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New Journal of Physics

Stochastic and deterministic phase slippage in quasi-one-dimensional superconducting nanowires exposed to microwaves

Myung‐Ho Bae, R. C. Dinsmore, Mitrabhanu Sahu, Alexey Bezryadin

Published Apr 17, 2012• 10 citations

Abstract

We study current–voltage ( V – I ) characteristics of short superconducting nanowires of length ∼100 nm exposed to microwave (MW) radiation of frequencies between 2 and 15 GHz. The radiation causes a decrease of the average switching current of the wire. This suppression of the switching current is modeled assuming that there is one-to-one correspondence between Little's phase slips, which are microscopic stochastic events induced by thermal and quantum fluctuations, and the experimentally observed switching events. We also find that at some critical power P * of the radiation a dissipative dynamic superconducting state occurs as an extra step on the V – I curve. It is identified as a phase slip center (PSC), which is essentially a deterministic and periodic in-time phase rotation. With the dependence of the switching currents and the standard deviations observed at the transitions: (i) from the supercurrent state to the normal state and (ii) from the supercurrent state to the PSC regime, we conclude that both of the two types of switching events are triggered by the same microscopic event, namely a single-phase slip. We show that the Skocpol–Beasley–Tinkham model is not applicable to our MW-driven PSCs, probably due to the tendency of the PSC to synchronize with the MW. Through the analysis of the switching current distributions at a sufficiently low temperature, we also present evidence that quantum phase slips play a role in switching events even under MWs.

DOI: 10.1088/1367-2630/14/4/043014

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We study current–voltage ( V – I ) characteristics of short superconducting nanowires of length ∼100 nm exposed to microwave (MW) radiation of frequencies between 2 and 15 GHz. The radiation causes a decrease of the average switching current of the wire. This suppression of the switching current is modeled assuming that there is one-to-one correspondence between Little's phase slips, which are microscopic stochastic events induced by thermal and quantum fluctuations, and the experimentally observed switching events. We also find that at some critical power P * of the radiation a dissipative dynamic superconducting state occurs as an extra step on the V – I curve. It is identified as a phase slip center (PSC), which is essentially a deterministic and periodic in-time phase rotation. With the dependence of the switching currents and the standard deviations observed at the transitions: (i) from the supercurrent state to the normal state and (ii) from the supercurrent state to the PSC regime, we conclude that both of the two types of switching events are triggered by the same microscopic event, namely a single-phase slip. We show that the Skocpol–Beasley–Tinkham model is not applicable to our MW-driven PSCs, probably due to the tendency of the PSC to synchronize with the MW. Through the analysis of the switching current distributions at a sufficiently low temperature, we also present evidence that quantum phase slips play a role in switching events even under MWs.

In quasi-one-dimensional nanowires, superconductivity is destroyed by phase slip events. Phase slips can be caused by thermal activation over a free energy barrier (TAPS) or quantum tunneling through the barrier (QPS). Quantum phase slip is an example of macroscopic quantum tunneling. Here, we report the observation of QPS experimentally separated from interference of TAPS in aluminum nanowires. This separation between the low-temperature QPS and the high-temperature TAPS regions is made possible by a phase slip free superconducting region stabilized by the dissipative environment viz. the normal electrodes. Individual QPSs are detected by means of a single-shot voltage measurement protocol, in which they appear as stochastic switching events from the superconducting to the normal state.

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.

Phase slip is the intrinsic fluctuation of the order parameter and leads to the dissipation of superconductors. Here we propose a photon-assisted phase-slip model in superconducting nanowires to explain the phase-slip rate under photon irradiation. In this phenomenological model, incident photons destroy large quantities of Cooper pairs and reduce the free-energy barrier of phase slips, resulting in proliferation in the phase-slip events and leading to superconducting transition. The switching rates from the superconducting state of a niobium nitride nanowire under various photon irradiation (4.4 mW/m

{}^{2}

--4.4 W/m

{}^{2}

) and temperatures (2.3--3.7 K) are investigated through the distribution of switching currents in the experiment. The experimental data can be well fitted by our deduced expression of phase-slip rate after eliminating the influence of external noise. Our model develops the phase-slip theory under incident photons and is promising to reveal the intrinsic detection mechanism of the superconducting nanowire single-photon detector.

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.

Quantum phase slippage (QPS) in a superconducting nanowire is a new candidate for developing a quantum bit [Mooij et al. New J. Phys. 2005, 7, 219; Mooij et al. Nat. Phys. 2006, 2, 169; Khlebnikov http://arxiv.org/abs/quant-ph/0210019 2007]. It has also been theoretically predicted that the occurrence of QPS significantly changes the current-phase relationship (CPR) of the wire due to the tunneling between topologically different metastable states [Khlebnikov Phys. Rev. B 2008, 78, 014512]. We present studies on the microwave response of the superconducting nanowires to reveal their CPRs. First, we demonstrate a simple nanowire fabrication technique, based on commercially available adhesive tapes, which allows making thin superconducting wire from different metals. We compare the resistance vs temperature curves of Mo(76)Ge(24) and Al nanowires to the classical and quantum models of phase slips. In order to describe the experimentally observed microwave responses of these nanowires, we use the McCumber-Stewart model [McCumber J. Appl. Phys. 1968, 39, 3113; Stewart Appl. Phys. Lett. 1968, 12, 277], which is generalized to include either classical or quantum CPR.

Abstract Quantum phase slip (QPS) is the fundamental manifestation of macroscopic quantum tunneling (MQT). We measure the distribution of the switching current I sw in quasi-one-dimensional superconducting NbN nanowires in the temperature range of 0.2–5.1 K. The escape temperature T esc extracted from the I sw distributions exhibits saturation at temperatures below 1.2 K, indicating a transition into the MQT state. We investigate the single-photon response of the nanowire and find that the QPS rate increases with incident light power in the MQT state. We propose the photon-enhanced quantum phase-slip model, which establishes a quantitative relationship between the quantum phase-slip rate and the incident photon energy, generalizing the phase-slip dynamics into the photon-induced non-equilibrium MQT regime.