arXiv subjects
Publications and source records attributed to J. K. Jain.
We demonstrate the formation of composite fermions in two-dimensional quantum dots under high magnetic fields. The composite fermion interpretation provides a simple way to understand several qualitative and quantitative features of the numerical results obtained earlier in exact diagonalization studies. In particular, the ground states are recognized as compactly filled quasi-Landau levels of composite fermions.
We investigate, using finite size numerical calculations, the spin-polarized fractional quantum Hall effect (FQHE) in the first excited Landau level (LL). We find evidence for the existence of an incompressible state at $ν= \frac{7}{3} = 2+\frac{1}{3}$, but not at $ν= 2+\frac{2}{5}$. Surprisingly, the 7/3 state is found to be strongest at a finite thickness. The structure of the low- lying excited states is found to be markedly different from that in the lowest LL. This study also rules out FQHE at a large number of odd-denominator fractions in the lowest LL.
This is a comment published in Phys. Rev. Lett. vol. 73, page 1051 (1994).
We show that the excitation spectrum of interacting electrons at filling factor $ν=ν^*/(2ν^*+1)$ is well described in terms of non-interacting composite fermions at filling factor $ν^*$, but does not have a one-to-one correspondence with the excitation spectrum of non-interacting electrons at $ν^*$. In particular, the collective modes of the fractional quantum Hall states are not analogous to those of the integer quantum Hall states. We also speculate on the nature of the compressible state at $ν=1/2$.
We consider the ``fractional quantum Hall atom" in the vanishing Zeeman energy limit, and investigate the validity of Hund's maximum-spin rule for interacting electrons in various Landau levels. While it is not valid for {\em electrons} in the lowest Landau level, there are regions of filling factors where it predicts the ground state spin correctly {\em provided it is applied to composite fermions}. The composite fermion theory also reveals a ``self-similar" structure in the filling factor range $4/3>ν>2/3$.
We investigate the spectrum of interacting electrons at arbitrary filling factors in the limit of vanishing Zeeman splitting. The composite fermion theory successfully explains the low-energy spectrum {\em provided the composite fermions are treated as hard-core}.
We consider a channel of an incompressible fractional-quantum-Hall-effect (FQHE) liquid containing an island of another FQHE liquid. It is predicted that the resistance of this channel will be periodic in the flux through the island, with the period equal to an odd integer multiple of the fundamental flux quantum, $ϕ_{0}=hc/e$. The multiplicity depends on the quasiparticle charges of the two FQHE liquids.
We provide numerical evidence that the ground state of a short range interaction model at $ν=1/2$ is incompressible and spin-singlet for a wide range of repulsive interactions. Furthermore it is accurately described by a trial wave function studied earlier. For the Coulomb interaction we find that this wave function provides a good description of the lowest lying spin-singlet state, and propose that fractional quantum Hall effect would occur at $ν=1/2$ if this state became the global ground state.
The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides an accurate and complete microscopic description of the strongly correlated many-body states in the low-energy bands. Thus, somewhat like in Landau's fermi liquid theory, there is a one-to-one correspondence between the low energy Hilbert space of strongly interacting electrons in the fractinal quantum Hall regime and that of weakly interacting electrons in the integer quantum Hall regime.