The second topic - polarons and molecular IVs

A second interesting discussion going on right now concerns hysteresis in molecular electronic device current-voltage characteristics. There have been a number of papers that have reported hysteretic IV curves in molecular systems, where applying a high bias can make the system undergo a transition from a low-conductance state to a higher conductance state. That higher conductance state persists until the bias voltage is cycled back down to some value below the turn-on voltage. This sort of hysteresis is interesting from the practical perspective: if the high/low conducting states are long-lived, one could imagine making a memory or logic out of devices with these properties. The main scientific question, then, is what is the underlying mechanism for this conductance switching?

One candidate that has been suggested by a number of people is polaronic. A polaron is a charge carrier accompanied by a geometric distortion of the charge carrying medium. The basic idea is that one can start with a neutral molecule, transfer an electron onto that molecule, and once that electron is there, the molecule could distort in such a way as to greatly lower the total energy of the system. The result is that the molecule could trap that additional electron via a geometric deformation. If the neutral and charged states of the molecule have significantly different couplings to the source and drain electrodes, this kind of trapping could conceivably lead to hysteretic switching between conductance states. Such a strong electron-vibrational coupling would basically make the effective on-site repulsion, U (for the no vibrational coupling case), be renormalized downward, all the way to a negative value.

This problem is interesting because it's fundamentally non-perturbative, at least in the electron-vibrational coupling, and generally non-equilibrium, too. Theorists have therefore been arguing about the right way to solve this system. As always, the whole point of this kind of theory is to come up with a toy model that includes all the essential physics and omits nothing of importance, and then use some method to solve it. If one leaves out the coupling between the electronic level and the leads, and considers just a single electronic level, this problem can be solved analytically, with no hysteresis showing up. One can include the coupling to the leads in some limit, and solve using Hartee-Fock techniques, again finding no hysteresis. One can choose a different set of limits, and find hysteresis; and finally, one can do a more sophisticated treatment of the nonequilibrium aspects and find telegraph-like switching rather than hysteresis. The big question is, which if any of these models are really relevant to the regime of experiments? It's highly likely that much switching in experiments really has to do with the geometry of the molecule-metal bond, rather than anything this exotic. Of course, that doesn't mean it's not worth trying to examine this question deliberately through experiments....