  We investigate a particular phase transition between two different tunneling
regimes, direct and injection (Fowler-Nordheim), experimentally observed in the
current-voltage characteristics of the light receptor bacteriorhodopsin (bR).
Here, the sharp increase of the current above about 3 V is theoretically
interpreted as the cross-over between the direct and injection
sequential-tunneling regimes. Theory also predicts a very special behaviour for
the associated current fluctuations around steady state. We find the remarkable
result that in a large range of bias around the transition between the two
tunneling regimes, the probability density functions can be traced back to the
generalization of the Gumbel distribution. This non-Gaussian distribution is
the universal standard to describe fluctuations under extreme conditions.
