Coulomb interaction and transport in tunnel junctions and quantum dots

Abstract

In the first part of the paper the AC conductance of a quasi-one-dimensional tunnel junction involving a potential barrier is calculated in linear response. Its frequency dependence is used to define a dynamical capacitance. The influence of phase breaking electron-phonon interactions is investigated. It is argued that Coulomb interaction is of minor importance at higher frequencies and that dynamic and static capacitances are the same. The argument provides a high-frequency limit for turnstile operation. In the second part, the quantum mechanical properties of few interacting electrons in quantum dots are considered. Including the spin degree of freedom, the spectral properties of up to four interacting electrons confined within a quasi-one-dimensional system of finite length with Coulomb interactions are investigated by numerical diagonalization. The limitations of the description in terms of a capacitance are discussed. For sufficiently low density the electrons become localized, forming a Wigner molecule. The energetically lowest excitations are identified as vibrational and tunneling modes, both being collective modes involving all the electrons.