On the effect of dielectric environment on oscillations of the Fermi energy of an elliptic metallic nanowire

The size dependences of the Fermi energy of 1D metallic systems with an elliptic cross section in a dielectric medium has been obtained in the model of free electrons and a cylindrical potential well of finite depth. The calculations have been carried out for Au wires in SiO$_2$ and in Al$_2$O$_3$. It has been shown that a change in the geometry of the cross section and the presence of the dielectric environment lead to a decrease in the Fermi energy, whereas the general character of the size dependences is preserved.