Quantum charge fluctuations in a superconducting grain

M. Houzet; D. A. Pesin; A. V. Andreev; L. I. Glazman

doi:10.1103/PhysRevB.72.104507

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Quantum charge fluctuations in a superconducting grain

M. Houzet, D. A. Pesin, A. V. Andreev, L. I. Glazman

DOI 10.1103/PhysRevB.72.104507 · Physical Review B

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Abstract

We consider charge quantization in a small superconducting grain that is contacted by a normal-metal electrode and is controlled by a capacitively coupled gate. At zero temperature and zero conductance G between the grain and the electrode, the charge Q as a function of the gate voltage Vg changes in steps. The step height is e if Δ<Ec, where Δ and Ec are, respectively, the superconducting gap and the charging energy of the grain. Quantum charge fluctuations at finite conductance remove the discontinuity in the dependence of Q on Vg and lead to a finite step width ∝G2Δ. The resulting shape of the Coulomb blockade staircase is of a novel type. The grain charge is a continuous function of Vg while the differential capacitance, dQ∕dVg, has discontinuities at certain values of the gate voltage. We determine analytically the shape of the Coulomb blockade staircase also at nonzero temperatures.