Even-odd asymmetry of a superconductor revealed by the Coulomb blockade of Andreev reflection

Abstract

We have measured at low temperatures the current through a submicrometer superconducting island connected to two normal metal leads by ultrasmall tunnel junctions. As the bias voltage is lowered well below twice the superconducting energy gap, the current changes from being e periodic with gate charge to 2e periodic. This behavior is clear evidence that there is a difference in the total energy between the ground states of an even and odd number of electrons on the island. The 2e-periodic current peaks are the first observation of the Coulomb blockade of Andreev reflection.PACS numbers: 73.40. Gk, 73.40.Rw, 74.50.+r Systems with a small number of particles like nuclei behave differently if the number of particles is even or odd [1]. Does this symmetry breaking occur for a large metallic particle or "island" where the number of conduction electrons is macroscopic, say, 10^? In a superconductor, according to the BCS theory, the electronic state consists of pairs of electrons. At very low temperatures, a simple view is that all the electrons should condense into the ground state if their number is even. However, if the number is odd, one electron should remain in an excited quasiparticle state with energy A, the superconducting gap. This simple picture might not be applicable to a real experimental system because, for example, there might be quasiparticle states located within ksT of the Fermi level. Even one of these states, normally undetectable in usual tunneling experiments, could then capture and release single electrons and restore the even-odd symmetry.The isolated superconducting island can be conveniently probed by connecting it to metal leads via two tunnel junctions. If the tunnel junction resistances are much greater than the resistance quantum, then the charge on the island is quantized, and this Coulomb blockade electrometer can be used to probe the energy of the island [2]. In experiments with a device having both superconducting island and leads, the SSS electrometer [3], a current 2e periodic with a gate charge applied to the island has been measured for bias voltages in a certain range [4,5]. These 2e-periodic data, which could be observed only on some samples, display a complicated structure which is diflftcult to interpret since the basic model should at least include, in addition to the charging energy of the system, both quasiparticle and Josephson tunneling. Nevertheless, Tuominen et al. [5] have observed that the amplitude of the 2e-periodic component vanished at a temperature of about 300 mK, which they explain as the temperature at which a single quasiparticle of energy A can be thermally excited and thus restore the even-odd symmetry.In this Letter, we present the first measurements on a superconducting island with normal metal leads, the NSN electrometer. This system can be more readily understood because the two SN junctions do not allow Josephson tunneling [6]. The only allowed conduction process at low bias voltages is the Andreev reflection [7] of an electron into a hole on the N s...

Spectroscopy of discrete energy levels in ultrasmall metallic grains

“…Q 0 can of course be determined reasonably accurately by studying the largescale Coulomb oscillations of the I-V curve that occur as functions of V g at fixed V , a procedure that is well-established for mesoscopic SETs, for which indeed it has been possible to measure the ground state energy difference between a superconducting island with an even or odd number of electrons [62,[84][85][86][87][88]. However, a complication arises for the nanoscopic grains of present interest, due to the smallness of their gate capacitances (typically ≃ 0.1 aF): to sweep V g through one Coulomb oscillation, the gate voltage V g must be swept through a range so large (namely e/C g ≃ 1V) that during the sweep, RBT routinely observed small "rigid" shifts of the entire tunneling spectrum at random values of V g .…”

Charge-vortex interplay in a superconducting Coulomb-blockaded island

“…A large Coulomb energy E C = e 2 /(2C) compared to the temperature T prevents an extra electron from tunneling in and allows one to manipulate the charge state n of the island in a controllable way by varying the gate voltage V g = en g /C g across the capacitor C g . For an S island this physical picture becomes more complicated due to the electron number parity effect [7][8][9][10]. * Corresponding author: ivan.khaymovich@aalto.fi This effect consists in the 2e-periodic dependence of the observables on V g and thus provides a direct confirmation of the Cooper pair charge quantization.…”

Adiabatic quantum computation with Cooper pairs

“…In general, it coexists with the Cooper pair tunneling and makes junction dynamics irreversible. However, if both the temperature T and charging energy E C of the junctions are much smaller than the superconducting energy gap ∆, the quasiparticle tunneling is suppressed by the parity effects [22][23][24] to a level where it can be negligible on the macroscopic time scales [25,26]. Another dissipation mechanism is coupling to the electromagnetic excitations supported by the system of superconducting electrodes.…”