We investigate conductance and conductance fluctuations of two transmembrane proteins, bacteriorhodopsin and proteorhodopsin, belonging to the family of protein light receptors. These proteins are widely diffused in aqueous environments, are sensitive to visible light and are promising biomaterials for the realization of novel photodevices. The conductance exhibits a rapid increase at increasing applied voltages, over a threshold value. Around the threshold value the variance of conductance fluctuations shows a dramatic jump of about 5 orders of magnitude: conductance and variance behaviours trace a second order phase transition. Furthermore, the conductance fluctuations evidence a non-Gaussian behaviour with a probability density function (PDF) which follows a generalized Gumbel distribution, typical of extreme-value statistics. The theoretical model is validated on existing current-voltage measurements and the interpretation of the PDF of conductance fluctuations is proven to be in line with the microscopic mechanisms responsible of charge transport.
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