Charging effects in ultrasmall quantum dots in the presence of time-varying fields

Abstract

The influence of charging effects on time-dependent transport in small semiconductor quantum dots with arbitrary level spectra is studied. Starting from an explicit time-dependent tunneling Hamiltonian, a non-Markovian Master equation is derived which is also valid in the nonlinear response regime. The many-body nonequilibrium distribution functions of the dot are calculated and the I-V characteristic of the structure including the displacement currents is obtained. New resonant features show up in the Coulomb oscillations and in the Coulomb staircase, and a new possibility to realize electronic pumps is described. 73.40.Gk, 73.20.Dx, 73.50.Mx, 73.50.Fq Typeset using REVTEX 1 The influence of the Coulomb interaction on low-temperature quantum transport through metallic or semiconducting islands (quantum dots) has been the subject of many theoretical and experimental papers (see, e.g., [1] and references therein). It shows up in a variety of interesting effects like, e.g., Coulomb blockade and resonant tunneling phenomena. However, the investigation of time-dependent perturbations and of fluctuations of the electrodynamic environement has started only recently, either neglecting charging effects [2–11] or considering the metallic case for time translational invariant systems [12,13]. An explicit time dependence of the applied voltages introduces a new energy scale h̄ω in the problem, and a multitude of new effects is expected to occur, some of them relevant to device applications such as high-frequency oscillators. In this letter, we consider an interacting quantum dot with an arbitrary level spectrum subject to an explicit time-dependent classical field. It can describe a periodic modulation of the Fermi energy in the leads (i.e. time-dependent bias voltages) or time-dependent perturbations for the quantum states in the dot. We are especially interested in the effects of the Coulomb interaction in the limit of low tunneling rates but finite level spacing, so that resonant tunneling with thermally broadened line shapes will occur. In contrast to rfs. [12,13], we calculate the complete time-dependent (many-body) distribution function of the dot using a non-Markovian Master equation approach. As a consequence we obtain new features in the Coulomb oscillations which can not be seen in the time-independent case or for continuous level spectra like in metals. Furthermore, for certain asymmetric level structures in the nonlinear response regime, a new mechanism to realize an electronic pump is described. An important consistency check for our formalism is the fact that the sum of all currents into the system (including the displacement currents) is conserved [9]. We have included the displacement currents in our formalism within the Coulomb-blockade model to make our calculations more realistic. However, since we are mostly interested in the case of low capacitances (where charging effects are important), we do not obtain a significant influence of the displacement currents on the I-V characteristics. 2 As a model for an interacting quantum dot coupled to two reservoirs by tunnel junctions with capacitances CL and CR, we will use the time-dependent tunneling Hamiltonian H(t) = H0(t) + V (t) +HT . Here, H0(t) = ∑

Cite this paper

@inproceedings{Bruder1993ChargingEI, title={Charging effects in ultrasmall quantum dots in the presence of time-varying fields}, author={Christoph Bruder}, year={1993} }