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arXiv:1302.2808 · Physical Review B

NbSi nanowire quantum phase-slip circuits: dc supercurrent blockade, microwave measurements, and thermal analysis

C H Webster, J. C. Fenton, T. T. Hongisto, S. P. Giblin, Alexander B Zorin, Paul A. Warburton

Published Apr 18, 2013• 54 citations
arXivHTMLPDF

Abstract

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 ${V}_{\mathrm{c}}$, 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.

DOI
10.1103/physrevb.87.144510

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This thesis describes a series of theoretical proposals of novel circuits that embed ultrathin superconducting nanowires with coherent quantum phase-slips (QPS). The motivation for our proposals is twofold: firstly, to facilitate unambiguous experimental verification of coherent phase-slips. Secondly, to suggest superconducting devices with new features and functionalities. The first circuit is a driven LC oscillator with the superconducting inductance subject to QPS. We have studied the effect of QPS in two limits: for small and for large phase-slip amplitudes. We expect that weakQPS (whereweakmeans that the QPS amplitude is small compared to the resonance frequency) have ameasurable effect when the oscillator is resonantly driven. The charge induced by the gate affects the quantum interference of QPS with opposite shifts and thus the effect of QPS is periodic in gate voltage. 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Abstract Quantum phase slip (QPS) is an important effect that occurs in one-dimensional (1D) or quasi-1D superconducting (SC) materials. Due to the extremely high requirements on the uniformity and quality of SC nanowires, it is currently very challenging to obtain repeatable and controllable QPS devices. Here, we report a systematic study of the QPS effect in NbN SC nanowires. High-quality NbN nanowires with different widths are fabricated by combining the processes of photo-lithography, electron beam lithography, and inductively coupled plasma etching. It is found that the electrical transport of the nanowires showed a systematic variation with the wire width, and a clear evolution from single to multiple QPS events with the decrease in wire width is uncovered at low temperatures. Based on these experimental results, the phase diagram reflecting the evolution of the physical states of the nanowires with wire width and temperature is obtained. In addition, we observed the features of the critical voltage, which is a characteristic of the occurrence of coherent QPS (cQPS), in samples with a width of 36 nm in the multiple QPS region. It is worth noting that this cQPS behavior was detected in a non-high-impedance environment.

Superconductor Science and Technology•Jan 30, 2024•3 citations
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.
We consider the dynamics of a quantum phase-slip junction (QPSJ), a dual Josephson junction, connected to a microwave source with frequency ${\ensuremath{\omega}}_{\mathrm{mw}}$. With respect to an ordinary Josephson junction, a QPSJ can sustain dual Shapiro steps, consisting of well-defined current plateaus at multiple integers of $e{\ensuremath{\omega}}_{\mathrm{mw}}/\ensuremath{\pi}$ in the current-voltage $(I\text{\ensuremath{-}}V)$ characteristic. The experimental observation of these plateaus has been elusive up to now. We argue that thermal as well as quantum fluctuations can smear the $I\text{\ensuremath{-}}V$ characteristic considerably. In order to understand these effects, we study a current-biased QPSJ under microwave irradiation and connected to an inductive and resistive environment. We find that the effect of the fluctuations is governed by the resistance of the environment and by the ratio of the phase-slip energy and the inductive energy. Our results are of interest for experiments aiming at the observation of dual Shapiro steps in QPSJ devices for the definition of a new quantum current standard.
Quantum phase slips (QPS) or the macroscopic quantum tunneling (MQT) of a nanowire’s order parameter through an activation energy barrier have remained the subject of intense debate for many years. They are expected to occur at low enough temperature where thermally activated phase slips (TAPS) have been frozen out in analogy with Josephson junctions where the macroscopic tunneling of phase at low temperatures has been conclusively experimentally demonstrated. We address this question by following a similar experimental strategy to that employed for establishing MQT in JJs. By measuring switching current distributions, we can probe the phase slip rate and determine if it corresponds to thermal activation or quantum tunneling. Having established that the behavior we see is consistent with being in the quantum regime, we can alter properties of the nanowires and see if the response is consistent with the expectations of the quantum model. To do this we employ an in-situ modification technique using high bias voltage pulses. Using these pulses, we can change resistance, critical temperature, critical current and morphology of the nanowire. We can also change the shunting capacitance of the nanowire by altering the photolithography step used to create the nanowires electrodes. The resulting response of the nanowires agrees well with being in the quantum tunneling dominated regime. An interesting side benefit of the pulsing technique is that we can exactly set the nanowires switching current to a desired value. This may be instrumental in the development of superconducting nanowire qubits.
A quantum current standard dual to the Josephson voltage standard has been trumpeted as a primary application for the phenomenon of coherent quantum phase-slips (CQPS) in superconducting nanowires, but it requires a dc transport geometry, distinct from the ring geometry in which CQPS have been probed by microwave spectroscopy measurements. We present measurements on NbN nanowires with a width of 15 nm and including integrated thin-film resistors to provide a high-impedance environment. Analysis shows that the nanowire behavior is in line with expectations. The results demonstrate that the process is promising both for future dc transport CQPS measurements and for the fabrication of other circuits in which low-width superconducting nanowires are required.
The phenomenon of coherent quantum phase-slips (CQPS) in superconducting nanowires was some time ago proposed to be the exact dual of the Josephson effect, a proposal accompanied by predictions of a new quantum current standard dual to the Josephson voltage standard. Unambiguous experimental observation of CQPS in nanowire structures has only recently been achieved through microwave spectroscopy which showed an avoided crossing between flux states for a superconducting ring interrupted by a superconducting nanowire. This observation raises expectations that the CQPS quantum current standard and a slew of CQPS devices dual to devices containing Josephson junction might be realised, including a tunable capacitance, a sensitive charge detector and small-signal detector. To date, experimental evidence for CQPS in a dc transport geometry has not been considered conclusive, and the impact of decoherence in CQPS devices still remains to be evaluated. We present experimental work which has enabled us to crystallise pertinent issues which have prevented the realisation of CQPS in dc transport experiments to date.
This thesis describes a series of theoretical proposals of novel circuits that embed ultrathin superconducting nanowires with coherent quantum phase-slips (QPS). The motivation for our proposals is twofold: firstly, to facilitate unambiguous experimental verification of coherent phase-slips. Secondly, to suggest superconducting devices with new features and functionalities. The first circuit is a driven LC oscillator with the superconducting inductance subject to QPS. We have studied the effect of QPS in two limits: for small and for large phase-slip amplitudes. We expect that weakQPS (whereweakmeans that the QPS amplitude is small compared to the resonance frequency) have ameasurable effect when the oscillator is resonantly driven. The charge induced by the gate affects the quantum interference of QPS with opposite shifts and thus the effect of QPS is periodic in gate voltage. The experimental observation of such dependence would unambiguously identify the quantum coherence of phase-slips. The other crucial effect of QPS is that they produce uncommon non-linearities in the proposed device. The distinctive feature of these non-linearities is the oscillatory dependence on number of photons n with a local period of the order of pn. We analyzed the regime where the QPS correction becomes large by employing a semiclassical approximation as well as by solving the full quantum mechanical equations. At semiclassical level, the QPS-induced non-linearities persist until very high photon number and they result in amultitude ofmetastable states. This was illustrated in the responses of the oscillator: the QPS-induced non-linearities cause deviations fromthe otherwise Lorentzian curve that represents the number of photons N versus detuning. At sufficiently large phase-slip amplitudes this results in an impressive characteristic, a "corkscrew" shape. At any given detuning one finds a multitude of states that differ in the number of photons. About half of these states are stable. At quantum level, we have demonstrated that there is indeed a single quantum state corresponding to the semiclassical metastable states. We have found that these states are robust, their switching time is exponentially long, although they encompass only a few photons. The QPS oscillator is highly tunable: small changes of the driving force, detuning, or charge induced change the number of stable states, thereby enabling easy manipulation of the number of photons. All these features of the phase-slip oscillator make it useful for a wide range of applications, such as ultra-sensitive measurements, quantum manipula- tion and naturally, an unambiguous experimental verification of coherent QPS. In Chapter 3 we propose a series of devices that illustrate the emergence of Coulomb blockade from coherent QPS in thin superconducting wires. The basic ideas is that QPS create an isolation in a wire which is similar to the isolation required by Coulomb blockade. We exploit this idea and suggest setups that are derived from Cooper-pair box and Cooper-pair transistor, so we refer to them as QPS-box and QPS-transistor, respectively. Our main goal was to demonstrate that the devices exhibit sensitivity to a charge induced by a gate electrode, this being the main signature of Coulomb blockade. We analyze the emergence of discrete charging in the limit of strong phaseslips. We investigated six distinct regimes that are realized depending on the relation between the three characteristic energy scales: inductive and charging energy, and QPS amplitude. In both cases the charge sensitivity appears already for small QPS amplitudes as a perturbative correction to the ground-state energy. In both cases, the charge-sensitive part of the perturbative correction is exponentially suppressed in the limit of low impedance. In contrast to the QPS-box, the QPStransistor exhibits both flux and charge sensitivity that makes it potentially useful for measurements. However, if the QPS amplitude becomes of the order of either charging energy (large impedance regime) or inductive energy (small impedance regime), both devices showdiscrete charge states that followthe commonCoulomb blockade pattern of "crossing parabolas". The crossover to Coulomb blockade occurs differently in the limits of large and small impedance. For QPS-transistor, we have analyzed the flux sensitivity (superconducting current) as well as combined flux-charge sensitivity. For a symmetric QPS-transistor we have found a variable separation at specific values of induced charge that leads to double degeneracy of the states at q/e = 1 and half-integer external flux. We have calculated the superconducting current through QPS-transistor to show the non-triviality of the device. Experimental realization of these devices (achievable with the state-or-theart technology), will unambiguously prove the Coulomb blockade as an effect of coherent phase-slip processes. For completeness, we discuss the Josephson-based devices that are dual to QPS-box and QPS-transistor. In Chapter 4 we propose a way to realize quantum synchronization of Josephson and Bloch oscillations in a superconducting device. Essentially, this implies the synchronization of quantumconjugated variables: phase and charge. A circuit comprising of a QPS junction, series resistor and biased by a d.c. voltage exhibits Bloch physics of the charge variable. To ensure well-defined classical oscillations, the resistor needs to be large compared to the resistance quantum. We couple this Bloch subcircuit with a Josephson subcircuit in which the phase variable performs thewell-known Josephson oscillations. Themain effect of the coupling is the transfer of oscillating voltage/current from Josephson/Bloch to Bloch/Josephson part, whereby the voltage/current is multiplied with an amplification coefficient. This amplification coefficient is required to be high for stable synchronization. This is achieved by using an LC-resonator with high quality factorQ. The synchronization takes place in a rather broad interval of frequencies near the LC oscillator’s resonant value. Owing to this synchronization, the transresistance of our device exhibits a typical devil’s staircase curve, very similar to (fractional) Quantum Hall samples. In principle, fluctuations of phase and charge could could destroy the synchronization. Using the quantum description in the framework of Keldysh action formalism, we have investigated the effect of fluctuations on our circuit. The minimum synchronization error rate is shown to be exponential in Q. There is also significant practical interest in the field on metrology. The suggested device can be used to close the famous "metrological triangle" for threemetrological standards: those of resistance, voltage and current—within a single device.
Abstract Quantum phase slip (QPS) is an important effect that occurs in one-dimensional (1D) or quasi-1D superconducting (SC) materials. Due to the extremely high requirements on the uniformity and quality of SC nanowires, it is currently very challenging to obtain repeatable and controllable QPS devices. Here, we report a systematic study of the QPS effect in NbN SC nanowires. High-quality NbN nanowires with different widths are fabricated by combining the processes of photo-lithography, electron beam lithography, and inductively coupled plasma etching. It is found that the electrical transport of the nanowires showed a systematic variation with the wire width, and a clear evolution from single to multiple QPS events with the decrease in wire width is uncovered at low temperatures. Based on these experimental results, the phase diagram reflecting the evolution of the physical states of the nanowires with wire width and temperature is obtained. In addition, we observed the features of the critical voltage, which is a characteristic of the occurrence of coherent QPS (cQPS), in samples with a width of 36 nm in the multiple QPS region. It is worth noting that this cQPS behavior was detected in a non-high-impedance environment.