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Dynamics of electrons in a superconductor

In this new study, researchers at our laboratory have investigated the dynamics of electrons in a superconducting niobium nanowire. The injection of a very small number of electrons is enough to drastically reduce the critical current flowing in a superconductor. This is due to the accumulation of energetic electrons from Cooper pairs broken by this very small injection current.

Published on 15 February 2023
In the ground state of a superconductor, electrons pair up to form so-called Cooper pairs. The temperature, a magnetic field, an electric current or an incident photon can break these pairs to restore single electrons also called quasi-particles. The presence of quasi-particles is therefore the sign of a weakening of superconducting properties, which can harm the proper functioning of superconducting circuits such as Qbits or, on the contrary, be used to make photon detectors.

Experimental set-up. The nanowire is in the center of the image (red box). The tip of the STM, symbolized by the blue triangle, is used to inject an electronic current (It) into the nanowire by tunnel effect (without contact). Simultaneously, the critical current of the nanowire (Ic) is detected when a voltage Vnanofil appears across its terminals.

We have studied the dynamics of quasiparticles using a scanning tunneling microscope (STM) operating at very low temperature (50 mK). An STM makes it possible to locally inject electrons into a device by controlling both their energy, by the electrical voltage Vb, and their rate of injection, by the tunneling current It. Each injected electron then transfers its energy to the superconductor either by direct Coulomb interaction with the Cooper pairs, or via a phonon, i.e. a vibration of the atomic lattice. Each broken Cooper pair thus releases two new very energetic quasi-particles which will in turn relax by breaking other Cooper pairs. This cascade leads to the formation of a cloud of quasi-particles, thus creating a hot spot which can limit the critical current Ic that a superconducting device is able to transport without transiting to its normal state. This is what we demonstrated by injecting quasi-particles into a niobium nanowire 300 nm wide and 2 µm long and simultaneously measuring its critical current. The latter, of about a hundred micro-amperes, could have been greatly weakened by a tunneling current a million times weaker. We have demonstrated that this attenuation is proportional to the product It Vb. It is therefore mainly due to a heating effect well described by a thermal model, thus ending a debate on a hypothetical electric field effect proposed in the literature to explain the dependence of Ic with a gate voltage in a superconducting transistor. This was actually a measurement artifact due to leakage currents between the gate and the superconducting nanowire, the effect of which had been underestimated until then.

Moreover, by examining small deviations from the thermal model measured for different values of the tunneling current, we were able to model the dynamics of formation of the cloud of quasi-particles and determine a relaxation time of their energy of the order of 40 ps. This information is fundamental for optimizing the performance of photon detectors or protecting Qbits from quasiparticle poisoning. 

Measurement of the critical current as a function of the injection voltage for different tunnel currents. The dotted horizontal line indicates the value of the critical current without quasi-particles injected.

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