Polarizability of a carrier in an isolated well of a quantum-well wire

Polarizability (${\mathrm{\alpha }}_{\mathit{p}}$) values are estimated for an electron confined to move within the well of a quasi-one-dimensional (Q1D) GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As superlattice system with a square cross section. The values of ${\mathrm{\alpha }}_{\mathit{p}}$ obtained by two different methods, one using the expression for the dipole moment and the second from an estimate of the shift of the peak position of the wave function, are in good agreement with each other. The electron-lattice coupling leads to a uniform shift of the binding energies by an amount -αħω. While this result is different from that of a Q2D system, the values of ${\mathrm{\alpha }}_{\mathit{p}}$ are of the same order for both Q1D and Q2D systems. Our results also show that ${\mathrm{\alpha }}_{\mathit{p}}$ increases with well widths and depends on the direction of the electric field with reference to an axis defined parallel to an edge of the square cross section.