A Landauer Formula for Bioelectronic Applications

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.

What Can We Learn from Protein-Based Electron Transport Junctions?

“…Remarkably, though, the observed T -independence of ETp via proteins over ≥ ∼5 nm is consistent with results of optically monitored ET in frozen (glassy) protein solutions, 26 and in single protein crystals, 27 raising the question what can be the mechanism of ETp over these longer distances, if not tunneling? Several ideas addressing this question have been presented for organic molecules 19 and proteins, 25 but how these are applicable to ETp via large proteins is not clear. Still, as an electron current can also be viewed as a flow of holes in the opposite direction, aromatic amino acids, e.g., tryptophan and tyrosine, 28 may play an important role because of their potential of hole formation and currents, as exemplified by hole hopping.…”

“…This experimental result is also one of the consequences of a Landauer model-based theory. 25 Thus, when ETp proceeds by tunneling, any electron residence time near the nuclei (none for pure tunneling) is too short to allow forming a new chemical species. Importantly, the electrodes’ presence assures a time-independent availability of “source” and “drain electrons”.…”

Electrochemical Potential‐Driven High‐Throughput Molecular Electronic and Spintronic Devices: From Molecules to Applications

“…We will not discuss the theory,asdetails on charge-transport theory from the Landauer and Marcus perspective can be found in the literature. [36][37][38][39][40][41] Along with the pros of electro-chemical techniques,there are also certain cons,which we will briefly review in this article.Therefore,the prime aim of this Review is to provide ac omprehensive discussion on these applications and their future scope.…”

Off-resonant coherent electron transport over three nanometers in multi-heme protein bioelectronic junctions

“…Here, we use the Breit-Wigner approximation of the transmission function [33,53] where each molecular state forms the Lorentzian peak of the width given by its coupling to the left and right electrodes, respectively. The transmission is then sum of such peaks…”