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Journal of Applied Physics

Optimization of charge sensitivity of a single electron tunneling transistor with a superconducting grain

Ulrik Hanke, K. A. Chao, Y. M. Galperin

Published Jul 15, 1996• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.362864

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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.
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.
Here, we report the operation of a superconducting single-electron transistor (S-SET) as a fast and nearly quantum-limited charge-sensitive amplifier. By operating the S-SET such that Cooper pair tunneling is resonant across both of its tunnel junctions, we are able to achieve an excellent charge sensitivity of δq = 1.6 × 10-6e/√(Hz), while also minimizing back action. We find that near its optimal operating point, the S-SET can have both a very low noise temperature Tn≈ 50 mK and a large power gain ASET>;>; 1. These results indicate that our S-SET operates within a factor of 2 of the quantum limit.
We develop a microscopic theory for charge transfer through a single-electron transistor containing a superconducting grain. Both tunnel current and shot noise are shown to be sensitive to the parity of the electron number on the grain. In particular, tunneling may cross over from pair channels to two distinct single-particle channels at finite voltage. The two corresponding threshold voltages are sensitive to the circuit parameters. While it is difficult to identify them from the I-V curve, they can be determined from the normalized zero-frequency noise and the finite-frequency noise spectrum.
Abstract Single‐charge tunneling through a voltage‐biased SSS transistor with a capacitively coupled gate and an electromagnetic environment is considered. The dc Cooper‐pair current in the blockade region of quasiparticle tunneling is studied. Basing on a two‐level approximation, which can be used in the realistic case of low temperatures and small environment resistances, the mean dc Cooperpair current, the noise power spectrum, and the charge resolution are calculated as functions of the driving voltage and the external charge on the island.
It is shown that the noise-limited charge sensitivity of a single-electron transistor using superconductors (of either SISIS- or NISIN-type) operating near the threshold of quasiparticle tunneling, can be considerably higher than that of a similar transistor made of normal metals or semiconductors. The reason is that the superconducting energy gap, in contrast to the Coulomb blockade, is not smeared by the finite temperature. We also discuss the increase of the maximum operation temperature due to superconductivity and the peaklike features on the I–V curve of SISIS structures.
We show how population inversion (PI) occurs in a two-level system (TLS) while measuring its charge using a capacitively coupled superconducting single-electron transistor (SSET), biased in the subgap regime, where the current through the SSET is carried by different cycles involving tunneling of both Cooper pairs and quasiparticles. The PI is directly associated with the resonant nature of the Cooper-pair tunneling. We also show how the SSET may strongly relax the TLS, although there is negligible current flowing through the SSET, i.e. it is turned off. The calculation of the quantum back-action noise is based on a real-time Keldysh approach. We specifically discuss the case of a Cooper Pair Box qubit with the SSET capacitively coupled as read-out device.