Three-level mixing and dark states in transport through quantum dots

Abstract

We consider theoretically the transport through the double quantum dot structure of the recent experiment of C. Payette et al. [Phys. Rev. Lett. 102, 026808 (2009)] and calculate stationary current and shotnoise. Three-level mixing gives rise to a pronounced current suppression effect, the character of which charges markedly with bias direction. We discuss these results in connexion with the dark states of coherent population trapping in quantum dots.PACS numbers: 73.63. Kv, 73.50.Td, 73.23.Hk In a recent experiment [1], Payette and co-workers studied the transport through a double quantum dot (DQD) in which the source-side QD (QD1) had a single electronic level within the transport window, whilst the drain-side dot (QD2) possessed three (see Fig. 1). Gate voltages enabled the position of the former "s-level" to be adjusted and thus used as a probe of the second QD. Due to non-ellipticity, the levels of QD2 were found not to be the familiar Fock-Darwin (FD) levels [2], but rather mixtures of them. This gave rise to a distinctive feature in the tunneling magnetospectrum consisting of an avoided crossing with a central line running through it. Strikingly, this central current line was not continuous as a function of magnetic field, as one might expect, but rather showed a strong suppression near the centre of the avoided crossing. The authors of Ref.[1] suggested a connection between this phenomenon and that of the all-electronic coherent population trapping (CPT) of Refs. [3,4,5,6]. It is the aim of this paper to explore this connexion further.We use a master equation treatment and calculate stationary current and shotnoise. We consider a sourcedrain bias direction both as in Ref.[1] (forward bias), as well in the opposite direction (reverse bias). Both bias directions yield a current suppression, but as our calculations here reveal, the character is rather different in each case. In forward bias, the current suppression valley is wide (proportional to the mixing energy between the levels) as observed in the experiment of Ref.[1] and the shotnoise is subPoissonian. In the reverse bias configuration, the current suppression valley is narrow (proportional to the coupling rate with the leads) and the current statistics are strongly superPoissonian. We argue that only in the latter case does the current blocking mechanism bear strong resemblance to coherent population trapping. I. MODELWe assume strong Coulomb blockade such that at most one excess electron can occupy the DQD at any one time and write the Hamiltonian of the complete system as1: Double quantum dot with a bias window that includes the single probe s-level in QD1 and three levels of QD2. The depicted bias configuration is as in Ref.[1], which we describe here as forward bias. In the sequential tunneling regime, electron tunneling is described by the rates ΓL from left lead to QD1, ΓR from QD2 to the right lead, and by γα; α = 0, ± between the dots.The Hamiltonian of the first dot reads H 1 = ǫ s |s s| with |s denoting the single QD1 s-type orbital. De...

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