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We consider a two-dimensional random resistor network (RRN) in the presence of two competing biased processes consisting of the breaking and recovering of elementary resistors. These two processes are driven by the joint effects of an electrical bias and of the heat exchange with a thermal bath. The electrical bias is set up by applying a constant voltage or, alternatively, a constant current. Monte Carlo simulations are performed to analyze the network evolution in the full range of bias values. Depending on the bias strength, electrical failure or steady state are achieved. Here we investigate the steady state of the RRN focusing on the properties of the non-Ohmic regime. In constant-voltage conditions, a scaling relation is found between /(0) and V/V(0), where is the average network resistance, (0) the linear regime resistance, and V0 the threshold value for the onset of nonlinearity. A similar relation is found in constant-current conditions. The relative variance of resistance fluctuations also exhibits a strong nonlinearity whose properties are investigated. The power spectral density of resistance fluctuations presents a Lorentzian spectrum and the amplitude of fluctuations shows a significant non-Gaussian behavior in the prebreakdown region. These results compare well with electrical breakdown measurements in thin films of composites and of other conducting materials.

Shot-noise suppression is investigated in nondegenerate diffusive conductors by means of an ensemble Monte Carlo simulator. The universal 1͞3 suppression value is obtained when transport occurs under elastic collision regime provided the following conditions are satisfied: (i) The applied voltage is much larger than the thermal value; (ii) the length of the device is much greater than both the elastic mean free path and the Debye length. By fully suppressing carrier-number fluctuations, long-range Coulomb interaction is essential to obtain the 1͞3 value in the low-frequency limit.[ S0031-9007(98)05732-9] PACS numbers: 72.70. + m, 73.23.Ad, 73.50.Td In recent years kinetic phenomena in mesoscopic structures are offering a fascinating scenario for fundamental research [1]. One of the most up-to-date subjects is shotnoise suppression in disordered conductors. Here, the excess noise power has been predicted to comprise exactly one-third of the full shot-noise value S I 2eI. This result has been credited to different theoretical approaches as applied to several microscopic models of disordered conductors. For a phase-coherent model Beenakker and Büttiker [2] obtained the result using a bimodal distribution of transmission eigenvalues with the help of random matrix theory to calculate averages. For a semiclassical 1D model which includes Pauli principle Nagaev [3] found the same result using a Boltzmann kinetic approach within an elastic and energy independent relaxation-time approximation. For a semiclassical sequential tunneling model de Jong and Beenakker [4] obtained the 1͞3 value within a Boltzmann-Langevin approach in the limit of an infinite number of equal barriers and independently from the value of their transmission coefficient. Compatible results have been found by Liu et al.[5] from a semiclassical implementation of a Monte Carlo simulation which includes Pauli principle. For a phase-coherent model Nazarov [6] has proven the universality of this result in the diffusive limit for arbitrary shape and resistivity distribution of the conductor as long as its length is greater than the carrier mean free path. Experimental evidence of the reduced shot-noise level close to the predicted 1͞3 value in diffusive mesoscopic conductors has been provided in [7][8][9].From the above it is argued that the 1͞3 value of the suppression factor g S I ͞2eI is a universal phenomenon whose physical meaning should lay beyond classical or quantum mechanics and originate from some unifying concept. The aim of this Letter is to address this issue. We conjecture that discreteness of charge transport is at the basis of such a concept, and that a transport dominated by elastic interactions is ultimately the physical reason for the 1͞3 suppression independently from the quantum or classical approach used. Both the (apparently unrelated) coherent [2] and semiclassical [3] contexts where the reduction factor 1͞3 has appeared assume a degenerate Fermi gas, and the noise reduction comes from the regulation of electron motion by the ...

Nanoscale electron transport through the purple membrane monolayer, a two-dimensional crystal lattice of the transmembrane protein bacteriorhodopsin, is studied by conductive atomic force microscopy. We demonstrate that the purple membrane exhibits nonresonant tunneling transport, with two characteristic tunneling regimes depending on the applied voltage ͑direct and Fowler-Nordheim͒. Our results show that the purple membrane can carry significant current density at the nanometer scale, several orders of magnitude larger than previously estimated by macroscale measurements. DOI: 10.1103/PhysRevE.76.041919 PACS number͑s͒: 87.80.Ϫy, 73.40.Rw, 85.65.ϩh The purple membrane ͑PM͒ is a two-dimensional crystal lattice naturally present in the cell membrane of Halobacterium salinarum. It is composed of a lipid bilayer and a single-protein species, the Bacteriorhodopsin ͑bR͒, in a lipidto-protein ratio of 10 ͑mol/ mol͒. Bacteriorhodopsin acts as a light-driven proton pump, converting solar energy into an electrochemical proton gradient across the cell membrane ͓1,2͔. Its functional stability under different environmental conditions combined with easy and large production has made bR a model protein for studies of charge transport on cell membranes, as well as an excellent candidate for bioelectronic applications ͓3,4͔.Despite its enormous interest, only a few studies regarding the electron transport measurements of a single PM layer have been reported so far, leading to an incomplete and controversial picture ͓5-7͔. The main obstacle encountered in measuring the electrical conductivity of the PM monolayer ͑ϳ5 nm thick͒ resides on providing reliable electrical contact at the electrode-membrane interface. Measured currents can dramatically differ by orders of magnitude from measurement to measurement on supposedly identical conditions, being extremely sensitive to the electrode-membrane distance as well as the applied load on the membrane. To date, two methods have been reported: ͑i͒ measuring the current of a monolayer confined between two submillimeter-sized electrodes ͓5͔ and ͑ii͒ probing the nanoscale conductivity of the monolayer using a scanning tunneling microscope ͑STM͒ ͓6,7͔. The millimeter-sized electrode configuration demands a flat and hole-free monolayer covering the entire electrode surface, which is, however, difficult to fabricate. Furthermore, averaging of biological information on a macroscale level is inherent to this method. To study electron conduction at the molecular level, scanning probe techniques are by far the most appropriate approach. STM, however, has an intrinsic limit in the tunneling current feedback for insulating samples which impedes the control and quantification of the probe-membrane distance and forces applied on the biomolecules.In this article we use conductive atomic force microscopy ͑C-AFM͒ as an extremely controlled method to provide a comprehensive and unambiguous model of electron conduction in the PM monolayer. Conductive AFM has demonstrated to be well suited to studying th...