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Applied Physics Letters

Superconducting single-electron transistor coupled to a locally tunable electromagnetic environment

Wei Dong Lu, A. J. Rimberg, Kevin D. Maranowski

Published Dec 19, 2002• 5 citations
Publisher

Abstract

We have developed a system consisting of a superconducting single-electron transistor (S-SET) coupled to a two-dimensional electron gas (2DEG), for which the dissipation can be tuned in the immediate vicinity of the S-SET. Such tuning can be performed easily, and provides access to a significant range of environmental impedances. For temperatures above 100 mK, we find qualitative agreement between measured changes in the S-SET conductance versus dissipation and a model incorporating electromagnetic fluctuations in both the S-SET leads and the 2DEG.

DOI
10.1063/1.1530731

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We have developed a system consisting of a superconducting single-electron transistor (S-SET) coupled to a two-dimensional electron gas (2DEG), for which the dissipation can be tuned in the immediate vicinity of the S-SET. Such tuning can be performed easily, and provides access to a significant range of environmental impedances. For temperatures above 100 mK, we find qualitative agreement between measured changes in the S-SET conductance versus dissipation and a model incorporating electromagnetic fluctuations in both the S-SET leads and the 2DEG.
We have developed a novel system consisting of a superconducting single-electron transistor (S-SET) coupled to a two-dimensional electron gas (2DEG), for which the dissipation can be tuned in the immediate vicinity of the S-SET. Within linear response, the S-SET conductance varies nonmonotonically with increasing 2DEG impedance. We find good agreement between our experimental results and a model incorporating electromagnetic fluctuations in both the S-SET leads and the 2DEG, as well as low-frequency switching of the S-SET offset charge.
We have developed a novel system consisting of a superconducting single-electron transistor (S-SET) coupled to a two-dimensional electron gas (2DEG), for which the dissipation can be tuned in the immediate vicinity of the S-SET. To analyze our results, we have developed a model of the environment for S-SET/2DEG systems that includes electromagnetic fluctuations coupled both through the S-SET leads and capacitively to the S-SET central island. We analyze this model, treating the leads as finite transmission lines, to find the probability function P(E) for exchanging energy E with the environment. We also allow for the possibility of low-frequency fluctuations of the S-SET offset charge. We compare our calculations with measurements of SET conductance versus 2DEG conductance and find good agreement for temperatures 100 mK, while unexplained discrepancies emerge for lower temperatures. By including the effects of charge averaging we are also able to predict the shape and evolution of IV curves as the 2DEG in the vicinity of the S-SET is changed.
A novel model system is developed to study the effects of the environment on transport properties of a superconducting single-electron transistor (S-SET). The impedance of a two-dimensional electron gas (2DEG) 50 nm below the sample surface serving as the environment can be tuned in situ. A quantum dot is readily formed in the 2DEG. Josephson tunneling processes in the SET are suppressed and quasiparticle tunneling processes are enhanced as the 2DEG is confined. Important energetic parameters of the SET such as the charging energy EsbcE\\sb{c}Esbc and superconducting energy gap triangle\\triangletriangle remain almost unchanged in this process.
This thesis will be divided into two parts. In the first part, theory and results of a novel system in which a superconducting single-electron transistor (S-SET) coupled to a two-dimensional electron gas (2DEG) serving as a tunable electromagnetic environment for the S-SET will be discussed, including effects of dissipation, resonant tunneling with photon emission, and photon-assisted tunneling. In the second part, we discuss the techniques for which the SET is incorporated in an RF resonant circuit, resulting in an ultra high charge sensitivity and bandwidth. After the 2DEG is confined into a quantum dot, random telegraph signals (RTS) caused by individual electrons tunneling on and off the dot have been observed. In the equilibrium configuration, the occupational probabilities of the charge states of the dot can be directly measured from the RTS and were found to follow a Fermi distribution. In the non-equilibrium configuration, the RTS correctly detected the onset of the current through the dot.
We measure the effect of dissipation on the minimum zero-bias conductance, G(min)0, of a superconducting single electron transistor (sSET) capacitively coupled to a two-dimensional electron gas (2DEG) in a GaAs/AlGaAs heterostructure. Depleting the 2DEG with a back gate voltage decreases the dissipation experienced by the sSET in situ. We find that G(min)0 increases as the dissipation is increased or the temperature is reduced; the functional forms of these dependences are compared with the model of Wilhelm et al. in which the leads coupled to the sSET are represented by lossy transmission lines.
We have directly measured the quantum noise of a superconducting single-electron transistor (S-SET) embedded in a microwave resonator consisting of a superconducting LC tank circuit. Using an effective bath description, we find that the S-SET provides damping of the resonator modes proportional to its differential conductance and has an effective temperature that depends strongly on the S-SET bias conditions. In the vicinity of a double Cooper pair resonance, when both resonances are red detuned the S-SET effective temperature can be well below both the ambient temperature and the energy scale of the bias voltage. When blue detuned, the S-SET shows negative differential conductivity,