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Applied Physics Letters

Single-electron transistor strongly coupled to an electrostatically defined quantum dot

Wei Dong Lu, A. J. Rimberg, Kevin D. Maranowski, Arthur C. Gossard

Published Oct 23, 2000• 20 citations
Publisher

Abstract

A system is described in which an Al-based superconducting single-electron transistor (S–SET) is fabricated directly above an electrostatically defined quantum dot formed in a two-dimensional electron gas. This arrangement allows the coupling capacitance between the S–SET central island and the dot to be comparable to the tunneling capacitances of the dot. As a result, the measured sensitivity of the S–SET referred to charge on the dot is 1.2×10−4 e/Hz, about an order of magnitude better than previously reported results. The increased sensitivity makes this system ideally suited for broadband measurements such as study of individual tunneling events.

DOI
10.1063/1.1320455

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A system is described in which an Al-based superconducting single-electron transistor (S–SET) is fabricated directly above an electrostatically defined quantum dot formed in a two-dimensional electron gas. This arrangement allows the coupling capacitance between the S–SET central island and the dot to be comparable to the tunneling capacitances of the dot. As a result, the measured sensitivity of the S–SET referred to charge on the dot is 1.2×10−4 e/Hz, about an order of magnitude better than previously reported results. The increased sensitivity makes this system ideally suited for broadband measurements such as study of individual tunneling events.
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 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.
The radio-frequency superconducting single electron transistor (RF-SET) is a highly sensitive and fast electrometer operating near the quantum limit. The back-action current noise of the SET induces voltage fluctuations on the system it is coupled to, dephasing its charge states. Here we propose to study the back action of the RF-SET by means of a double quantum dot (DQD) and, an RF-SET electrostatically coupled to one of the two dots. The inelastic current through the DQD is very sensitive to the spectral density of the voltage fluctuations in the nearby environment. By properly choosing the dot size and inter-dot tunnel barrier thickness, one can cause inelastic process to dominate the transport processes. A measurement of the inelastic current through the double dot system can then be used to calculate the spectral density of noise associated with the RF-SET and hence its back action. The design, fabrication and characterization of an RF-SET/DQD system is discussed in this work. Real-time studies of electron dynamics in coupled dots are also addressed.
Assuming the absence of 1/f noise, we have calculated the charge sensitivity (CS) of a capacitive-coupled double-junction single electron tunneling transistor (SETT) with a superconducting grain, operating at low temperature and low bias voltage such that the tunneling current is dominated by the Andreev process. In this case the effect of co-tunneling is suppressed without using the complicated fabrication method. We have used a realistic sample to demonstrate the procedure of optimizing the CS of a SETT with respect to relevant physical parameters and structure parameters. With the presently available fabrication technology, our theoretical analysis can serve as a guide for increasing the CS of a SETT beyond 10−6 e/√Hz.
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.