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arXiv:1109.3634 · Physical Review Letters

Single-Charge Transistor Based on the Charge-Phase Duality of a Superconducting Nanowire Circuit

T. T. Hongisto, Alexander B Zorin

Published Feb 27, 2012• 74 citations
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Abstract

We propose a transistorlike circuit including two serially connected segments of a narrow superconducting nanowire joint by a wider segment with a capacitively coupled gate in between. This circuit is made of amorphous NbSi film and embedded in a network of on-chip Cr microresistors ensuring a sufficiently high external electromagnetic impedance. Assuming a virtual regime of quantum phase slips (QPS) in two narrow segments of the wire, leading to quantum interference of voltages on these segments, this circuit is dual to the dc SQUID. Our samples demonstrated appreciable Coulomb blockade voltage (analog of critical current of the SQUIDs) and periodic modulation of this blockade by an electrostatic gate (analog of flux modulation in the SQUIDs). The model of this QPS transistor is discussed.

DOI
10.1103/physrevlett.108.097001

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We propose a transistorlike circuit including two serially connected segments of a narrow superconducting nanowire joint by a wider segment with a capacitively coupled gate in between. This circuit is made of amorphous NbSi film and embedded in a network of on-chip Cr microresistors ensuring a sufficiently high external electromagnetic impedance. Assuming a virtual regime of quantum phase slips (QPS) in two narrow segments of the wire, leading to quantum interference of voltages on these segments, this circuit is dual to the dc SQUID. Our samples demonstrated appreciable Coulomb blockade voltage (analog of critical current of the SQUIDs) and periodic modulation of this blockade by an electrostatic gate (analog of flux modulation in the SQUIDs). The model of this QPS transistor is discussed.
We propose a transistor-like circuit including two serially connected segments of narrow superconducting nanowire joint by a wider segment with capacitively coupled gate in between. This circuit is made of amorphous NbSi film and embedded in a network of on-chip Cr microresistors ensuring sufficiently high external electromagnetic impedance. Assuming virtual regime of quantum phase slips (QPS) in two narrow segments of the wire, leading to correlated single Cooper pair tunneling, this circuit is dual to the dc SQUID. Our samples demonstrated appreciable Coulomb blockade voltage (analog of critical current of the SQUIDs) and periodic modulation of this blockade by electrostatic gate (analog of flux modulation in the SQUIDs). The model of this QPS transistor is discussed.
The single Cooper pair josephson transistor is a device that exhibits at the same time charge quantization and phase coherence. Coherent quantum phase slip phenomenon is “dual” the Josephson phase coherence, while the charge quantization is dual to the flux quantization. We present the experimental demonstration and the theoretical description of a new superconducting device–single flux transistor, which is dual to the single Cooper pair transistor. Our transport measurements show the periodic modulation of the critical voltage by the external magnetic field. The obtained current-voltage characteristics show the hysteretic behavior, which we attribute to the intrinsic self-heating of charge carriers.
To illustrate the emergence of Coulomb blockade from coherent quantum phase-slip processes in thin superconducting wires, we propose and theoretically investigate two elementary setups, or devices. The setups are derived from the Cooper-pair box and Cooper-pair transistor, so we refer to them as the QPS box and QPS transistor, respectively. We demonstrate that the devices exhibit sensitivity to a charge induced by a gate electrode, this being the main signature of Coulomb blockade. Experimental realization of these devices will unambiguously prove the Coulomb blockade as an effect of coherence of phase-slip processes. We analyze the emergence of discrete charging in the limit of strong phase slips. We have found and investigated six distinct regimes that are realized depending on the relation between three characteristic energy scales: inductive energy, charging energy, and phase-slip amplitude. For completeness, we include a brief discussion of dual Josephson-junction devices.
We present a detailed report of microwave irradiation of ultranarrow superconducting nanowires. In our nanofabricated circuits containing a superconducting NbSi nanowire, a dc blockade of current flow was observed at low temperatures below a critical voltage Vc{V}_{\mathrm{c}}Vc​, a strong indicator of the existence of quantum phase-slip (QPS) in the nanowire. We describe the results of applying microwaves to these samples, using a range of frequencies and both continuous-wave and pulsed drive, in order to search for dual Shapiro steps which would constitute an unambiguous demonstration of quantum phase-slip. We observed no steps, and our subsequent thermal analysis suggests that the electron temperature in the series CrO resistors was significantly elevated above the substrate temperature, resulting in sufficient Johnson noise to wash out the steps. To understand the system and inform future work, we have constructed a numerical model of the dynamics of the circuit for dc and ac bias (both continuous-wave and pulsed drive signals) in the presence of Johnson noise. Using this model, we outline important design considerations for device and measurement parameters which should be used in any future experiment to enable the observation of dual Shapiro steps at experimentally accessible temperatures and, thus, lead to the development of a QPS-based quantum current standard.
Superconducting circuits that operate by propagation of small voltage or current pulses, corresponding to propagation of single flux or charge quantum, are naturally suited for implementing spiking neuron circuits. Quantum phase-slip junctions (QPSJs) are 1-D superconducting nanowires that have been identified as exact duals to Josephson junctions, based on charge-flux duality in Maxwell’s equations. In this paper, a superconducting quantized-charge circuit element, formed using quantum phase-slip junctions, is investigated for use in high-speed, low-energy superconducting spiking neuron circuits. By means of a SPICE model developed for QPSJs, operation of this superconducting circuit to produce and transport quantized charge pulses, in the form of current pulses, is demonstrated. The resulting quantized-charge-based operation emulates spiking neuron circuits for brain-inspired neuromorphic applications. Additionally, to further demonstrate the operation of QPSJ-based neuron circuits, a QPSJ-based integrate and fire neuron circuit is introduced, along with simulation results using WRSPICE. Estimates for operating speed and power dissipation are provided and compared to Josephson junction and CMOS-based spiking neuron circuits. Current challenges are also briefly mentioned.
The manipulation of single charge quanta in solid state systems has been a field of active interest for several decades. At the basis of such structures lays the Coulombic repulsion between electrons in a small metallic island yielding the so-called Coulomb-blockade regime. Many quantum phenomena, such as the tunnelling effect or the Josephson coupling in superconducting junctions, have been exploited so far to control the charging state of a conducting island, and enable a number of applications ranging from on-chip cooling and current generation to single-photon detection. Yet, in all Coulombic systems the external control parameters play a crucial role, reaching sometimes a rather complex experimental configuration. Here we show that quantum interference established in a superconducting nanowire can provide a phase-tunable energy barrier which allows charge manipulation with enhanced functionalities. This additional degree of freedom for single electronics stems from the coupling between magnetic flux-dependent proximity effect and charging levels discretization present in a Coulomb-blockaded island. Our quantum interference nanostructure represents the first realization of a superconducting hybrid single-electron transistor called SQUISET in which the charging landscape is phase-coherently manipulated by an external magnetic flux. The interferometric nature of the transistor adds new perspectives to single electronics making it a promising alternative building block in quantum metrology, coherent caloritronics, and quantum information technology.