Effective mass in quasi two-dimensional systems

– The effective mass of the quasiparticle excitations in quasi two-dimensional systems is calculated analytically. It is shown that the effective mass increases sharply when the density approaches the critical one of metal-insulator transition. This suggests a Mott-type of transition rather than an Anderson-like transition. The experimental measurements can be reproduced in this way without any additional parameter. The explanation of the metal to insulator transition (MIT) at low temperatures in quasi two-dimensional systems is still a strongly debated task. A critical discussion of different approaches can be found in Ref. [1]. The generic feature of MIT transition is the rapid change from insulating to conducting behavior when the density is increased very slightly at low temperatures. This density driven MIT transitions are usually referred to as Mott transitions. The characteristic feature of the Mott-Hubbard transition is that the increasing effective mass is the reason for increasing resistivity ρ = m/enτ while the Anderson scenario would assume a vanishing relaxation time nτ . It is obvious that this feature characterizes the transition rather than the nature of the insulating state itself, see for details [2]. In a recent experiment [3] it was shown that the effective mass is increasing sharply when approaching the critical density. This would underline the Mott picture rather than the Anderson transition. Here in this letter we want to substantiate this picture by a quantitative explanation of the experimental values of the effective mass. To this end we will introduce a new approximation which is based on the large mass difference between transport electrons and scattering impurity of donor ions. Our model consists in electrons scattering with heavy ions within the quasi twodimensional gas. In this way we will describe the transition due to Coulomb correlation and not the nature of the insulating state itself. Assuming the motion restricted to the x−y plane, the Coulomb potential in this cylindrical Fermi surface is Vab(qx, qy) = 2πeaebh̄/ √ q x + q 2 y . We want to determine the quasiparticle mass which will be compared to the experimental results. To this end we will use the standard quasiparticle picture based on the Green’s function method. As generally known, within this approach the quasiparticle energy and the mass of the model are determined by the real part of the selfenergy according to the following formulas.