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arXiv:1403.6643

The energy landscape of a superconducting double dot

N. J. Lambert, Mark Edwards, A. A. Esmail, Felix A. Pollock, Brendon W. Lovett, Andrew J. Ferguson

Published Mar 26, 2014• 0 citations
arXivHTMLPDF

Abstract

We consider the energetics of a superconducting double dot, comprising two superconducting islands coupled in series via a Josephson junction. The periodicity of the stability diagram is governed by the competition between the charging energy and the superconducting gap, and the stability of each charge state depends upon its parity. We also find that, at finite temperatures, thermodynamic considerations have a significant effect on the stability diagram.

DOI
10.48550/arxiv.1403.6643

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We consider the energetics of a superconducting double dot, comprising two superconducting islands coupled in series via a Josephson junction. The periodicity of the stability diagram is governed by the competition between the charging energy and the superconducting gap, and the stability of each charge state depends upon its parity. We also find that, at finite temperatures, thermodynamic considerations have a significant effect on the stability diagram.
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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.
The work presented in this thesis investigates transitions between quantum states in superconducting double dots (SDDs), a nanoscale device consisting of two aluminium superconducting islands coupled together by a Josephson junction, with each dot connected to a normal state lead. The energy landscape consists of a two level manifold of even charge parity Cooper pair states, and continuous bands corresponding to charge states with single quasiparticles in one or both islands. These devices are fabricated using shadow mask evaporation, and are measured at sub Kelvin temperatures using a dilution refrigerator. We use radio frequency reflectometry to measure quantum capacitance, which is dependent on the quantum state of the device. We measure the quantum capacitance as a function of gate voltage, and observe capacitance maxima corresponding to the Josephson coupling between even parity states. We also perform charge sensing and detect odd parity states. These measurements support the theoretical model of the energy landscape of the SDD. By measuring the quantum capacitance in the time domain, we observe random switching of capacitance between two levels. We determine this to be the stochastic breaking and recombination of single Cooper pairs. By carrying out spectroscopy of the bath responsible for the pair breaking we attribute it to black-body radiation in the cryogenic environment. We also drive the breaking process with a continuous microwave signal, and find that the rate is linearly proportional to incident power. This suggests that a single photon process is responsible, and demonstrates the potential of the SDD as a single photon microwave detector. We investigate this mechanism further, and design an experiment in which the breaking rate is enhanced when the SDD is in the antisymmetric state rather than the symmetric state. We also measure the quantum capacitance of a charge isolated double dot. We observe 2e periodicity, indicating the tunnelling of Cooper pairs and the lack of occupation of quasiparticle states. This work is relevant to the range of experiments investigating the effect of non-equilibrium quasiparticles on the operation of superconducting qubits and other superconducting devices.
We consider the hybrid setup formed by a metallic dot, capacitively coupled to a superconducting island SSS connected to a bulk superconductor by a Josephson junction. Charge fluctuations in SSS act as a dynamical gate and overscreen the electronic repulsion in the metallic dot, producing an attractive interaction between two additional electrons. As the offset charge of the metallic dot is increased, the dot charging curve shows charge-skipping positive steps $(+2\ensuremath{\mid}e\ensuremath{\mid})$ followed by negative ones $(\ensuremath{-}\ensuremath{\mid}e\ensuremath{\mid})$ signaling the occurrence of a negative differential capacitance. A necessary condition for such an effect is that the capacitance coupling the two islands should be larger than the Josephson junction capacitance. A proposal for experimental detection is given, and potential applications in nanoelectronics are outlined.
Evidence is reported that topological effects in graph-shaped arrays of superconducting islands can condition superconducting energy gap and transition temperature. The carriers giving rise to the new phase are couples of electrons (Cooper pairs) which, in the superconducting state, behave as predicted for bosons in our structures. The presented results have been obtained both on star and double comb-shaped arrays and the coupling between the islands is provided by Josephson junctions whose potential can be tuned by external magnetic field or temperature. Our peculiar technique for probing distribution on the islands is such that the hopping of bosons between the different islands occurs because their thermal energy is of the same order of the Josephson coupling energy between the islands. Both for star and double comb graph topologies the results are in qualitative and quantitative agreement with theoretical predictions.