Edge state spectroscopy in GaAs quantum wires*

We probe the integer quantum Hall edge states in a GaAs/AlGaAs 2D electron gas at low electron temperature T_e ≈ 10mK using an adjacent, tunnel coupled quantum wire. The tunnelling current peaks when energy and momentum conservation are fulfilled. A vector magnetic field provides a momentum kick to the tunnelling electrons and allows for spectroscopic imaging of more than the first ten Landau level edge states with nanometer real space resolution and down to magnetic fields around 10 mT where n_bulk ≈ 500. Upon increasing the field, these states are compressed towards the sample edge, until eventually they become magnetically depopulated and move back into the bulk. In addition the spectroscopy experiment reveals spin splitting, fermi-level pinning, demonstrates the chiral nature of the current carrying edge states, and allows us to extract the exchange interaction in the quantum Hall regime. Theoretical predictions using both, an analytical model and numerical solutions from a single particle Schrödinger solver for hard wall confined Landau levels show excellent agreement with the experiment over the entire range of magnetic field.