Unconventional fractional quantum Hall states in the lowest Landau level with hollow-core correlation

The conventional fractional quantum Hall effect (FQHE) states in the lowest Landau level with filling factors n/(2np+1) and n/(2np-1) are well understood by the composite fermion theory. The integer quantum Hall effect of Composite fermions which are bound state of electrons with even (2p) number of vortices each containing one unit of flux quantum, with effective filling factor n is the responsible mechanism for occurring these FQHE states. However, there are some unconventional states like 4/11, 5/13, 6/17, and 3/8 which are the states between the conventional states 1/3 and 2/5. These unconventional states respectively correspond to the fractional filling 1/3, 2/3, 1/5, and 1/2 of composite fermions in the second effective Landau level of composite fermions. The conventional FQHE of these fractionally filled composite fermions in the second effective Landau level does not reproduce these unconventional states. In this talk, I will provide a compelling theoretical evidence that the FQHE states at 4/11 and 5/13, observed a decade ago, are example of a new class of unconventional FQHE states: they occur due to the condensation of composite fermions into an incompressible "hollow-core" liquid wherein they maximally avoid pairs with relative angular momentum three.