In-plane tunnelling between one- and two-dimensional electron systems

Lateral tunnelling spectroscopy between a two-dimensional (2D) and a one-dimensional (1D) electron system in an AlGaAs/GaAs heterostructure is accomplished by preparing a thin barrier using atomic force microscope lithography. The barrier transmission and the electron density in the electrodes are controlled by a global top gate. At gate voltages below the onset of tunnelling the 1D system exhibits quantized conductance. Higher gate voltage enables to probe the 1D density of states in the tunnelling conductance as a function of the tunnelling bias voltage between 2D and 1D electrode and to directly read the subband separation. At large modulation amplitudes a second set of long-period oscillations appears, which reflects the crossing of 1D levels through the Fermi energy due to the change of the 1D confining potential with tunnelling bias voltage.