Statistical distribution of Coulomb blockade peak heights in adiabatically pumped quantum dots

p2 18 � ≈ 1.2 upon breaking time-reversal symmetry. This is the pumping analog of the statistical theory of Coulomb blockade conductance peaks. In recent years, the phenomenon of adiabatic quantum pumping in quantum dots has attracted a lot of theoretical and experimental attention. It is the generation of a d.c. current in the absence of a bias voltage by periodic modulations of two or more parameters, such as the shape of the dot or a magnetic field, that modify the quantum-mechanical properties of the system. The idea of adiabatic pumping was pioneered by Thouless [1] for electrons at zero temperature in an isolated one-dimensional periodic potential. Using cyclic variations of the potential, electrons can be pumped one by one through the system. Following early realizations of electron pumps based on ”classical” sequential pumping mechanisms [2, 3], attention is now focussed on adiabatic quantum pumping in quantum dots [4, 5, 6, 7]. A quantum dot is a small metallic or semiconducting island, confined by gates and connected to electron reservoirs (leads) through quantum point contacts [8]. Almost all investigations of quantum pumping to date, including the first experimental observation [6], involved open quantum dots. Only very recently, quantum pumping in closed dots has for the first time been considered. In Ref. [7], Levinson et al. study adiabatic pumping mediated by resonant transmission through a quantum dot which is isolated from the leads through tunneling point contacts. They predict a quantized pumped current at zero temperature, if the two tunneling barriers are varied in such a way that the loop which describes the pumping cycle in parameter space encircles the entire resonance line. Here we also consider adiabatic quantum pumping via resonant transmission through a nearly-closed quantum dot at low temperatures, but in a new regime, employing small periodic changes in the dot potential. This pumping mechanism differs from Ref. [7] in two significant ways: firstly, the tunneling rates are only slightly perturbed around a point of the resonance line, and as a result the pumped current is not quantized. Secondly, for such small modulations of the potential (linear response), which correspond to small perturbations of the energy level spectrum of the dot, the pumped current exhibits Coulomb blockade oscillations as a function of the Fermi energy of the dot. These are of the same origin as the well-known fluctuations in the conductance through a quantum dot in the Coulomb blockade regime [9, 10]: they result from the spatial structure of the quasi-bound wavefunction of the dot close to the leads and reflect how well this wavefunction couples to the electron states in the leads. We calculate the statistical distribution of the pumped current peak heights both in presence and absence of time-reversal symmetry (TRS). This leads to the prediction of an experimentally observable increase of the average pumped peak height upon breaking TRS. Consider a quantum dot that is weakly-coupled to two single-mode leads via tunneling point contacts with transmission probabilities T1 and T2, see Fig. 1. If the strengths of the tunneling barriers are varied periodically as V1(t) = V 1+δV1 sin(ωt) and V2(t) = V 2+δV2 sin(ωt+ φ), with δV1,2 ≪ V 1,2, a current is pumped into lead 1 which is given by, at zero temperature [4],