Are Current Discontinuities in Molecular Devices Experimentally Observable?

Abstract

An ongoing debate in the first-principles description of conduction in molecular devices concerns the correct definition of current in the presence of non-local potentials. If the physical current density j = (−ieh/2m)(Ψ∗∇Ψ − Ψ∇Ψ∗ ) is not locally conserved but can be re-adjusted by a non-local term, which current should be regarded as real? Situations of this kind have been studied for example, for currents in saturated chains of alkanes, silanes and germanes, and in linear carbon wires. We prove that in any case the extended Maxwell equations by Aharonov-Bohm give the e.m. field generated by such currents without any ambiguity. In fact, the wave equations have the same source terms as in Maxwell theory, but the local non-conservation of charge leads to longitudinal radiative contributions of E, as well as to additional transverse radiative terms in both E and B. For an oscillating dipole we show that the radiated electrical field has a longitudinal component proportional to ω ˆP, where ˆP is the anomalous moment∫ Î(x)xd3 x and Î is the space-dependent part of the anomaly I = ∂t ρ + ∇ · j. For example, if a fraction η of a charge q oscillating over a distance 2a lacks a corresponding current, the predicted maximum longitudinal field (along the oscillation axis) is EL,max = 2ηω2 qa/(c2r). In the case of a stationary current in a molecular device, a failure of local current conservation causes a “missing field” effect that can be experimentally observable, especially if its entity depends on the total current; in this case one should observe at a fixed position changes in the ratio B/i in dependence on i, in contrast with the standard Maxwell equations. The missing field effect is confirmed by numerical solutions of the extended equations, which also show the spatial distribution of the non-local term in the current.