* Corresponding author. E-mail address: wilhelm@tfp.physik.uni-karlsruhe.de (F.K. Wilhelm) Physica B 280 (2000) 418}419 The nonequilibrium mesoscopic SNS transistor Frank K. Wilhelm*, Gerd Scho K n, Andrei D. Zaikin Institut fu ( r Theoretische Festko ( rperphysik, Universita ( t Karlsruhe, D-76128 Karlsruhe, Germany Forschungszentrum Karlsruhe GmbH, Institut fu ( r Nanotechnologie, D-76021 Karlsruhe, Germany Abstract We describe an SNS junction with a control voltage applied in parallel to the interfaces within the framework of the quasiclassical theory. This voltage allows to control and even reverse the supercurrent through the junction. Extending our previous work (Phys. Rev. Lett. 81 (1998) 1682), we will discuss limitations and performance of the device in non-ideal situations in connection to recent experiments (Nature 397 (1999) 43). 2000 Elsevier Science B.V. All rights reserved. Keywords: Mesoscopic physics; Proximity e!ect; Superconductivity We are going to study the structure [1] depicted in Fig. 1 within the quasiclassical theory (see e.g. Ref. [2]), the basic features of which have already been discussed in Ref. [3]. From the superconducting electrodes, correla- tions are induced into the normal metal (proximity ef- fect). Their decay length depends on energy: correlations with energy <E (E "D/d) decay exponentially, while those with +E carry a supercurrent. In the "rst step, we analyze the Usadel equation and calculate the &spectral supercurrent' j (see Fig. 2). It is an odd function of , shows a proximity induced mini-gap [2], K3.2E at "0, which closes as is approach- ing , then jumps to a "nite value, then decreases expo- nentially and changes its sign in slow oscillations. In an ideal mesoscopic wire, the distribution function obeys a di!usion equation without inelastic relaxation between two reservoirs at "$e</2. Its solution has two temperature-rounded steps at the electrochemical potentials of both reservoirs. The step heights depend on the position along the wire. The physical supercurrent is found convoluting the distribution function with the spectral supercurrent. It was shown for ¹"0 in Ref. [3] and later in experiments [4], that by applying < the supercurrent can be suppressed and even reversed, mak- ing the SNS-junction a -junction. As ¹ increases, this -junction-regime is shifted to higher voltages (see Fig. 3) and can be realized if ¹< . E . This explains, why the -junction behavior could not be observed in the "rst series of experiments [1]. For shorter junctions with d& , the position of the -junction crossover is limited to the gap energy (see inset of Fig. 3). Our theory contains several approximations, treating the spectral and the kinetic part in quasi-1D. In the view of recent experiments [5], we will now discuss quantitat- ive limitations. If ¸< . d, the low-energy states will couple to the nor- mal reservoirs thus lifting the gap into a pseudogap and weakening the proximity e!ect. This increases the low- energy contribution to the supercurrent compared to Fig. 2 and consequently shifts the -junction crossover to slightly higher energies. If d; / l , l , the proximity e!ect will be cut o! leading to similar e!ects. Our study only takes current lines into account, which run straight in x-direction between the superconducting contacts. Bent current lines, spanning deeper into y- direction will give an additional contribution. As they are longer than d, their contribution will decay faster than the straight lines. Consequently, the low-energy part will again be more emphasized. This prediction is in agree- ment with recent calculations within the assumption of weak proximity e!ect [6]. For the kinetic equation, we found that there is strong nonequilibrium at the site of the superconducting reser- voirs, which should be in equilibrium. This is possible, as the change in the distribution function is antisymmetric 0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 8 0 4 - 9