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Physical Review Letters

Single-electron charging of a superconducting island

D. V. Averin, Yuli V. Nazarov

Published Sep 28, 1992• 190 citations
Publisher

Abstract

We have calculated the quasiparticle current through a superconducting island in the Coulomb blockade regime. The current depends strongly on the parity of the total number of free electrons in the island. This dependence reflects the difference between ground-state properties of the superconductor with even and with odd number of electrons.

DOI
10.1103/physrevlett.69.1993

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We have calculated the quasiparticle current through a superconducting island in the Coulomb blockade regime. The current depends strongly on the parity of the total number of free electrons in the island. This dependence reflects the difference between ground-state properties of the superconductor with even and with odd number of electrons.
We present a superconducting device showing a clear parity effect in the number of electrons, even when there is, on average, a single nonequilibrium quasiparticle present and the parity of the island switches due to quasiparticles tunneling in and out of the device at rates on the order of 100 Hz. We detect the switching by monitoring in real time the charge state of a superconducting island connected to normal leads by tunnel junctions. The quasiparticles are created by Cooper pairs breaking on the island at a rate of a few kilohertz. We demonstrate that the pair breaking is caused by the backaction of the single-electron transistor used as a charge detector. With sufficiently low probing currents, our superconducting island is free of quasiparticles 97% of the time.
We show that charge transfer through a small superconducting (S) island of a single-electron transistor is strongly affected by vorticity. This interplay of charge and rotational degrees of freedom in a mesoscopic superconductor occurs through the effect of vorticity on the quantum mechanical spectrum of electron-hole excitations. The subgap quasiparticle levels in vortices can host an extra electron, thus suppressing the so-called parity effect in the S island. We propose to measure the collective dynamics of vorticity and electric charge via the charge pumping effect caused by alternating vortex entry and exit controlled by a periodic magnetic field.
The number of electrons in small metallic or semiconducting islands is quantised. When tunnelling is enabled via opaque barriers this number can change by an integer. In superconductors the addition is in units of two electron charges (2e), reflecting that the Cooper pair condensate must have an even parity. This ground state (GS) is foundational for all superconducting qubit devices. Here, we study a hybrid superconducting-semiconducting island and find three typical GS evolutions in a parallel magnetic field: a robust 2e-periodic even-parity GS, a transition to a 2e-periodic odd-parity GS, and a transition from a 2e- to a 1e-periodic GS. The 2e-periodic odd-parity GS persistent in gate-voltage occurs when a spin-resolved subgap state crosses zero energy. For our 1e-periodic GSs we explicitly show the origin being a single zero-energy state gapped from the continuum, i.e., compatible with an Andreev bound states stabilized at zero energy or the presence of Majorana zero modes.
We have measured the supercurrent branch of a superconducting single electron transistor as a function of gate charge, temperature, and magnetic field. At low temperature and magnetic field, the switching current goes from a minimum to a maximum when the gate charge is varied from 0 to e, as expected for an island in the ground state with an even electron number. When the odd electron number ground state becomes populated by an increase of temperature or field, the Josephson tunneling is strongly suppressed, in agreement with theoretical predictions.
We find that if two superconducting islands of different number parity are linked by a tunnel junction, the unpaired electron in the odd island has a tendency to tunnel into the even island. This process leads to fluctuations in time of the number parity of each island, giving rise to a random telegraph noise spectrum with a characteristic frequency that has an unusual temperature dependence. This new phenomenon should be observable in a Cooper-pair pump and similar single-electron tunneling devices.
The charge on a superconducting island coupled to a superconducting electrode by a Josephson junction is determined in the region where the gap energy and the single-electron charging energy of the island are of comparable magnitude. The Coulomb staircase describing the incremental charging of the island in response to a biasing voltage is studied. The rounding of the staircase corners due to thermal and quantum fluctuations is found to depend on the parity of the island charge in the adjacent tread. This should allow for an experimental disentanglement of the effects of quantum charge fluctuations from thermal fluctuations.