Modeling of nonlinear and non-stationary multi-vortex behavior of CDWs at nanoscales in restricted geometries of internal junctions

We report on studies of stationary states and their transient dynamic for an incommensurate charge density wave (ICDW) in a restricted geometry of two spatial dimensions. The model takes into account multiple fields in mutual nonlinear interactions: the amplitude and the phase of the complex order parameter, and distributions of the electric and chemical potentials, of the density and the current of normal carriers. We observed spontaneous formation of vortices (the ICDW dislocations), and followed events of their creation and the subsequent evolution. The vortices appear when the voltage across, or the current through, the sample exceed a threshold. The number of vortices remnant in the reconstructed stationary state increases stepwise – in agreement with experiments, while a much greater number of vortices appears during the intermediate transient states. The vortex core concentrates the electric dipole leading to sharp drops of the electric and chemical potentials across the core. That can lead to enhanced inter-layer tunneling making the core to be a self-tuned microscopic tunneling junction. The results are applied to experiments on nano-fabricated mesa-junctions. They also appeal to modern efforts of the field-effect transformations in correlated electronic systems.