Quantum Conductivity for Metal-Insulator-Metal Nanostructures

We present a methodology based on quantum mechanics for assigning quantum conductivity when an ac field is applied across a variable gap between two plasmonic nanoparticles with an insulator sandwiched between them. The quantum tunneling effect is portrayed by a set of quantum conductivity coefficients describing the linear ac conductivity responding at the frequency of the applied field and nonlinear coefficients that modulate the field amplitude at the fundamental frequency and its harmonics. The quantum conductivity, determined with no fit parameters, has both frequency and gap dependence that can be applied to determine the nonlinear quantum effects of strong applied electromagnetic fields even when the system is composed of dissimilar metal nanostructures. Our methodology compares well to results on quantum tunneling effects reported in the literature and it is simple to extend it to a number of systems with different metals and different insulators between them.