arXiv subjects

Jainendra K. Jain

Publications and source records attributed to Jainendra K. Jain.

59 records · Page 4Linked to original sources

arXiv2003

Two-dimensional electron system in high magnetic fields: Wigner crystal vs. 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.

cond-mat.mes-hall↗

arXiv2002

Theoretical Search for Nested Quantum Hall Effect of Composite Fermions

Almost all quantum Hall effect to date can be understood as {\em integral} quantum Hall effect of appropriate particles, namely electrons or composite fermions. This paper investigates theoretically the feasibility of nested states of composite fermions which would lead to a quantum Hall effect that cannot be understood as integral quantum Hall effect of composite fermions. The weak residual interaction between composite fermions will play a crucial role in the establishment of such quantum Hall states by opening a gap in a partially filled composite-fermion level. To treat the problem of interacting composite fermions, we develop a powerful method that allows us to obtain the low energy spectra at composite fermion fillings of $ν^*=n+\bar ν$ without making any assumption regarding the structure of composite fermions in the topmost partially filled level. The method is exact aside from neglecting the composite-fermion Landau level mixing, and enables us to study rather large systems, for example, 24 particles at a total flux of 62 $hc/e$, for which the dimension of the lowest Landau level Hilbert space is $\sim 10^{17}$. We have investigated, for fully spin polarized composite fermions, several filling factors between 1/3 and 2/5 using this approach. The results indicate that any possible incompressibility at these fractions is likely to have a fundamentally different origin than that considered earlier.

cond-mat.mes-hall↗

arXiv2002

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 non-interacting composite fermions. However, the weak residual interaction between composite fermions appears 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.

cond-mat.mes-hall↗

arXiv1999

Masses of composite fermions carrying two and four flux quanta: Differences and similarities

This study provides a theoretical rationalization for the intriguing experimental observation regarding the equality of the normalized masses of composite fermions carrying two and four flux quanta, and also demonstrates that the mass of the latter type of composite fermion has a substantial filling factor dependence in the filling factor range $4/17 > ν> 1/5$, in agreement with experiment, originating from the relatively strong inter-composite fermion interactions here.

cond-mat.mes-hall↗

arXiv1999

Magneto-roton excitation of fractional quantum Hall effect: Comparison between theory and experiment

A major obstacle toward a {\em quantitative} verification, by comparison to experiment, of the theory of the excitations of the fractional quantum Hall effect has been the lack of a proper understanding of disorder. We circumvent this problem by studying the {\em neutral} magneto-roton excitations, whose energy is expected to be largely insensitive to disorder. The calculated energies of the roton at 1/3, 2/5 and 3/7 fillings of the lowest Landau level are in good agreement with those measured experimentally.

cond-mat.mes-hall↗