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The microscopic mechanism that enables the transport properties of the NW to be affected by the phases of the superconducting order parameter is Andreev reflection19. This is the quantum process by which an electron impinging from the normal side onto the interface between a normal metal and a superconductor is retroreflected as a hole (that is, a time-reversed electron) that picks up the phase of the superconducting order parameter. When two or more superconductors are connected to the nanowire (NW), multiple Andreev scattering processes can occur between them such that transport through the NW will depend on the differences between the phases of the order parameters20.

The physical realization of this scheme is shown in Fig. 1a and consists of a heavily-doped InAs semiconducting NW on top of which three fingers of superconducting (S) vanadium (V) are deposited, thus implementing a superconducting quantum interference device (SQUID, ref. 21). Two Au normal-metal electrodes (N) are coupled to the ends of the NW to allow detection of the current Iwire flowing through the wire. A close-up of the device core is shown in Fig. 1b. Time-dependence, and possibly pumping, arises from biasing the loop with a current ISQUID larger than the critical current Ic of the SQUID, thus the phase differences φ1 (t) and φ2 (t) across the two Josephson junctions cycle in time at the Josephson frequency νJ=V SQUID/Φ0, where V SQUID is the voltage developed across the SQUID and Φ0≃2×10−15 Wbis the flux quantum. Furthermore, φ1(t) and φ2(t) can be shifted by a constant term δ φ=2πΦ/Φ0 originating from an applied magnetic flux Φ threading the loop. This scheme has the advantage that no high-frequency signal needs to be applied to the sample, thus simplifying the set-up and minimizing the impact of stray capacitances: the time-dependent signal is self-generated as a result of the a.c. Josephson effect.

Figure 1: InAs Josephson quantum electron pump.
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a, Pseudo-colour scanning electron micrograph of the device. An InAs nanowire (NW) is connected to three ≃250-nm-wide V/Ti superconducting contacts, forming two ≃50-nm-long Josephson weak-links and realizing a superconducting quantum interference device (SQUID). Two Au/Ti leads, placed at a relative distance of ≃1.5 μm, are contacted to the ends of the NW to allow current detection. The structure was fabricated using electron-beam lithography and evaporation of metals. The normal-state resistance of the SQUID is ∼250 Ω, whereas that of the Au/NW/Au line is ∼3.5 kΩ. b, Blow-up of the device core showing the two V/InAs/V Josephson junctions and the two Au electrodes. c, Inset: SQUID voltage (V SQUID) versus current (ISQUID) characteristics at Φ=0 and Φ=Φ0/2 (Φ is the applied magnetic flux and Φ0 is the flux quantum) showing a maximum critical current of ∼235 nA. Φ0 corresponds to a magnetic field of ≃1.4 Oe applied through an effective loop area of ∼14.6 μm2. Main panel: Φ-dependent modulation of the SQUID critical current Ic. Dashed line is the theoretical behaviour of a tunnel and resistively-shunted junction SQUID assuming an asymmetry of ∼4% between the critical currents of the two weak-links. Data in c are taken at T=250 mK.

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Below the critical temperature of the superconductors (Tc≃4.65 K) a Josephson current flows through the SQUID across the NW. The SQUID voltage–current characteristics at 250 mK are shown in the inset of Fig. 1c for two representative values of Φ. Whereas for Φ=0 the characteristic shows a clear dissipationless regime with a critical current Ic≃235 nA, for Φ=Φ0/2it behaves almost linearly, with Ic largely suppressed. The full Ic (Φ) dependence (main panel of Fig. 1c) shows the characteristic pattern of a superconducting interferometer. The theoretical curve of a conventional (that is, described by the RSJ model) SQUID (ref. 22) is shown for comparison (dashed line, see Supplementary Information).

Figure 2a shows a sketch of the pumping measurement set-up. A d.c. current ISQUID is fed through the SQUID terminals while the voltage drop V SQUID is measured against Φ. The N electrodes are grounded and Iwire is sensed with an ammeter. The N and S parts of the circuit have no common ground, therefore preventing any direct net charge transfer from the SQUID to the NW.

Figure 2: Experiment set-up and transfer function characteristics.
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a, Schematic drawing of the Josephson quantum electron pump set-up. A d.c. current ISQUID is fed into the SQUID terminals through a floating source while the voltage drop V SQUID is recorded against the applied magnetic flux Φ threading the ring. When ISQUID exceeds the SQUID critical supercurrent the a.c. Josephson effect sets in, inducing a current Iwire which flows in the NW. Iwire is sensed through an ammeter. S and N denote superconductors and normal metals, respectively. b, Colour plot of the SQUID flux-to-voltage transfer function versus Φ and ISQUID. is antisymmetric in Φ and ISQUID. c, Colour plot of the NW flux-to-current transfer function versus Φ and ISQUID. d, Colour plot of the NW flux-to-voltage transfer function versus Φ and ISQUID. Data are taken with a voltmeter in an open-circuit configuration, that is, without allowing Iwire to flow. Note the markedly different behaviour exhibited by and , which are almost symmetric in Φ as well as in ISQUID. All measurements are taken at T=250 mK using a low-frequency phase-sensitive technique to get higher sensitivity and reduced noise.

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In the following we will concentrate our attention on the symmetries in Φ and ISQUID exhibited by the measured signal, as these are of crucial importance for the interpretation of the experiment. The low-temperature SQUID flux-to-voltage transfer function versus Φ and ISQUID is shown in Fig. 2b. In particular, is a Φ0-periodic function of Φ and is antisymmetric in Φ and ISQUID. By contrast, the flux-to-current transfer function of the NW, (Fig. 2c), besides exhibiting the same periodicity in Φ0, shows a drastically different behaviour, being almost symmetric in both Φ and ISQUID. A similar behaviour, with the same symmetries of , is exhibited by the NW flux-to-voltage transfer function, (Fig. 2d), where V wire is measured with open NW contacts. and result from different but complementary measurements, and the evidence of such a similarity suggests that both represent the same physical mechanism (see Supplementary Information). As we shall argue, the nature of the symmetries exhibited by and is compatible with quantum pumping mechanisms.

In general, the pumped current is not expected to show definite parity with Φ (refs 17, 18), therefore Iwire can have a flux-symmetric component as well. This, however, could be ascribed also to other mechanisms than pumping. In addition, Iwire is not even expected to possess any definite parity with ISQUID. To extract a pure pumped current contribution from the whole measured signal, we focus on the component of Iwire that is antisymmetric in Φ, IwireA, as it is predicted to be a fingerprint of quantum pumping in the Josephson quantum electron pump (JQEP, ref. 16). After Φ-integration of , IwireA is obtained as IwireA=[Iwire(Φ,ISQUID)−Iwire(−Φ,ISQUID)]/2. The result of this procedure is shown in Fig. 3a, which shows IwireA versus Φ and ISQUID at 250 mK. The Φ0 periodicity together with the antisymmetry imply that IwireA vanishes at Φ=Φ0/2, and its sign and magnitude can be changed by varying Φ. Notably, IwireA is almost symmetric in ISQUID. The theoretical IwireA calculated for the JQEP geometry through a dynamical scattering approach23,24,25, assuming the existence of multiple independent modes in the NW, is shown in Fig. 3b (see Supplementary Information). Although rather idealized, the model is an essential tool to predict the pumped current symmetries of the JQEP. Remarkably, summing over many NW modes yields IwireA, which is almost symmetric in ISQUID, in agreement with the experiment.

Figure 3: Flux and ISQUID dependence of the antisymmetric part of the current flowing in the NW.
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a, Colour plot of IwireA versus ISQUID and Φ. b, Colour plot of the theoretical zero-temperature IwireA versus ISQUID and Φ. The calculation was performed for the JQEP geometry, assuming the same asymmetry between the Josephson junctions as in the experiment. Icmax is the sum of the critical currents of the two Josephson junctions, R is the total shunting SQUID resistance, and RK≃25.8 kΩ is the Klitzing resistance (see Supplementary Information for further details). c, Colour plot of IwireA versus ISQUID and Φ, shown over a wider range of ISQUID. d, IwireA versus Φ for a few representative values of ISQUID. The latter are indicated as dashed lines of the same colour as in c. e, IwireA versus V SQUID for a few selected values of Φ. f, IwireA versus V SQUID plotted over a smaller range of V SQUID for the same Φ values as in e. The slope in the linear regime, expressed in pA GHz−1, is denoted as η. In e and f the error bars represent the standard deviation of the current values calculated over several measurements, and the upper horizontal scale is expressed in terms of the Josephson frequency νJ. All measurements are taken at T=250 mK.

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Figure 3c shows IwireA versus Φ and ISQUID over a wider range of SQUID currents. Specifically, IwireA turns out to be a non-monotonic function of ISQUID, initially increasing, then being suppressed for large ISQUID. This is emphasized in Fig. 3d, where IwireA(Φ) is plotted for selected values of ISQUID. IwireA is a sinusoidal-like function of Φ, with an amplitude that depends on ISQUID, and reaches its maximum at Φ∼(1/4)Φ0 and Φ∼(3/4)Φ0.

The full IwireA(V SQUID) dependence for a few values of flux is shown in Fig. 3e and highlights both the monotonic linear increase for low V SQUID and suppression at large V SQUID. The symmetry in V SQUID (that is, in ISQUID) is emphasized as well. Furthermore, |IwireA| is maximized at |V SQUIDmax|≈0.4 mV, independently of Φ, where it reaches values exceeding 20 pA. By converting V SQUIDmax in terms of the Josephson frequency we get νJ≃190 GHz, with a corresponding time, νJ−1∼5 ps, which is comparable to τD=W2/D≃4 ps, that is, the time required by electrons to diffuse in the NW between the Josephson junctions. In the above expression W≃250 nm is the width of the SQUID central electrode (Fig. 1b), which we assume to coincide with the separation between the weak-links, whereas D≃0.015 m2 s−1 is the diffusion coefficient of the NW (ref. 26). The transition between the regime of IwireA enhancement as a function of V SQUID to the one of IwireA suppression can be explained in terms of the ability of the electrons to follow adiabatically the time-dependent parameters up to a maximum frequency set by τD−1. Another possible contribution to the suppression observed at higher V SQUID might stem from weakening of the a.c. Josephson coupling at high applied current27.

The IwireA(V SQUID) dependence, plotted over a reduced bias range, is shown in Fig. 3f. In particular, IwireA shows a linear behaviour, with a slope η that depends on the applied flux and achieves values as high as several 10−1 pA GHz−1. In the so-called ‘adiabatic regime’, that is, where the pumped current is expected to vary linearly with frequency, η would therefore correspond to some 10−3 electrons per pump cycle.

The role of temperature (T) is shown in Fig. 4a, which shows IwireA versus V SQUID at Φ=(3/4)Φ0 for increasing temperatures. IwireA monotonically decreases on increasing T, which can be ascribed to the influence of thermal smearing as well as thermally induced dephasing, and is suppressed for T≳3.5 K. We stress that the aforementioned temperature is substantially smaller than Tc, the latter setting the disappearance of both the Josephson effect and superconductivity in the JQEP. The IwireA (T) dependence at the same flux is shown in Fig. 4b for a few ISQUID values. Specifically, IwireA begins to round off at lower temperatures, indicating a saturation, whereas it is damped at higher T. The low-temperature behaviour suggests that current tends to saturate on reducing temperature when the ‘effective’ separation between Josephson junctions becomes of the same order as the electron thermal coherence length in the NW, nm at 250 mK, where ℏis the reduced Planck constant and kB is the Boltzmann constant. By contrast, the decay of LT at higher temperatures may be considered as one of the predominant decoherence mechanisms leading to IwireA suppression. Further study is needed to clarify this point.

Figure 4: Temperature dependence of the antisymmetric part of the current flowing in the NW.
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a, IwireA versus ISQUID measured at several bath temperatures T. b, IwireA versus T at selected bias currents ISQUID. Note the saturation of IwireA at low temperature as well as its suppression at high temperature. The error bars represent the standard deviation of the current values calculated over several measurements. Dashed lines in both a and b are guides to the eye, and all measurements are taken for Φ=(3/4)Φ0.

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It is worthwhile emphasizing that other effects that might manifest in the JQEP would yield currents characterized by symmetries markedly different from the ones predicted for quantum pumping (see Supplementary Information). Among these we note (1) any spurious current due to asymmetry between the junctions, which is always dominated by a component symmetric in Φ and antisymmetric in ISQUID; (2) any thermocurrent generated by a different power dissipated in the two junctions, which is expected to be predominantly symmetric in both Φ and ISQUID.

We finally note that other normal conductors than InAs NWs could be used for the implementation of the JQEP. This might pave the way for the investigation of the interplay between superconductivity-induced quantum pumping and exotic electronic states existing, for instance, in graphene28 or in carbon nanotubes29.

Methods

Selenium-doped InAs NWs were grown by chemical beam epitaxy on an InAs 111B substrate. Gold catalyst particles were formed by thermal dewetting (at 520 °C for 20 min) of a 0.5-nm-thick Au film under tertiarybutylarsine (TBA) flux. NWs were grown for 2 h at 420 °C using TBA, trimethylindium (TMI) and ditertiarybutylselenide (DTBSe) metallorganic precursors with line pressures of 2.0 torr, 0.3 torr, and 0.4 torr, respectively. NWs have diameters of 90±10 nm and are around 2.5 μm long. Transport parameters were estimated over an ensemble of nominally identical 1 μm-long NW field effect transistors using a charge control model30 and a numerical evaluation of the gate capacitance. Carrier density was estimated to be n=1.8±0.8×1019 cm−3 and electron mobility μ=300±100 cm2 V−1s−1. The devices were fabricated using a technique of dry cleavage of the NWs onto Si/SiO2 substrates (500 nm oxide on intrinsic Si). Contacts were obtained by a two-step aligned process: thermal evaporation of Ti/Au (10/80 nm) was performed first and followed by electron-beam deposition of Ti/V (15/120 nm) in a UHV chamber21. InAs NWs were treated with a NH4Sx solution before each evaporation step to obtain transparent metal-NW contacts26.

The magneto-electric characterization of the devices was performed in a filtered 3He refrigerator (two-stage RC- and π-filters) down to ∼250 mK using a standard 4-wire technique. Current injection at the SQUID terminals was obtained by using a battery-powered floating source, with voltage and current being measured by room-temperature preamplifiers. Derivative measurements (flux-to-voltage as well as flux-to-current transfer functions) were performed with a standard low-frequency lock-in technique by superimposing a small modulation on the applied magnetic field.