Probing picosecond depairing currents in type-II superconductors

MainThe amplitudes of critical quantities in superconductors, namely the critical temperature (Tc), critical magnetic field (Hc) and critical current density (Jc), are essential observables that yield insight into the physics of these materials, as well as important figures of merit for their application. In this context, type-II superconductors have attracted greater interest due to their high Tc values compared with type-I superconductors. In type-II systems, the magnetic penetration depth (λ) is larger than the superconducting coherence length (ξ), which leads to the formation of magnetic vortices. Consequently, some thermodynamic critical quantities are split into lower and upper critical values. For example, the critical magnetic field divides into the lower and upper critical fields, denoted as Hc1 and Hc2 (Fig. 1a), respectively.Fig. 1: Critical magnetic fields and current densities in type-II superconductors.a, Critical magnetic fields in type-II superconductors. Hc1 and Hc2 are the lower and upper critical magnetic fields, respectively. Above Hc1, magnetic vortices penetrate the superconductor. Above Hc2, superconductivity is totally suppressed. Hc is the thermodynamic critical magnetic field at which the magnetic field expulsion energy cost equals the condensation energy gain. Due to the formation of vortices above Hc1, Hc is inaccessible experimentally. b, Critical current densities in type-II superconductors. Jc1 corresponds to the cases where the self-magnetic field of current reaches Hc1 and magnetic vortices penetrate sample (bottom left, vortices indicated as oversized red circles for clarity). Jc* is the thermodynamic depairing current density at which the quasiparticle energy shift exceeds the gap size Δ, and Cooper pairs start depairing (top left, quasiparticle energy dispersion with J = 0 and J > Jc* shown in blue and red). However, the depinning of vortices and subsequent self-heating at current densities above the conventional critical current density Jc inhibit the observation of Jc*, and this conventionally inaccessible region is indicated by the shaded red colour.When the applied magnetic field H exceeds Hc1, vortices—each with characteristic size on the order of the coherence length ξ—begin to penetrate into the superconductor (Fig. 1a). As the applied magnetic field H increases further, more vortices enter the material while the sample remains superconducting. Superconductivity persists until the field surpasses Hc2, at which point vortices occupy the entire sample and superconductivity is fully suppressed1. The thermodynamic critical field Hc is defined as the field at which the magnetic field expulsion energy \({(H}_{\rm{c}}^{2}/4{\pi })\times V\) equals the free energy difference between normal and superconducting states \(\left({F}_{{\rm{N}}}-{F}_{{\rm{S}}}\right)\), and is located between Hc1 and Hc2. Due to the formation of vortices above Hc1, magnetic field is not fully expelled around the sample and, thus, Hc is experimentally not accessible.Similarly, in superconducting electronics the maximum current a superconductor can sustain is also a critical parameter. This limit is defined by the conventional critical current density Jc, set by vortex depinning through the Lorenz force (Fig. 1b), which leads to resistive heating and a subsequent transition to the normal state2,3,4,5,6,7. However, Jc is not an intrinsic material property associated with the microscopic superconducting parameters, but rather strongly depends on the defect density within the material, which determines the vortex pinning potential.A thermodynamic depairing current density denoted as Jc*, can be defined when the quasiparticle energy shift \(\hslash {{\bf {k}}_{\rm{F}}} \normalsize \cdot {{\bf{v}}_{\rm{s}}}\) equals the superconducting gap Δ (ref. 1) (here, \({{\bf{k}}_{\mathrm{F}}}\) is the Fermi momentum and \({{\bf{v}}_{\rm{s}}}\) is the velocity of Cooper pairs; Fig. 1b). Above Jc*, superconductivity is no longer the energetically favoured state and Cooper pairs dissociate into normal carriers. Jc* is therefore an intrinsic property of the superconducting material and sets the fundamental upper limit for the supercurrent.Although the depairing mechanism has been theoretically predicted and experimentally suggested8,9,10,11,12,13,14,15,16, direct transport measurements of the depairing current density Jc* remain challenging. When a d.c. current density exceeds Jc, vortex penetration and subsequent self-heating set in over timescales on the order of nanoseconds17,18,19, driving the sample into the normal sate before Jc* can be observed.Here, we use a picosecond ultrafast electrical transport platform to investigate the dynamics of type-II superconductors subjected to strong, ultrashort current pulses, focusing on both s-wave and d-wave superconductors. The core idea is that, within picosecond timescales, the penetration of vortices is inertially frozen near the edges, as their speed is intrinsically limited to tens of nanometres per picosecond (tens of kilometres per second)7,19,20,21,22,23, which leads to negligible energy dissipation and leaves the bulk of the sample unaffected.d.c. and picosecond electrical transport measurementsFor this study, we choose a representative s-wave superconductor, NbN, and a representative d-wave superconductor YBa2Cu3O7 (YBCO). Detailed device fabrication procedures are provided in Supplementary Information, section 2.The d.c. transport properties of both NbN and YBCO samples were first characterized, as shown in Fig. 2. Conventional critical current densities of approximately 100 GA m−2 and slightly below 50 GA m−2 were observed for NbN at 7 K and YBCO at 50 K, respectively.Fig. 2: Conventional critical current densities Jc in s-wave and d-wave type-II superconductors.a, Measurements of Jc in the s-wave superconductor NbN at 7, 8.5 and 10 K, with Tc = 15 K. b, Measurements of Jc in the d-wave superconductor YBCO at 50 and 60 K, with Tc = 85 K.Source dataFigure 3 displays the picosecond electrical transport measurements on the s-wave superconductor NbN; analogous measurements for the d-wave superconductor YBCO are provided in Supplementary Information, section 6. The device architecture is shown in Fig. 3a. A NbN thin film, approximately 20 nm thick, is connected to three pairs of photoconductive switches with a coplanar waveguide.Fig. 3: Picosecond ultrafast electrical transport measurements on NbN.a, Illustration of device architecture. The picosecond current pulses are launched from the middle pair of voltage-biased photoconductive switches (grey patches) with illuminating 515-nm laser beams. The incoming/reflected and transmitted pulses are sampled with one of the left and right pairs of unbiased switches, respectively. b, Measurements at 7 K and 20 K, below and above Tc = 15 K, respectively. At 7 K, the reflected pulses show an inductive feature and ~90% of the incoming pulses transmits through. At 20 K, the incoming pulses partially reflect and partially transmit through, due to sample’s resistive response. c, Measurements at 7 K with different peak current densities of incoming pulses. Here, the labels indicate the peak current densities of the transmitted pulses for direct comparison. At 6.5 × Jc, the response closely resembles the sample’s response at 20 K, indicating strong suppression of superconductivity. All curves shown here are normalized by the peak electrical field of incoming pulses.Source dataPicosecond current pulses (full width at half maximum ~2 ps) are launched by illuminating the middle pair of voltage-biased photoconductive switches with 515-nm, femtosecond laser pulses24,25,26,27,28,29. The pulse is referenced using one of the unbiased switches on the left-hand side of the sample, without interaction with the superconductor. Reflected and transmitted pulses are then sampled at later time delays using the same unbiased switch on the left-hand side and the one on the right-hand side, respectively. Details of the calibration procedure are provided in Supplementary Information, section 5. Figure 3b shows the normalized incoming (EIN), reflected (ER) and transmitted (ET) electric field at T = 7 K and 20 K, corresponding to temperatures below and above the superconducting critical temperature Tc = 15 K. The electric field E(t) is directly related to the current density J(t) through the expression \(E(t)\times w=S\times J(t)\times {Z}_{0}\), where w is the gap between the ground plane and signal line, S is the sample cross-section area, and \({Z}_{0}\approx 50\,\Omega\) is the wave impedance of the coplanar waveguide.At T = 7 K, the reflected pulse exhibits a small inductive response proportional to \({L}_{\mathrm{kin}}\times {\rm{d}}{I}_{T,\mathrm{ps}}(t)/{\rm{d}}t\), where \({L}_{\mathrm{kin}}\) is the kinetic inductance of the sample and \({I}_{T,\mathrm{ps}}(t)\) is the transmitted current pulse. The majority of the incoming pulse is transmitted, with the transmitted peak reaching approximately 90% of the incident peak. By contrast, at 20 K, the pulses are partially reflected and transmitted owing to the resistive behaviour of the sample in the normal state.Figure 3c displays the response of the NbN sample at T = 7 K under both weak (~0.2 × Jc) and strong (~6.5 × Jc) current pulse drive, where Jc is the d.c. critical current density measured at 7 K. These values correspond to the peak current amplitudes of the transmitted current pulses for comparative analysis.Under weak current pulse drive, the sample response is consistent with the previously described superconducting behaviour. However, under strong current pulse drive, the response closely resembles the one observed for small amplitude pulses in the normal state at 20 K. This observation suggests that strong picosecond current pulses can transiently suppress superconductivity, probably through the instantaneous depairing of Cooper pairs into normal carriers.Observation of intrinsic depairing