Dynamic correlation and polaronic effects on the correlational properties of finite-temperature electron quantum wire

Abstract

Abstract We study the role of dynamic correlation and polaronic effects on the correlational properties of a GaAs-based electron quantum wire at finite-temperature T. The dynamics of electron correlations is incorporated through the self-consistent mean-field approximation of Hasegawa and Shimizu (the qSTLS theory) and the polaronic effects via the Fröhlich interactions. Results are presented for the static correlation functions, dynamic structure factor and electron’s contact probability over a wide range of T and electron number density r s . We find that for a fixed wire width b and T, electrons undergo a transition from the quantum liquid to Wigner crystal state due to the dynamics of severely correlated electrons at a critical r s = r s c . The inclusion of polaronic effects along with the conventional electron-electron interactions tends to increase r s c significantly at each T ultimately improving the quantum phase diagram. The electron’s contact probability exhibits a non-monotonic T-dependence which remains positive over a broader range of r s owing to the inclusion of polaronic effects. Besides, we explore the effect of phonon contribution on the plasmon energy of the quantum wire at non-zero T and find that there is splitting in the energy into two branches namely, plasmonlike and phononlike with former having energy lower than the latter. Both of the energy modes show consistent blue shift with rise in T, get damp at a critical wave vector q c , and q c decreases with T. Finally, we calculate the finite-T polaronic contribution to the free energy whose magnitude increases with T as r s → 0 and it becomes almost constant at sufficiently high r s .