Electronic states in hyperbolic-boundary crescent-shaped quantum wires

A fully two-dimensional study of the electronic sub-bands in crescent-shaped quantum wires is presented. The confinement energies and the wave functions are compared by means of an aspect ratio to those produced by the adiabatic approximation. Guidelines for applying the adiabatic model are provided and the adiabatic quantum number classification scheme is discussed. "Non-adiabatic" states are determined among the first few sub-bands and a built-in dipole is identified. The energy spectrum is explored as a function of wire dimensions achievable by present-day technology. Wire parameters corresponding to maximized sub-band separations are determined.