Energy Dependence of Current Noise in Superconducting/Normal Metal Junctions

Abstract

Interference of electronic waves undergoing Andreev reflection in diffusive conductors determines the energy profile of the conductance on the scale of the Thouless energy. A similar dependence exists in the current noise, but its behavior is known only in few limiting cases. We consider a metallic diffusive wire connected to a superconducting reservoir through an interface characterized by an arbitrary distribution of channel transparencies. Within the quasiclassical theory for current fluctuations we provide a general expression for the energy dependence of the current noise.PACS numbers: 74.45.+c,74.40.+k,72.70.+m Interference of electronic waves in metallic disordered conductors is responsible for weak localization corrections to the conductance [1]. If these are neglected, the probability of transferring an electron through the diffusive medium is given by the sum of the modulus squared of the quantum probability amplitudes for crossing the sample along all possible paths. This probability is denoted as semiclassical, since quantum mechanics is necessary only for establishing the probability for following each path independently of the phases of the quantum amplitudes. In superconducting/normal metal hybrid structures, interference contributions are not corrections, they may actually dominate the above defined semiclassical result for temperatures and voltages smaller than the superconducting gap. This is seen experimentally as an energy dependence of the conductance on the scale of the Thouless energy. Indeed, the energy dependence comes from the small wavevector mismatch, linear in the energy of the excitations, between the electron and the Andreev reflected hole. This is responsible for the phase difference in the amplitudes for two different paths leading to interference. The effect is well known and explicit predictions and measurements exist for a number of systems [2,3,5].Interference strongly affects the current noise too [6]. The largest effects are expected in the tunneling limit, when the transparency of the barrier is small and its resistance is much larger than the resistance of the diffusive normal region. Then, the conductance has a strong non linear dependence at low bias (reflectionless tunneling) [2,3]. This is actually the case, but the zero-temperature noise (or shot noise) does not give any additional information on the system since it is simply proportional to the current, as shown numerically in a specific example in Ref.[4] and quite generally in Ref. [7]. The double tunnel barrier system has been considered in Ref. [8]. In the case of a diffusive metal wire in contact with a superconductor through an interface of conductance G B much larger than the wire conductance G D , Belzig and Nazarov [9] found that the differential shot noise, dS/dV , shows a reentrant behavior, as a function of the voltage bias, similar, but not identical, to the conductance one. (The extension of the Boltzman-Langevin approach to the coherent regime in Ref.[10] neglects this difference.) In order to comp...

Full Counting Statistics in Quantum Contacts

“…( 37) multiplied with τK it follows that it does not matter, where the noise is evaluated, as it should be. From these equations the generalization of the Boltzmann-Langevin equation to superconductors can be derived [57], which allows for a faster numerical solution. The results for the energy dependent noise is shown in the left panel Fig.…”