ABSTRACT
The instability in the polaron problem has been analyzed by Peeters and Devreese, who have shown that the instabilities obtained in the various polaron models are rather mathematical artifacts and consequences of the approximations employed. In a polaron gas with electron-electron interaction, one can change the effective coupling constant by changing the electron density, which is precisely the many-particle screening effect. Das Sarma studied for the first time the screening effects on the polaronic interaction in a quasi-two-dimensional structure and showed that many-body effects would lead to an appreciable decrease in the polaron mass correction. However, the static random-phase approximation might overestimate the screening effect because it does not take into account the effect of exchange and correlation hole which exists around each electron. The effect of the exchange and correlation hole is to prevent other electrons from coming close to the one that participates in the dielectric screening.
