Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2002-10-08
Phys. Rev. B 66, 155302 (2002)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
14 pages, 16 figures
Scientific paper
10.1103/PhysRevB.66.155302
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 $\nu^*=n+\bar \nu$ 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.
Jain Jainendra K.
Mandal Sudhansu S.
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