of quasiparticle excitations in the fractional quantum Hall effect

We investigate the 1/3 fractional quantum Hall state with one and two quasiparticle excitations. It is shown that the quasiparticle excitations are best described as excited composite fermions occupying higher composite-fermion quasi-Landau levels. In particular, the composite-fermion wave function for a single quasiparticle has 15% lower energy than the trial wave function suggested by Laughlin, and for two quasiparticles, the composite fermion theory also gives new qualitative structures.

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arXiv2003

Composite-fermion crystallites in quantum dots

The correlations in the ground state of interacting electrons in a two-dimensional quantum dot in a high magnetic field are known to undergo a qualitative change from liquid-like to crystal-like as the total angular momentum becomes large. We show that the composite-fermion theory provides an excellent account of the states in both regimes. The quantum mechanical formation of composite fermions with a large number of attached vortices automatically generates omposite fermion crystallites in finite quantum dots.

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arXiv2003

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 general there exists a ladder of flavor changing excitations in which composite fermions shed none, some, or all of their vortices. The lowest energy excitations are obtained when the composite fermions do not change their flavor, whereas in the highest energy excitations they are stripped of all of their vortices, emerging as electrons in the final state. The results are relevant to the intriguing experimental discovery of Hirjibehedin {\em et al.} (cond-mat/0306152) of coexisting excitation modes of composite fermions of different flavor in the filling factor range $1/3>ν\geq 1/5$.

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arXiv2003

Composite fermions in the neighborhood of $ν=1/3$

We present extensive comparisons of the composite fermion theory with exact results in the filling factor range $2/5>ν>1/3$, which affirm that the composite fermion theory correctly describes the qualitative reorganization of the low energy Hilbert space of the strongly correlated electrons, and predicts eigenenergies with an accuracy of $\sim 0.1$ %. These facts establish the basic validity of the composite fermion description in this filling factor region.

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arXiv2003

Fractional statistics in the fractional quantum Hall effect

A microscopic confirmation of the fractional statistics of the {\em quasiparticles} in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at $ν=1/3$ and $ν=2/5$ 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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arXiv2003

Partially spin polarized quantum Hall effect in the filling factor range 1/3 < nu < 2/5

The residual interaction between composite fermions (CFs) can express itself through higher order fractional Hall effect. With the help of diagonalization in a truncated composite fermion basis of low-energy many-body states, we predict that quantum Hall effect with partial spin polarization is possible at several fractions between $ν=1/3$ and $ν=2/5$. The estimated excitation gaps are approximately two orders of magnitude smaller than the gap at $ν=1/3$, confirming that the inter-CF interaction is extremely weak in higher CF levels.

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