Quantum Charge Fluctuations in a Superconducting Grain

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 $V_g$ changes in steps. The step height is $e$ if $\Delta <E_c$, where $\Delta$ and $E_c$ 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 $V_g$ and lead to a finite step width $\propto G^2\Delta$. The resulting shape of the Coulomb blockade staircase is of a novel type. The grain charge is a continuous function of $V_g$ while the differential capacitance, $dQ/d{V}_g$, has discontinuities at certain values of the gate voltage. We determine analytically the shape of the Coulomb blockade staircase also at non-zero temperatures.

12 pages, 3 figures

References in corpus (4)

• Quantum Effects in Coulomb Blockade
• Spectroscopy of discrete energy levels in ultrasmall metallic grains
• Entangled electron current through finite size normal-superconductor tunneling structures
• Coulomb-blockade-induced bound quasiparticle states in a double-island qubit

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• Charge-Kondo Effect in Mesoscopic Superconductors Coupled to Normal Metals
• Signatures of topological ground state degeneracy in Majorana islands
• Effect of quantum fluctuations on even-odd energy difference in a Cooper-pair box
• Classical impurities and boundary Majorana zero modes in quantum chains
• Divergent beams of nonlocally entangled electrons emitted from hybrid normal-superconducting structures
• Strongly correlated electrons in superconducting islands with fluctuating Cooper pairs
• Energy relaxation of superconducting charge qubit via Andreev processes