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Single-electron transistor: Effects of the environment and detecting electron motion in real time

Wei Dong Lu

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

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.

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Applied Physics Letters•Dec 19, 2002•5 citations
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.
This thesis will discuss the principles, techniques and applications of the Radio Frequency Single Electron Transistor (RF-SET). In the first part, the operating principles of Single Electron Transistors (SETS) in the normal and superconducting states will be introduced. The general techniques of fabricating and calibrating SETs will also be introduced. In the second part, two of our recent experiments are reviewed. One is related to the sensitivity and linearity of superconducting RF-SETs. We found that the RF-SET achieves the best balance of charge sensitivity and linearity in the subgap regime, as opposed to the usual preferred working point in the above-gap regime. The second experiment relates to the real-time counting of single electrons. We demonstrated that the RF-SET can be used as a fast and ultra-sensitive electrometer which can even detect tunneling of a single electron inside a tunable quantum dot (QD) formed in a two dimensional electron gas (2DEG).
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.
The Single Electron Transistor (SET), especially its variation the radio frequency single electron transistor (RF-SET), is a fast and ultra-sensitive electrometer working in the vicinity of the quantum limit. In this thesis, the theory and techniques related to the SET in the normal state and the superconducting state are introduced The thesis focuses especially on our efforts of improving the sensitivity of superconducting RF-SET, including: the design and fabrication of an all superconducting near loss-less matching network for improving the RF modulation, our early investigation of the sensitivity and linearity of a superconducting SET (S-SET) subject to quantum fluctuations of quasiparticles and Cooper pairs under different tunneling mechanisms, and our recent work approaching the quantum sensitivity limit using a double Josephson quasiparticle (DJQP) cycle of a S-SET. Using an effective bath description, we have found that the S-SET provides damping of the resonator modes proportional to its differential conductance, and has an effective temperature that can be well below both the ambient temperature and the energy scale of the bias voltage. In the region of negative differential conductance (NDC), the S-SET shows negative damping and a negative temperature. In the final part of the thesis, I have demonstrated our first application of an RF-SET for real-time detection of electron tunneling through a quantum 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.
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 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.