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

Abstract

Experimental signatures of a Berry phase for composite fermions in the fractional quantum Hall effect provide support for the predictions that these composite fermions are Dirac particles. 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)3,4,5. A strong support for the CF theories comes from experimental confirmation of the predicted Fermi surface at ν = 1/2 (where ν is the Landau level filling factor) from the detection of the Fermi wavevector in semi-classical geometrical resonance experiments2,6,7,8,9. Recent developments in the theory of CFs10,11,12,13,14,15,16,17,18,19,20,21 have led to the prediction of a π Berry phase for the CF circling around the Fermi surface at half-filling10,14,17,18,19,20. 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 π Berry phase at ν = 1/2. We also discover that the conductivity of composite fermions at ν = 1/2 displays an anomalous linear density dependence, whose origin remains mysterious yet tantalizing.