Berry Phase and Anomalous Transport of the Composite Fermions at the Half-Filled Landau Level

Understand

The fractional quantum Hall effect (FQHE) in two-dimensional electron system (2DES) is an exotic, superfluid-like matter with an emergent topological order.

• From the consideration of Aharonov-Bohm interaction of 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).
• 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 wave vector in the semi-classical geometrical resonance experiments.
• Recent developments in the theory of CFs have led to a prediction of a $\pi$ Berry phase for the CF circling around the Fermi surface at half-filling.