Nonlocal effects in the shot noise of diffusive superconductor–normal-metal systems

Abstract

A cross-shaped diffusive system with two superconducting and two normal electrodes is considered. A voltage eV < ∆ is applied between the normal leads. Even in the absence of average current through the superconducting electrodes their presence increases the shot noise at the normal electrodes and doubles it in the case of a strong coupling to the superconductors. The nonequilibrium noise at the superconducting electrodes remains finite even in the case of a vanishingly small transport current due to the absence of energy transfer into the superconductors. This noise is suppressed by electron-electron scattering at sufficiently high voltages.PACS numbers: 72.70.+m, 74.40+k, 74.50+r Recently, the noise properties of hybrid systems involving superconducting (S) and normal (N) metals became a subject of intensive studies. 1 A key effect in these properties is the Andreev reflection, in which electrons incident from the normal metal are reflected from the NS interface as holes. In particular, it was found that in the zero-voltage limit, the shot noise in diffusive NS contacts with phase-coherent transport is doubled with respect to its value in a normal contact with the same resistance. 2,3 This doubling was interpreted as an effective doubling of electron charge and has been experimentally confirmed in a number of papers. [4][5][6] Quite recently, it was shown that the doubled shot noise in diffusive NS contacts survives at finite voltages of the order of the energy gap. 7 Moreover, this noise does not require a phase coherence 8 and may be described in terms of a semiclassical Boltzmann -Langevin equation. 9 In this approach, the increased noise in NS systems is due to an excess heating of electron gas rather than to the doubling of the effective charge.Along with studying the shot noise in two-terminal systems, a considerable attention received the noise in multiterminal structures. It was found that the noise of normal-metal diffusive structures with more than two electrodes may exhibit exchange effects 10 and nonlocal effects. 11 The latter imply that the noise in the system is affected by a presence of open contacts even in the absence of average current flow through them.Several authors also calculated current correlations in single-channel multiterminal NS systems. 12-14 In particular, it was found that the noise measured at the two normal electrodes in a four-terminal system depends on the phase difference between the two superconducting electrodes. 12 A current noise was also calculated at a tip placed on a multimode quantum-coherent NS structure. 15 In this paper, we consider nonlocal effects in multiterminal mesoscopic diffusive SN systems using the semiclassical description of noise. In particular, we report on a semiclassical "proximity" effect in the noise where the current noise in a normal conductor is increased by its contact with a superconductor. Another finding is that under certain conditions, a large noise may be induced in an SNS structure even by a small transverse transport current.Consi...

Thermal conductance and nonequilibrium superconductivity in a diffusive NSN wire probed by shot noise

“…The normal NW segments on both sides of the S contact are assumed to be much longer than the superconducting coherence length and the applied voltage is much higher than the Thouless energy, L D/eV , D/∆, where D is the diffusion coefficient. This allows to neglect the penetration of the superconducting condensate from the proximity region underneath the S contact into the normal segments and treat them as metallic diffusive conductors [18,19]. The length of the S segment (the part of the device consisting of a part of NW and S contact above it) is assumed to be much larger than both the NW diameter and the superconducting coherence length, which enables to us to describe the quasiparticle transport via this segment as effectively one-dimensional and neglect the processes of Cooper pair splitting and elastic cotunneling [29].…”

“…Following the semiclassical approach of Nagaev and Büttiker [18,19] we calculate the EEDs f 1 (ε) and f 2 (ε) on the two boundaries of the S segment at x = x 1 and x = x 2 , see Fig. 1.…”

“…A correspondence between the shot noise and thermal conductance is a generic effect not limited to the Majorana case. A doubling of the shot noise in disordered NS junctions [16,17] is fundamentally related to the suppressed heat transfer in the S-lead [18,19], and can be useful to probe the sub-gap density of states in such structures [20,21]. In NSN NW-based devices the shot noise and thermal conductance are directly re-lated in the limit of charge neutral quasiparticle transport, that was demonstrated in a recent experiment set up in a trivial superconducting phase [22].…”

“…Here, we investigate a diffusive NSN device in a semiclassical approach of Nagaev and Büttiker [18,19] and demonstrate the opportunity to extract thermal conductance from the shot noise measurements. We consider two different layouts widely used in Majorana setups with a central superconducting island either connected to a grounded macroscopic terminal or floating.…”