VOLUME 82, NUMBER 8 P H Y S I C A L R E V I E W L E T T E R S 22 FEBRUARY 1999

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Bruder and Imry Reply: In our recent Letter [1], wepointed out that there is an additional contributionthe magnetic response of a normal-metal-coated superducting cylinder (as compared to a planar proximity saple). Semiclassical trajectories that are localized atouter surface of the cylinder (glancing states) fail to “sethe superconductor; they lead to a paramagnetic cortion of the magnetic response at low temperatures. Thstates are more stable with respect to scattering than oin a normal cylinder because the presence of the suconductor modifies the spectrum of the normal layereliminates final states to be scattered into at low energ

Fauchèreet al.’s [2] Comment addresses the size of teffect that we describe. They argue that the ratio ofparamagnetic current produced by the glancing statesthe Meissner current given in Eq. (7) of our paper [1]reduced by screening. We agree; in fact, we discussscreening in the paragraph following Eq. (7). At the eof the paragraph, we mention a reduction byleffyd whereleff is the effectivepenetration depth in the proximitlayer andd is the thickness of the normal layer. Theffective penetration depth can be estimated [3] to

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2L,, where, is the elastic mean free path. F

the (almost) clean samples that we have in mind,leffis significantly larger than the London penetration delL, i.e., our estimate is much more favorable thanreduction factor given in the Comment. In our opinioit is the effective screening length that has to appin the estimate: In a perfectly clean system, thereno (local) screening [4], but a small concentrationimpurities leads to screening on a length scaleleff [3].A crucial point that we explain in the paragraph beloEq. (7) in our paper is that the paramagnetic currentIP isto be compared not to the full diamagnetic currentID butto the real Meissner current (also reduced by screeniIM . Therefore the final magnetic moment comparedour paramagnetic current can easily be on the ordepercents of that produced byIM . Since all of the otheravailable theoretical treatments lead to a saturation ofmagnetic response at low temperatures, we think thatis a significant correction. However, a true self-consistcalculation of the magnetic response is needed to sthe numbers.

We do not agree with Fauchèreet al. that our idea hasbeen presented before in Ref. [5]. In this work, thefluence of curvature in a proximity system has been sied within the quasiclassical theory of superconductivSince the effect that we describe is similar in nature tnormal persistent current (amplified by the presence ofsuperconductor), it cannot be obtained within the framwork of the quasiclassical theory of superconductivity.

In the last part of their Comment, Fauchèet al. address the temperature dependence of the co

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tion. They argue that it is not permissible to use ttemperature dependence of normal persistent currentthis connection. We do not understand this argumesince the glancing states are a special type of norpersistent currents. We also point out that there is anosource of temperature dependence caused by the los“protection” of the glancing states at higher temperaturFauchère et al. are right that ordinary normal-metapersistent currents can have either diamagnetic or pmagnetic signs. However, we have discussed the speproperties of the glancing states and we have showntheir orbital response is predominantly paramagneThis is due to their relatively large azimuthal velocitieas is discussed following Eq. (5) in our paper.

Finally, we would like to address the questionthe relation of our work to the experiment [6]. Thexperiment by Mota and co-workers [6] has remainunexplained for quite a number of years now. Wherethe effect that we discuss in our Letter may not accofor a complete disappearance of the diamagnetic respothat was found in some samples (this is clearly spelout in our Letter; explaining the experiment of Ref. [6is not our main purpose), we do predict a paramagnecorrection to the magnetic susceptibility of nonsingconnected proximity systems that should show up at ltemperatures. As far as we know, this is the first timsuch a reentrance effect was found theoretically. Inopinion, the effect that we describe is a first step towaan explanation of the experiments, and we suggestedcrucial experimental tests that can be used to checkrelevance of our idea.

Christoph BruderDepartement Physik und Astronomie, KlingelbergstrasseUniversität Basel, CH-4056 Basel, Switzerland

Yoseph ImryWeizmann Institute of ScienceDepartment of Condensed Matter PhysicsIL-76100 Rehovot, Israel

Received 25 September 1998 [S0031-9007(99)08506PACS numbers: 74.50.+r, 73.23.–b

[1] C. Bruder and Y. Imry, Phys. Rev. Lett.80, 5782 (1998).[2] A. Fauchère, V. B. Geshkenbein, and G. Blatter, preced

Comment, Phys. Rev. Lett.82, 1796 (1999).[3] W. Belzig, C. Bruder, and A. L. Fauchère, Phys. Rev.

58, 14 531 (1998).[4] A. D. Zaikin, Solid State Commun.41, 533 (1982).[5] W. Belzig, Diploma thesis, Universität Karlsruhe, 1995.[6] P. Visani, A. C. Mota, and A. Pollini, Phys. Rev. Let

65, 1514 (1990); A. C. Mota, P. Visani, A. Pollini, andK. Aupke, Physica (Amsterdam)197B, 95 (1994).

© 1999 The American Physical Society 1797