Charge parity in Josephson tunneling through a superconducting grain

Abstract

The Coulomb blockade in a small superconducting grain connected to two macroscopic electrodes by tunnel junctions is discussed. The ground state energy of the grain is sensitive to the parity of the number of electrons on it. For an odd number of electrons, this energy is shifted by the value of the superconducting gap Δ due to the presence of one unpaired electron. In the case of superconducting leads, the charge parity effects give rise to a threshold behavior of the critical Josephson current when Δ is suppressed below the charging energy E C, e.g., by a magnetic field. The critical current can be periodically modulated by the voltage of a gate electrostatically coupled to the grain. The character of this modulation changes at the threshold: sharp peaks of the critical current existing at large values of Δ, split on two components each when the gap is suppressed, because an odd-number state becomes accessible at certain values of the gate voltage. Simultaneously, the existence of a quasiparticle at the bottom of a continuous energy spectrum allows the low-bias dissipation in the grain at an odd-number state. We estimate the dissipative current through a superconducting double-junction system. We argue that even at Δ > E C the same dissipation mechanism can be activated if a small finite bias is applied, because of “poisoning” of the grain with an odd electron.