Quantum dot admittance probed at microwave frequencies with an on-chip resonator

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We have investigated the microwave frequency dynamic admittance of a quantum dot tunnel coupled to a two-dimensional electron gas. The measurements are made via a high-quality 6.75 GHz on-chip resonator capacitively coupled to the dot. The resonator frequency is found to shift both down and up close to conductance resonances of the dot corresponding to a change in the reactance of the system from capacitive to inductive (see Fig. 1). The observations are consistently explained in a scattering matrix model. The character of the reactance depends on the detuning of the dot from conductance resonance and on the magnitude of the tunnel rate to the lead with respect to the resonator frequency [1]. Inductive response is observed on a conductance resonance, when tunnel coupling and temperature are sufficiently small compared to the resonator frequency. Our measurement scheme using the microwave resonator for detecting finite frequency properties of semiconductor nanostructures has promise for future experiments in which the sensitivity of the resonator can be further exploited to, for example, measure the shot noise properties of a tunnel barrier in more detail.

Figure 1: (a) Measured change of resonator frequency for three different characteristic resonant dot lead coupling strengths ƴ. (b) Results of the scattering matrix model calculations using three different tunnel couplings: ƴ 1/h = 20 MHz, ƴ 2/h = 58 MHz, ƴ 3/h = 125 MHz.

[1] Quantum dot admittance probed at microwave frequencies with an on-chip resonator, T. Frey, P. J. Leek, M. Beck, J. Faist, A. Wallraff, K. Ensslin, T. Ihn, and M. Büttiker, Phys. Rev. B 86, 115303 (2012), also in arXiv:1207.0945v1