Evidence of Gumbel distributions of conductance fluctuations in bacteriorhodopsin thin films

By considering a set of experiments carried out on bacteriorhodopsin in vitro by Casuso et al (2007 Phys. Rev. E 76 041919), we extract the conductance as function of the applied voltage. The microscopic interpretation of experiments shows that charge transfer is ruled by a direct tunneling (DT) mechanism at low bias and by a Fowler-Nordheim (FN) tunneling mechanism at high bias. A nucleation region at the cross-over between the DT and FN regimes can be identified. A theoretical analysis of conductance fluctuations is performed by calculating the corresponding variance and the probability density functions (PDFs): these constitute a powerful indicator in order to understand the internal dynamics of the system. Conductance fluctuations are non-Gaussian and follow well the standard generalized Gumbel distributions G(a). In particular, at low bias, the PDFs are bimodal and can be resolved in at least a couple of G(a) functions with different values of the shape parameter a. The nucleation region is characterized by a single Gumbel distribution, G(1). At increasing bias, the G(1) distribution turns in a bimodal distribution. We discuss possible correlations between the voltage dependence of the G(a) and the microscopic mechanisms that determine the electrical response of the system.