Longitudinal polarizability and the electronic topological transitions in a quasi-one-dimensional electron gas

Abstract

The longitudinal polarization function of a quasi-one-dimensional electron gas (Q1DEG) confined in a semiconductor quantum well wire (QWW) is given in the random-phase approximation (RPA) for the cases where T = 0 K and T not equal 0 K, taking into account the lack of spatial invariance in the plane of the cross-section of the QWW. it is given as a sum of terms in the form of a spatial function, composed from the wavefunctions, and their complex conjugates, of two single-electron states and the polarizability for each allowed transition. The polarizability for a given transition is studied in terms of its frequency, momentum and temperature dependences, relating its behaviour with the electronic topological transition occurring in the Fermi domain. The results are analysed by representing the electron gas involved in the transition as composed from two quasi-particle subgases with different effective masses within the conduction band as an excitonic gas.