  We report a zero-bias peak in the differential conductance of a Quantum Point
Contact (QPC), which splits in an external magnetic field. The peak is observed
over a range of device conductance values starting significantly below
$2e^2/h$. The observed splitting closely matches the Zeeman energy and shows
very little dependence on gate voltage, suggesting that the mechanism
responsible for the formation of the peak involves electron spin. Precision
Zeeman energy data for the experiment are obtained from a separately patterned
single-electron transistor located a short distance away from the QPC. The QPC
device has four gates arranged in a way that permits tuning of the longitudinal
potential, and is fabricated in a GaAs/AlGaAs heterostructure containing
2-dimenional electron gas. We show that the agreement between the peak
splitting and the Zeeman energy is robust with respect to moderate distortions
of the QPC potential. We also show that the mechanism that leads to the
formation of the ZBP is different from the conventional Kondo effect found in
quantum dots.
