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arXiv:2608.27045

A Superconducting Phase Transition Single-Electron Transistor

Gorka Aizpurua-Iraola, Thomas H. Swift, Felix-Ekkehard von Horstig, Domenic Prete, James Kirkman, Grayson M. Noah, Fabio Olivieri, Alberto Gomez-Saiz, M. Fernando Gonzalez-Zalba

quant-phcond-mat.mes-hallcond-mat.supr-conSubmitted Aug 27, 2026• Announced Aug 28, 2026• 0 citations
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Abstract

Quantum computers require fast and accurate methods for qubit state detection. Phase-transition sensors exploit the abrupt change between two physical states of a material to achieve enhanced sensitivity and have enabled advanced detectors for quantum technologies, such as superconducting nanowire single-photon detectors. However, this sensing principle has not yet been applied to semiconductor spin qubits. Here, we demonstrate a superconducting phase-transition radio-frequency single-electron transistor (PTSET), a charge sensor for semiconductor spin qubits whose response is enhanced by a superconducting-to-normal phase transition. The transition is engineered by linking the sensor current to a low-critical-current, high-kinetic-inductance inductor integrated into the radio-frequency matching network. We demonstrate improvements in sensitivity of one and two orders of magnitude over conventional rfSETs in the large- and small-signal regimes, respectively. Our results establish phase-transition sensing as a route towards ultrasensitive, integrated charge sensors for semiconductor quantum computing and point to broader applications, including cryogenic photon detection for radio astronomy.

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9 pages, 4 figures

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Quantum computers require fast and accurate methods for qubit state detection. Phase-transition sensors exploit the abrupt change between two physical states of a material to achieve enhanced sensitivity and have enabled advanced detectors for quantum technologies, such as superconducting nanowire single-photon detectors. However, this sensing principle has not yet been applied to semiconductor spin qubits. Here, we demonstrate a superconducting phase-transition radio-frequency single-electron transistor (PTSET), a charge sensor for semiconductor spin qubits whose response is enhanced by a superconducting-to-normal phase transition. The transition is engineered by linking the sensor current to a low-critical-current, high-kinetic-inductance inductor integrated into the radio-frequency matching network. We demonstrate improvements in sensitivity of one and two orders of magnitude over conventional rfSETs in the large- and small-signal regimes, respectively. Our results establish phase-transition sensing as a route towards ultrasensitive, integrated charge sensors for semiconductor quantum computing and point to broader applications, including cryogenic photon detection for radio astronomy.
Recent studies of silicon spin qubits at temperatures above 1 K are encouraging demonstrations that the cooling requirements for solid-state quantum computing can be considerably relaxed. However, qubit readout mechanisms that rely on charge sensing with a single-island single-electron transistor (SISET) quickly lose sensitivity due to thermal broadening of the electron distribution in the reservoirs. Here we exploit the tunneling between two quantized states in a double-island single-electron transistor (SET) to demonstrate a charge sensor with an improvement in the signal-to-noise ratio by an order of magnitude compared to a standard SISET, and a single-shot charge readout fidelity above 99% up to 8 K at a bandwidth greater than 100 kHz. These improvements are consistent with our theoretical modeling of the temperature-dependent current transport for both types of SETs. With minor additional hardware overhead, these sensors can be integrated into existing qubit architectures for a high-fidelity charge readout at few-kelvin temperatures.
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).
The work involves a study of physical phenomena that take place at very small length scales, below one micro-meter. At temperatures roughly below one degree Kelvin, quantum-mechanical effects may rule in electronic transport. Macroscopic quantum-coherent effects that occur in metallic superconducting microstructures, are particularly intriguing. Large-scale quantum information processing is widely believed to be attainable utilizing such physical systems. This work concentrates on answering the question of how the described quantum-mechanical systems may be used as sensitive measuring devices. Considerable attention is paid to energy-storing metallic microstructures whose electrical properties resemble those of the familiar inductor or capacitor. This research involves primarily experimental investigations conducted around temperatures of 0.1 Kelvin. Methods both at low and at radio frequencies have been used. The experimental findings have been modelled theoretically, and theoretical concepts for new physical phenomena have been introduced. An inductively measured radio-frequency Cooper-pair transistor, the L-SET, has been developed and experimentally verified in this work. Being highly sensitive, fast, and non-invasive, the L-SET appears to be the most promising method for measuring electric charge. Sensitivity in charge measurements of 20 millionths of the electron charge (micro-e) within one second, and an input bandwidth of 100 MHz, have been demonstrated. It has been shown theoretically that the ultimate measurement accuracy is about 0.1 micro-e within a second. A new phase detector based on the Cooper-pair transistor has been proposed. This system has also been shown to be potentially usable as a quantum bit. A new type of radio-frequency single-electron transistor built using a multi-walled carbon nanotube has been fabricated and operated. Technologies have been developed in order to make the physical nano- or microstructures. A method has been presented to fabricate non-superconducting tunnel junctions. Consequences of the inverse superconducting proximity effect on the studied superconducting structures were considered. Measurement procedures were investigated for a new low-noise nanoamplifier, the Bloch-oscillating transistor. Single superconducting tunnel junctions were tested as detectors of energy states of the environment, or of noise.
Ultrasensitive detectors and readout devices based on the radio frequency single electron transistor (rf-SET) combine near quantum-limited sensitivity with fast operation. Here we describe a twin rf-SET detector that uses two superconducting rf-SETs to perform fast, real-time cross-correlated measurements in order to distinguish subelectron signals from charge noise on microsecond time scales. The twin rf-SET makes use of two tuned resonance circuits to simultaneously and independently address both rf-SETs using wavelength division multiplexing and a single cryogenic amplifier. We focus on the operation of the twin rf-SET as a charge detector and evaluate the cross talk between the two resonance circuits. Real-time suppression of charge noise is demonstrated by cross correlating the signals from the two rf-SETs. For the case of simultaneous operation, the rf-SETs had charge sensitivities of δqSET1=7.5μe∕Hz and δqSET2=4.4μe∕Hz.
This thesis focuses on implementing radio frequency (rf) reflectometry techniques for dispersive detection of charge and spin dynamics in nanoscale devices. I have investigated three aspects of rf reflectometry using state-of-the-art silicon (Si) complementary metal-oxide-semiconductor (CMOS) nanowire field effect transistors (NWFETs). First, a high-sensitivity capacitive gate-based charge sensor is developed by optimising the external matching circuit to detect capacitive changes in the high frequency resonator. A new circuit topology is used where superconducting niobium nitride (NbN) inductor is connected in parallel with a single-gate Si NWFET resulting in resonators with loaded Q-factors in the 400-800 range. For a resonator operating at 330 MHz, I have achieved a charge sensitivity of 7.7 μe/Hz\mu e/\sqrt{\text{Hz}}μe/Hz​ and, when operating at 616 MHz, I get 1.3 μe/Hz\mu e/\sqrt{\text{Hz}}μe/Hz​. This gate-based sensor can be used for fast, accurate and scalable techniques for quantum state readout in Si CMOS based quantum computing. Second, this new circuit topology for the resonator is used with a dual-gate Si NWFET. This dual-gate device geometry provides access to a double quantum dot (DQD) system in few electron regime. The spin-state of the two-electron DQD system is detected dispersively using Pauli spin blockade between joint singlet S(2,0) and triplet T−_-−​(1,1) states in a finite magnetic field BBB. The singlet-triplet relaxation time T1T_1T1​ at B=4.5B=4.5B=4.5~T is measured to be $\sim$1 ms using standard homodyne detection technique. Third, I expand the range of applications of gate-based sensing to accurate temperature measurements. I have experimentally demonstrated a primary thermometer by embedding a single-gate Si NWFET with the rf capacitive gate-based sensor. The thermometer, termed as gate-based electron thermometer (GET), relies on cyclic electron tunneling between discrete energy levels of a quantum dot and a single electron reservoir in the NWFET. I have found that the full-width-half-maximum (FWHM) of the resonator phase response depends linearly with temperature via well known physical law by using the ratio kB/ek_\text{B}/ekB​/e between the Boltzmann constant and the electron charge. The GET is also found to be magnetic field independent like other primary thermometers such as Coulomb blockade and shot noise thermometers.