Polaron and conduction band non-parabolicity effects on the binding energy, diamagnetic susceptibility and polarizability of an impurity in quantum rings

Abstract

By employing a variational approach, we have investigated the effect of conduction band non-parabolicity (NP) on the binding energy ( E b ) and the susceptibility diamagnetic ( χ d i a ) of a donor impurity confined in wurtzite G a N / G a 1 − x A l x N quantum rings (QRs) with finite confinement potential in the presence of an electric field ( F ) applied in the z – direction. The combined effect of conduction band NP and interaction between electron-bulk longitudinal optical (LO) phonon on the E b and the χ d i a are also investigated in the case of infinite confinement potential. It is illustrated that the E b decreases progressively with F , particularly for large height ( H ) or for small radial thickness ( Δ R ) of QR, and the polaronic correction to the E b increases slightly with the increase of the electric field. In the case of infinite potential, the combined effects of NP and polaron leads to a more enhancement on the E b and χ d i a particularly for an on-center donor impurity. In addition, we have examined the dependence of the polarizability ( α p ) on the sizes of QR and the electric field with and without polaron effect. It is shown that the α p increases (decreases) with H (applied the electric field) and it is nearly insensitive to the polaron effect for the strong confinement. Our findings show also that the polaronic effect tends to decrease the α p , especially for thick QR. • The polaron effect enhances the binding energy and the diamagnetic susceptibility. • The binding energy and the diamagnetic susceptibility increases with the non-parabolicity effect. • Polaron effect tends to decrease the polarizability especially for larger quantum rings. • Polarizability decreases with increasing electric field especially for thick quantum rings.