Quantum Transport with Two Interacting Conduction Channels in Gold-Azurin-Bismuth Solid-State Junctions

The fundamental question of ‘what is the transport path of electrons through proteins?’ initially introduced while studying long-range electron transfer between localized redox centers separated by proteins <i>in vivo</i> is also highly relevant to the transport properties of solid-state, dry metal-protein-metal junctions because the characteristic Fermi wavelength, <i>λ_F</i>, of the involved electrons is smaller than the contact footprint of the proteins. Under such conditions, the transport path appears to depend on the coupling of the proteins to the leads. For example, in one of the ‘work horses’ of biomolecular electronics, Au-<i>Azurin(Az</i>)-Au junctions, the electrons characterized by <i>λ_F</i> ~ 0.5 nm appear to be transported coherently by off-resonance tunneling if Az is strongly coupled to the leads and by coherent resonance tunneling associated with levels of the redox center, if it is weakly coupled to the leads. Transport in the latter case is especially puzzling because the modest coupling values invoked for its quantification are sufficiently small to allow the tunneling charges to reside in the resonance levels a sufficient time for structural relaxation (reorganization), which should then entail non-coherent transport by a hopping, i.e., activated hops with tunneling between them.<br/>Here, we report of conductance measurements of molecular ensemble nanopore junctions of Au-Az-bismuth(Bi), with well-defined geometry and containing ~2000 proteins in each pore. We argue that since electrons in Bi have <i>λ_F</i> longer than the protein footprint, transport takes place in these junctions by two interacting conducting channels, characterized by different time scales. The slow and fast channels are associated with the redox center and the protein matrix, respectively, and consequently transport takes place in the first channel by a sequential (non-coherent) process and by coherent non-resonant tunneling in the second channel. The resulting overall observed conductance behavior suggests that the two channels are capacitively coupled and that the broad level responsible for the off-resonance tunneling changes its energy in response to the charge occupation of the weakly coupled (redox) channel. This in turn also suggests that transport in these junctions is dominated by the off-resonance (fast) channel, while the slow (redox) channel contribute directly to conductance only negligibly and instead affects transport by intramolecular gating.