Active Quasiparticle Suppression in a Non-Equilibrium Superconductor.

Quasiparticle (qp) poisoning is a major issue that impairs the operation of various superconducting devices. Even though these devices are often operated at temperatures well below the critical point where the number density of excitations is expected to be exponentially suppressed, their bare operation and stray microwave radiation excite the non-equilibrium qp's. Here we use voltage-biased superconducting junctions to demonstrate and quantify qp extraction in the turnstile operation of a superconductor-insulator-normal metal-insulator-superconductor single-electron transistor. In this operation regime, excitations are injected into the superconducting leads at a rate proportional to the driving frequency. We reach a reduction of density by an order of magnitude even for the highest injection rate of 2.4 × 108 qp's per second when extraction is turned on.

In superconducting circuits, it is important to minimize the number of non-equilibrium quasiparticles, as they deteriorate the operation of various devices, such as the coherence of quantum bits based on Josephson junctions[1−5] or Majorana nanowires,[6,7] cooling power of superconducting microcoolers,[8,9] sensitivity of kinetic inductance detectors,[10−12] and performance of superconducting resonators in other applications.[13,14] In principle, bringing the system to temperatures T much below the superconducting transition should reduce the number of excitations, as at kBT ≪ Δ (here kB is the Boltzmann constant and Δ is the superconducting energy gap) their equilibrium number density nqp is suppressed exponentially. It has been demonstrated, however, that, when the devices are operated, quasiparticle (qp) excitations are created, caused typically by the drive signals or by stray microwave photons from hotter stages of the refrigerator,[1,15−18] or by ionizing radiation.[19] To overcome this “qp poisoning”, several methods have been studied. These include introduction of normal metal traps,[20−22] geometry optimization,[15,23] vortex traps by magnetic field,[13,23−25] gap engineering by variation of the film thickness,[26−29] or phonon traps.[30,31] Recently, blockage of qp’s by a voltage-filter-tuned superconducting gap has been demonstrated,[32] and employing a lower gap superconductor as a qp trap has been analyzed in detail.[29] Although the crucial role of low qp density was identified already in early studies of superconducting qubits[33−35] and related single-charge circuits,[26,36] further understanding of the generation mechanisms and reducing nqp remains the topic of an ever increasing intense research activity[17,37−40] as the effort to increase the coherence times of superconducting qubits continues.

For radio frequency (rf) driven superconductor–insulator–normal metal–insulator–superconductor (SINIS) turnstiles,[41] operated as a source of quantized electric current,[42] both drive-induced and background qp’s are the most severe limitation to reaching metrological current quantization accuracy.[15,42] In this work, we show that such a hybrid single-electron transistor (SET, see Figure a for a typical sample) functions as a sensitive, practical, and quantitative detector of the qp density of its superconducting electrodes, that could be integrated with a variety of other mesoscopic superconducting devices to probe their nqp. Under rf drive, hybrid SETs present a turnstile for single electrons, a simple-to-operate candidate realization for a solid-state standard of electric current.[41,43] For a wide range of parameters, the output current I = ef is determined only by the drive frequency f and electron charge e (see Figure d for typical measurements in this regime). Here the non-equilibrium state results from qp injection (Figure b) when the drive signal at frequency f is applied to the gate electrode of the transistor. Earlier work[15] demonstrated that the influence of drive-induced and environmental qp’s to a SINIS turnstile can be reduced by improving the geometry of the S electrodes and by shielding from residual microwave radiation, respectively.

Figure 1

Qp extraction probed in a SINIS SET. (a) Electronic scheme for turnstile operation of the hybrid SET with an integrated S1IS2 cooler, together with a false color scanning electron microscope image of sample A. Light red marks the normal metal and blue the superconducting parts, with light (dark) blue designating the lower (higher) gap superconductor. (b) Schematic sketch of the device. Quasiparticles are injected to the narrow lead where relaxation is inefficient. Qp excitations are extracted via biased S1IS2 junctions, and recombination and scattering processes are still present along the lead. The inset shows that when the S1IS2 junction is biased at eVSIS = |Δ1 – Δ2| the singularities in the qp densities of states match and excitations are transferred from the lead with Δ1 to the reservoir with Δ2. (c) IV curves of sample B in the positive bias regime, for a large number of different gate voltages. The red lines are simulations for the envelope curves, and the blue dots are the experimental data. (d) Measurements for sample A in the turnstile operation at f = 10 MHz with Vb = 120, 160, and 200 μV as blue, red, and yellow symbols, respectively. Here the current is measured against the amplitude of the gate signal Ag, and the red dashed line illustrates the ideal value of I = ef for the first plateau.

Here we combine the turnstile with an independent, in situ control—both extraction and injection—of qp’s. The qp poisoning can be reduced by suitably voltage biasing superconductor–insulator–superconductor (S1IS2) junctions with different superconducting gaps (Δ1 and Δ2, respectively) where excitations are extracted from S1 to S2 as long as Δ1 < Δ2.[44−47] In an important experiment, this effect has been used to cool one of the leads of a single-Cooper pair transistor[48] in a similar manner as refrigeration by normal metal–insulator–superconductor junctions[49−51] has been used to cool down the normal lead. However, when using a single Cooper-pair transistor, it was not possible to control the mechanism or rate of qp creation, making it more difficult to quantify the population reduction due to the biased S1IS2 junction. On the contrary, hybrid single-electron transistors allow for quantitative control. To that end, here we demonstrate that direct S1IS2cooling of the turnstile leads offers promise to fully extract the drive-induced qp’s under typical pumping conditions, in particular when bulky or thick electrodes cannot be utilized.

The evacuation of qp’s is manifested by the stabilization of current to ef in the SET turnstile operation.[15] The qp extraction can be tuned by varying the voltage biasing of the S1IS2 junction. However, non-equilibrium qp’s are also subjected to recombination and diffusion processes along the electrode, as depicted in panel b of Figure . Due to the exponential dependence of on Δ, the number of excitations is lower in the higher gap film. Here denotes the normal-state density of states at the Fermi energy and T is the electronic temperature of the superconductor. Therefore, providing sufficient energy to qp’s in the lower gap superconductor, biasing the junction such that the singularities in the superconducting densities of states align, will promote a transfer to the higher-gap superconductor (see the inset of Figure b).[52] Although two superconductors with different energy gaps are required, the qp extraction in a voltage-biased tunnel junction is in sharp contrast to those gap engineering methods[26−29] where qp’s are passively trapped in lower-gap regions away from the relevant operational zones of the device. To implement the qp evacuation and the probing of nqp experimentally, we fabricate and measure a series of aluminum-based samples, cooled down in a dilution refrigerator reaching an electronic base temperature of Tb ≈ 50 mK.

Here we show detailed results for two devices for confirmation of results, both with copper as the turnstile normal-metal island, separated by aluminum-oxide barriers from two aluminum leads. The samples were patterned by electron-beam lithography, and metal deposition was done by multiangle shadow electron-beam evaporation; see the Supporting Information for further details on the fabrication process. One of the leads (left in Figure a) is made wide to trap qp’s passively, while the other (right) is long and narrow, this way promoting an excess qp population: due to the geometry, qp diffusion away from the turnstile junction and their subsequent relaxation is intentionally poor in this narrow lead.[15] The samples were fabricated using standard electron-beam lithography and shadow mask techniques. The narrow lead is the S1 part of a S1IS2 Superconducting QUantum Interference Device (SQUID), whereas the fork-shaped electrode forms S2 with a higher superconducting gap. The different superconducting gaps are achieved by depositing a thicker aluminum layer as the turnstile lead (d1 ≈ 70 nm) and a thinner one for the rest of the SQUID (d2 ≈ 8 nm).[53] A magnetic field perpendicular to the plane of the sample is applied to produce a flux Φ = Φ0/2 (here Φ0 = h/(2e) is the magnetic flux quantum) in the SQUID loop and therefore suppress the supercurrent in the S1IS2 junctions so that subgap VSIS can be applied[48] (see also the Supporting Information).

We characterize the samples by sweeping the gate voltage Vg between the “closed” (ng = 0) and “open” (ng = 0.5) states (with ng = CgVg/e, where Cg is the gate capacitance) and stepping the SET bias voltage Vb. The S1IS2 junctions are first kept unbiased, named as the “cooler-off” case. The main parameters of the samples have been extracted from these measurements by fitting the measured current I to current–voltage curves calculated with a master equation approach taking into account sequential tunnelling and Andreev reflections[54] (see, for example, the Supporting Information and ref (55)). One of these fits can be seen in Figure c. For sample A (B), the total normal-state tunnel resistance is RT = 159.9 kΩ (63.0 kΩ), the charging energy of the island Ec = 0.95Δ1 (0.50Δ1), the thickness of the N island d = 30 nm (40 nm), and the Dynes parameter[18] η = 1.0 × 10–4 (7.5 × 10–5). For both samples, the superconducting energy gap Δ1 of the leads is 180 μeV, and the island’s lateral dimensions l × w are 1 μm × 100 nm. See the Supporting Information for further details on the employed model where it is explicit that the island temperature is calculated according to power balance and that the area of a single conduction channel can be extracted from these data. However, it is more precise to extract Ach from pumping measurements, since the effects of the second-order tunnelling are more pronounced in that operation regime. Since qp diffusion is altered by the different lead shapes,[15] the DC fits were made by leaving the temperature of the long lead as a free parameter and assuming the base temperature of 50 mK for the wide lead, estimating an electronic temperature of ∼150 mK for the long lead. The values of Ach, 9.5 nm2 (10 nm2) for sample A (B), are lower by about a factor of 2 compared to previously reported values,[56] yet the fits are relatively insensitive to the exact value of this parameter. We estimate these values from data with the cooler bias VSIS near a certain optimal point, where the Andreev effects are more noticeable, as will be seen later. By analyzing the differential conductance of the SQUID, it was possible to estimate Δ2 to be ∼235 and ∼240 ± 5 μeV for samples A and B, respectively.

The strong cooling by the superconducting junctions is evident in the turnstile operation of the SET shown in Figure . In this regime, a sinusoidal signal with an offset equivalent to ng = 0.5 is applied to the gate electrode and the amplitude of this signal is swept while the SET current is measured. The presented data shows these measurements zoomed to the first current plateau (see Figure d for a typical measurement in a wider range) for both samples. The plots display the behavior with the SQUID at zero bias and at a finite bias close to where optimum cooling is achieved. Besides displacing the plateau level from the expected value of I = ef, an elevated qp density in the leads close to the junctions makes the level depend on the SET bias voltage and hence the values of the current at the plateaus will spread.[15] In the two cases of Figure , the “cooler-on” curves show a smaller deviation from the expected current than the cooler-off ones. Additionally, the bias dependence of the plateau level is weaker with the cooler active. All of this means that the density of excitations has been suppressed in the narrow lead by biasing the S1IS2 junctions. For these particular devices, the remaining deviation is explained by the relatively low Ec < Δ which promotes Andreev tunnelling, as well as by leakage current[55] and remnant qp population as will be seen later.

Figure 2

Improvement of the I = ef pumping plateaus by the S1IS2 cooler. Data for the cooler-off (open diamonds) and cooler-on (filled triangles) cases compared with a model based on a master equation approach (solid black lines). Blue, red, and yellow curves correspond to Vb = 120, 160, and 200 μV, respectively. (a) Sample A operating at 80 MHz; in the cooler-on case, the SQUID is biased at 60 μV. (b) Sample B operating at 100 MHz; here in the cooler-on cases, the SQUID is biased to 50 μV.

To quantify the reduction of the qp density, the pumping data at the plateau shown in Figure are compared with a model (black solid curves) based on a master equation approach similar to that in the DC case. In the model, the temperature of the island is varied at each amplitude value according to the proper power balance. Furthermore, since the used signal frequencies are high (, with τeff being the effective qp relaxation time), it is suitable to model the system as if the temperature of the superconductors was constant throughout the operation cycle.[16] Additionally, electron–electron relaxation is assumed to be fast enough to avoid branch imbalance. With these assumptions, the comparisons with the data are done with the temperature of the narrow lead as the only free parameter (device parameters are fixed by the DC measurements). As noted before, nqp is related to the effective electron temperature T in the superconducting lead obtained by means of the thermal balance model. These simulations allow one to deduce that the biasing of the S1IS2 junctions effectively cools the narrow long lead. Furthermore, the use of the pumping operation of a hybrid SET as a sensitive detector of qp’s is justified by these calculations. Figure a shows a specific example of sample B biased at Vb = 100 μV and gate modulated with an amplitude of around Ag = 3.5 mV. There it is evident that the plateau level grows with the excitation density in the lead. The behavior is nearly linear at high population but flattens for low values.

Figure 3

Sensitivity of current plateau to qp’s. (a) Calculated curves showing how the current at the plateau varies with the qp density. The parameters of sample B were used in these calculations along with a bias of Vb = 100 μV and a gate amplitude of Ag = 3.5 mV. (b) Measured current at the plateau as a function of the bias applied to the S1IS2 cooler for device A at f = 40 MHz. From bottom to top, the curves correspond to Vb = 120, 160, and 200 μV, respectively. (c) As in part b for B at 20 MHz. (d) As in part c for 80 MHz. Dashed black lines indicate the optimal biasing point of the cooler.

The behavior of the qp density when the cooler bias changes is analyzed by performing measurements where VSIS is swept while the gate drive amplitude Ag is fixed to approximately the middle of the first current plateau. Examples of such measurements are shown in Figure b for device A and in panels c and d for device B. The plateau level and the spreading of them for different bias values of the SET decrease until we reach eVSIS ≈ ±|Δ2 – Δ1|[57] (indicated by a dashed line in panels b–d). At this point, the temperature of the lead is at a minimum and it changes only weakly until a threshold at which it starts to grow rapidly. Therefore, we can assert that when the cooler bias voltage reaches the optimum point the excitation population in the lead is at a minimum and at higher biases it starts to grow up first at a low rate and then rapidly when there are peaks in subgap current of the S1IS2 SQUID (see the Supporting Information for further details). Similarly, biasing at VSIS < 0 affects the system in the same way but this time by extracting hole-like excitations (consider the inset in Figure b with the lower singularities aligned). We can also understand this by looking at the modeled cooling power of the S1IS2 junction[58] (see the Supporting Information for details) when it begins to grow with VSIS toward a sharp peak, where the lead temperature is minimum, and then it decreases dramatically, corresponding to the zone with finite but less efficient cooling. Finally, at eVSIS ≈ Δ2 + Δ1, qp’s are injected into the lead with the smaller gap. No sharp dip is observed in the measured I vs VSIS curves at eVSIS = |Δ2 – Δ1|, similar to earlier works on S1IS2 cooling.[47,48] The singularity matching peak in the cooling power is likely washed out due to low-frequency noise in the S1IS2 cooler bias voltage, finite subgap density of states, and local inhomogeneities in the superconducting gap.

The influence of the S1IS2 cooler is qualitatively the same for both samples and independent of the operation frequency as well as of the SET bias, although the plateau levels are different; see the Supporting Information for additional measurements to corroborate this fact. Note that this level approaches the ideal value but never reaches it even in the calculations for samples with low Ec < Δ (see Figure a). In these devices with low Ec, we observe a clear crossover from excess qp-dominated to Andreev-reflection-limited current quantization as the cooler is turned on.

We estimate the lead temperature for a wide range of operation frequencies. Figures a and b show that the lead temperature T extracted from the fitting procedure and in turn nqp (Figures c and d) grow with increasing frequency also in the cooler-on case. However, in sample B, the curve for the cooler-on case flattens at f > 40 MHz, since the SET behavior loses sensitivity to qp density in this operation regime (see Figure a). For the near optimal cooler bias (VSIS ≈ 50 and 60 μV for samples A and B, respectively), the dependence of nqp versus the operation frequency is resemblant. This comes from the fact that qp transport is dominated by diffusion. There is a dramatic drop in the qp density due to the biasing of the S1IS2 junctions. By linearly extrapolating the densities to the f = 0 limit, it is possible to see that there is a reduction between the “off” and “on” case by an order of magnitude also in this situation. We conclude that the cooler suppresses also the ever present excess qp population nqp,0, generated by a non-equilibrium environment,[59−61] which in turn should diminish the subgap current in the DC regime. On the other hand, it is seen that the biased S1IS2 junctions cannot totally remove this excess qp population in the leads. We expect that even more efficient evacuation can be achieved by placing the S1IS2 junction closer to the injection junction—or even under it—since the highest concentration of qp’s is near this point,[21,51] and further diffusion, recombination, and phonon pair breaking, among other phenomena, can thus be avoided.

Figure 4

Qp density variation as a function of drive frequency. Estimated narrow lead temperature during the turnstile operation as a function of the gate signal frequency (a) for sample A and (b) for sample B. Estimated qp density at the junction as a function of the pumping frequency (c) for sample A and (d) for sample B, corresponding to the data in panels a and b, respectively. The black solid lines are fittings to eq .

We measured further reference samples with identical aluminum lead geometry but without S1IS2 SQUIDs and obtained the qp densities in them (for results, see the Supporting Information). The qp densities are similar to those shown in Figure for the cooler-off case, and thus, there is no significant influence of the unbiased cooler junctions or the presence of their biasing circuit on the relaxation of the non-equilibrium excitations. Hence, the presented cooler-off densities should correspond approximately to densities in the case if the S1IS2 junctions were not present. Thus, the diffusion model in ref (15), which is based on heat conduction, without considering normal metal traps, should hold. Within this model, the qp density is given bywhere , ϖ, and ϑ are the dimensions of the lead (25 μm × 100 nm × 70 nm) and Pinj is the injected power which can be approximated by Δ1f in the driving regime of the experiment.[15] In the Supporting Information, we show that this is a good approximation. Notably, even at f = 100 MHz, the injected power for an aluminum-based device with Δ1 = 200 μeV is only around 3.2 fW, extractable by a submicron S1IS2 junction. In addition, ρn is the aluminum normal state resistivity. Based on measurements of a number of separate test structures, we estimate ρn ≈ 31 Ω nm at 77 K (see the Supporting Information for details). A few of these four-probe structures were cooled down to 4.2 K where we estimate a further 10% decrease of ρn below its 77 K value. The measured qp numbers are larger than those predicted by this model with no free parameters. Fitting eq to the data using ρn as a free parameter yields ρn ∼ 90 Ω  nm. These fits are shown as black lines in panels c and d of Figure . Further experiments are needed to understand the discrepancy, observed also in ref (62) for devices with higher charging energy.

At f = 0 and VSIS = 0, we estimate nqp,0 ≈ 250 μm–3 for both samples, obtained from fits to dc IV characteristics of the turnstile. These background qp densities for the cooler-off case are roughly 2 orders of magnitude higher than those observed for highly shielded SINIS turnstiles,[15] or superconducting qubits and resonators.[11,37,63] The excess in nqp,0 compared to ref (15) originates from the lack of a microwave-tight indium seal in the sample holders employed in these measurements and from the lack of any normal metal traps and restricted geometry—narrow, thin, long—of the S electrode with the S1IS2 junctions. To bring down nqp,0, a sample holder with a higher level of shielding can be utilized, and the S2 electrode can be fabricated with separate lithography and deposition steps that do not limit the junction geometry as with the multiangle shadow evaporation technique where both NIS and S1IS2 junctions are created with a single mask.

The applicability of the qp extraction and detection techniques considered in this work extends beyond SINIS turnstiles and improving the accuracy of their pumped current. First, one can envision straightforward integration of S1IS2 coolers, for instance, with absorbers of kinetic inductance detectors, or into superconducting resonators analogously to NIS coolers.[64] When the bottom electrodes of the junctions are fabricated in a separate lithography and deposition step, their area and geometry can be adjusted at will. Furthermore, instead of tuning the gap by the film thickness, different superconducting materials can be utilized. Second, the SINIS turnstile, demonstrated here to function as a sensitive and direct qp probe, can be combined with various superconducting devices to measure the background qp density. This high-impedance, non-invasive probe can test the level of microwave shielding also in setups with sensitive non-superconducting devices. Finally, we have shown the driven hybrid turnstile to act as a highly controlled qp injector that could be used to investigate the qp sensitivity and qp trap efficiency of superconducting qubits and other devices.

In summary, we have been able to demonstrate active extraction of non-equilibrium excitations from a superconductor. A more than 1 order of magnitude reduction from values as high as 5.8 × 103 to 260 μm–3 at the highest studied injection rate of 2.4 × 108 s–1 was achieved. Furthermore, in the limit of no qp injection (f → 0), we find a similar reduction, although a finite population of environmentally created excitations remains. Our work shows that the qp density in the superconducting electrodes can be controlled by active qp traps, here demonstrated for the first time with in situ control of qp injection.