prof. dr hab. inż. Arkadiusz Wójs (KFT PWr)

Złożone fermiony i topologiczne ciecze kwantowe ***** Composite fermions & topological quantum liquids

Fractional quantum Hall effect (FQHE) involves condensation of two dimensional electrons in a high magnetic field B into various topological quantum liquids at different Landau level (LL) filling fractions nu. The key concept in the FQHE theory is emergence of “composite fermions” (CFs) – electrons binding an even number (2p) of vortices of the many-body wave function. The CFs are collective, topological particles which can loosely be viewed as e-charged fermions in a reduced magnetic field B*. Most of about 75 filling factors at which FQHE has been observed so far belong to the so-called Jain sequence nu=n/(2pn±1) which can be understood in terms of essentially free CFs filling an integral number n of effective Landau-like “Λ levels” (ΛLs). But there are also a few others, like nu=5/2 or 4/11, crucially dependent on complex residual interaction among the CFs, and remaining the subject of intensive experimental and theoretical investigation. In this lecture, I will present the electron liquids of FQHE in the broader context of topological states of matter, introduce the grand concept of CFs, apply it to the puzzling states represented by nu=5/2 and 4/11, and review our recent (numerical) studies giving new insight into the microscopic origin of their incompressibility.