Berry phase and anomalous transport of the composite fermions at the half-filled Landau level

摘要

The fractional quantum Hall effect (FQHE) (1,2) in two-dimensional electron systems is an exotic, superfluid-like matter with an emergent topological order. From the consideration of the Aharonov-Bohm interaction between electrons and magnetic field, the ground state of a half-filled lowest Landau level is mathematically transformed to a Fermi sea of composite objects of electrons bound to two flux quanta, termed composite fermions (CFs) (3-5). A strong support for the CF theories comes from experimental confirmation of the predicted Fermi surface at nu = 1/2 (where nu is the Landau level filling factor) from the detection of the Fermi wavevector in semi-classical geometrical resonance experiments(2,6-9). Recent developments in the theory of CFs(10-21) have led to the prediction of a pi Berry phase for the CF circling around the Fermi surface at half-filling(10,14,17-20). In this paper we provide experimental evidence for the detection of the Berry phase of CFs in the fractional quantum Hall effect. Our measurements of the Shubnikov-de Haas oscillations of CFs as a function carrier density at a fixed magnetic field provide strong support for the existence of a pi Berry phase at nu = 1/2. We also discover that the conductivity of composite fermions at nu = 1/2 displays an anomalous linear density dependence, whose origin remains mysterious yet tantalizing.