We have measured I-V curves of single-crystalline lateral Bi nanoconst
rictions of a size of several hundred nanometers. The I-V curves are s
trongly non-linear at high currents when the voltage is measured with
probes at 4 mu m on either side of the constriction, the effect increa
sing with increasing magnetic field. Surprisingly, with voltage probes
at 4 and 55 mu m on one side of the constriction, we still find a wea
k non-linearity. We explain these observations with Zener tunnelling,
made possible by the strong electrical field in the constriction. We s
uggest that diffusion of tunnelling-induced excess carriers causes a n
on-local effect, which can be measured at some distance of the constri
ction.