Mathematical model and design of nanoeloctronic device based on metal-dielectric transition

A new type of nanoelectronic device based on stimulated Peierls-Mott transition is studied analytically and numerically. By means of conformal mappings a quantum mechanical potential for ballistic electrons moving on the conducting electrode has been calculated in terms of elliptic functions. The latter are parameterized by the geometrical characteristics of the nano-device and the governing voltage applied. The spectral zone structure of the effective Schrodinger operator has been calculated numerically for various sets of the device parameters. For the device fabricated from GaAs semiconductor the set of parameters which guarantee the stable metal-dielectric transition at liquid helium temperature has been found.