Abstract
Recent electronic transport experiments using metallic contacts attached to proteins identified some “stylized facts”, which contradict conventional wisdom that increasing either the spatial distance between the electrodes or the temperature suppresses conductance exponentially. These include nearly temperature-independent conductance over the protein in the 30 to 300 K range, distance-independent conductance within a single protein in the 1 to 10 nm range and an anomalously large conductance in the 0.1 to 10 nS range. In this paper, we develop a generalization of the low temperature Landauer formula, which can account for the joint effects of tunneling and decoherence and can explain these new experimental findings. We use novel approximations, which greatly simplify the mathematical treatment and allow us to calculate the conductance in terms of a handful macroscopic parameters, instead of the myriads of microscopic parameters describing the details of an atomic level quantum chemical computation. The new approach makes it possible to get predictions for the outcomes of new experiments without relying solely on high performance computing and can distinguish important and unimportant details of the protein structures from the point of view of transport properties.
Highlights
Electron transport measurements via metallic contacts attached to proteins show anomalous properties relative to electron transfer in homologous structures [1,2]
Bioelectronic measurements with metallic contacts chemically bound to molecules can be regarded as molecular junctions, and the Landauer–Büttiker (LB) formula is one of the best theoretical tools to describe quantum conductance at zero temperature in such systems [11]
In the opposite case, when the contacts are strong, electrons and holes enter the molecule via tunneling. This is a new regime not covered by the previous studies, and we show that the relation between electron transfer rate and the conductance breaks down
Summary
Electron transport measurements via metallic contacts attached to proteins show anomalous properties relative to electron transfer in homologous structures [1,2]. Bioelectronic measurements with metallic contacts chemically bound to molecules can be regarded as molecular junctions, and the Landauer–Büttiker (LB) formula is one of the best theoretical tools to describe quantum conductance at zero temperature in such systems [11]. It expresses the conductance in terms of the scattering matrix elements between metallic leads. A positively charged hole tunneling trough the molecule from the right to the left electrode with negative tunneling energy ε n − EF This way, both processes contribute to the net current with the same sign. We generalize Datta’s result for finite temperatures
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