SUPERCONDUCTING PROXIMITY EFFECT
by
Yagya Prasad Dhungana Department of Physics
Th 郡 is s な innitte(i
ifl ル Iffihinent q". the ル他 fflemen む ール r the aw'ard of 功 e 凌智 ree of 1X)CTOR OF PHILOSOPHY
to the
INDIAN INSTITUTE OF TECHNOLOGY,DELHI
NEW I)ELJU-1U)O16, INDIA January 1 997
鯛静
讐り
餌10 或。ぜ iぐ 1_ L T. iJELf
叫
9霜；1r；ルI ER，、R Y 笥負媛町 9粉1
Acc. No 奉ー一ー一－一－一一一
し（ 2ち 1
一一ー一ー一一ー一一ー
DEDICATED i り． . . .
PARENTS,
si: 外 lANA, SON GAURAV
and
DA UGHTER 】り s 丑旦．
雷、
CERTIFICATE
Fhis is to certi句 that thc thesis entitled Superconducting Proximity Effect, being subinittじ（I by Yagya Prasad I)huilgana 丘）r the award of tbc degree of Doctor od Phutosohpy, to tule Indian Institute of Technology, Dcliii, is a record of bonafide researchl work he has carried Out under my guidance and supervision.
Il my OpifliOlL this thesis has reached the standard fulfilling the requirements of all regし1lt1ti()flS relating to the dじgrec. The results contained ii1 this thesis have not been submitted to) any other University or Institute for the a'vard of any degree or diploma.
Professor K. P. Jamn Thesis Supervisor Physics Department,
Indian Institute of Technology, Delhi New Delhi-110016
I nd ja
ACKNOII 肥 EDGK 昭岡 VTS
J would like (()どkpl部 ny gratitude to my supeルsor Professor K. P. fain, who initiated me to 'Iiis subject and guided me at ea魂and eveクぶtage可this work・It has 1>く・ぐti a gた，(J! pie価t'肥to i切rk 'vider his invaluable guidance. His sustained encouragement ditting the d卿コit period and keen interest during lively disc如ions have always been an i/i‘アiration fr me血，ブ」ig the（りurse of t/Ijs research吻rk. t would not be anどraggeratiol1
びI s叩t/lat itおjust />eca町e of/urn the tu賀is is回奴t itむtoday．刀：e tin沼/spent叫ゾtu hi,il dulring niv IV、・!).1 V()l* will 12e u）加rgettnble for nび、vhole life.
I IVOUld ii如to e甲ress 刀W 功an加to Projおsor S. C. Abbi for his encouragement a,"!励！如． I <tLv<> <ple55 I叩gratitude to Dr. R. K. Sonifor his constant encouragement (itid help at difficult times. j will neverforget h加for his veクsensitive andり‘iipathetic attitu(Ie towards /ne.
Il般e to tliaik my colleagues in the LTR? Drs. A. K. 銃uk/a, H. S. Movi, R.
Raniaktiniar, C. Ranikumar, S. A,iand, S. Lambo, S. K. Ghosal, G. Suaran, M.
Zo pl，昭加ri，勝． J), Mishra, Ms. L. Gupta, and Mr. S．乃加athifor their加lp. I thank Mノ二 N. C. Naittival (i/id Mr. G. S. Rrnvatfor the lieクprovided by t/tent.
肋rds a,・e h1ot s啄ぐietii to e甲ress nりdeep emotional gratitude to mv pa>で）Its for t/t如－s叩1)0 r!，紹CII/α 如<1 bl郡ing front my childhood. 1 was bro噌/it 叩t') thむ 計昭e 加ca町ぐ of 功cir saぐ摩肥． I 'h如k ノny sお1ers L肥/a Devi and SliQi何a 姐d n'>
htりt/iers Su肥1tdra att'! Muktifor their continuo町attention towards m、、e・
I 叩ecialか琉a,破刀ty w加for lier continuous suppeだ姐dfor bearing the jmiii (>1?<! 1町加n of sクαratio'?伽ri,居'h ese押ars of川Ph. D. work. I am very sorクfor my 5<.),，働urau au,d da昭／lter Yes/ia that I was away frotti titeni at the time 、確en ti，の、
ど甲cc/ed me to加肥ar.
I should t/tank i，ぴ ho,>,e institution (Institute of勘gineering, Tribhuvan Unive,.siか，
焔tit tnandu，雄pal) for proト）漉昭 an 卑portunity and stuみ leave. I thank j IT Delhi,
（了overnment <ind pe叩le of 力，dia for p,りv/ding me <i chance and facilities for doing research in titis premier Institute.
It will be total i,びusticeびi don 't thank my co叩atriots doing research in IITD.
I spec加uy 'h如k 'Itose people from my /tome place staying in Delhi who provided nie /)5.
＼・（・
I101Ogic(tl s叩
port、功
ile awayfroni my place.尋守しザー。
で一斗一
ABSTRACT
The proximity layer is studied theoretically by using the Ginzburg-Landau equations t'or the calculation of induced superconductivity in normal metal and depressed supe!・じ（)IRIUじtivity in the supe】・conductor. The solutions of the Ginzhurg－いndau equations saLi sル d i ftしsive boundary conditions at the interface for the gap 加nction arid its derivative. These solutions are obtained in different limits in the normai metal and give di拝erent rじsuits iieai・the intじr血ce.
、 l'hじBogoliuhov-de Geiines equations are solved for both regions with the spatially depヒrdじtil superconducting gap. Wave functjons are expressed in terms of seif-consisient nieid functions and Bogoliubov quasi-particle operators using the Bogoliubov trans角！・1nation. T'he equations for the self-consistent field functions were solved in the Andreev limit. The solutions 拓r the sel仁consistent field hinctions are in the normal mlletal are totally di簸rent from 山e solution of previous works. An exact analytical solution is obtained拓r the gap in thick limit. Inside the superconductor, the gap function and the solutions of Bogoliubov-de Gennes equations are similar to those of previous works.
Numerical results show that significant changes in the magnitude of quasi-particle amplitudes are only within one or two coherence lengths from the interface. Away from that they are plain waves in the normal metal. The selかconsistent field functions are bound i n the superconductor for the energies below the superconducting gap. Although the self-consistent field functions vanish at the points far way from the inter塩ce, some interesLing じhanges CaIl be seen near the interねce for thじ enei・gies close to the
superconducting gap. Those with energies higher than thヒ galう ×・alue arじ oscillating functions. The spatial oscillations increase with energies.
The relationship between an app]ied voltage ami じし」ri、じnl in the induじed superconductivity region is analytically in the London limit. The value resistance of the superconductiv ity-induced region in interniビdiate statじし1し1じ to (jしII・re丁lt is lu1gt】じ1・（luaU (liai corresponding to the bulk s叩ei・conduetoi・． The expeじlatiし）n vlまluじs ut Uiじ induced c ui・re ni and charge densities are evaluated 拓r the suj）じrじ（)nd uじting grounしi statじ， by しI S jug functional techniques.
j 沢 ox" げ Iry EF! 昭 CT
()Inti()duct iOn ()
Andrecv Reflection 12
An山，ccv Assumllption 14
Model Proxhnity (unposite i (>
Methodology 17
CfiNZIfrJRGJ4NDA U EQ.
鳳
TIONS !9I nu・（）しluc t iぐ）n I <)
CHAr 7 男 R JI
-)
つーつ一
2.3
1『 一へ」 つー つ一
( 'JAJ>TEI? JIJ
3
CONi
男
NTSCHAP?男RI IN?
沢
ODUCTJON'I'he Pherlornじfl011 of Supei・conductivity
2 Overview of the i)cve1()prl1c「It ifl i'h<(>ry 3
3 Purpose of,' I'1iesis 5
i.2 3.2.i
Al 一
l り」
1 『1
MethO(1 Ol「 the Solution of Ginzburg-Landau Equations 21 Solution of Ginzburg-Landau Equations in the
SUPCI・COOdしictor 21
Solution of (;inzl)uI・g-I』I mmlJaしi 1:c1uItiOr)s in thle fl()rfl11Il
nlctal 23
3.2.3 Solution of Ginzhum・g-Landau EqしratiOnS in the nornial
metal in thick limit 26
Solution o1、 (I inzbしn・g-Landau Lし1しlati()fl.S iFl the norn1al
nieta! in thin limuit 2X
dサ っ一
『Aー
CHA Pi
万
RCHAP?ぞRy
lv BOGOLJUBOV-山(J?NNRS EQt'A 1'!<>勝 37
4. t Introduction 37
4.2 Solution of I3ogo!iuhov-de Geunじs iqしia(1( u1s ・1(1 4, 2 . 1 S（〕 lUtiOfl of 130g()1 iulう（)V-dC Gじflnじs 1.：しlilajinils ifl ii。）r】n11I
1 iieta I(ifl thiじk Jiniit） ・1() 4.2.2 Solution o)l" i3ogo1iubo"-dじ（lelll】じs I1(1U1111OflN ifl 0<。1 n1;tI
11)eraI in thin I inlit (io1・！ineai・i.c<Jじ115じ） ・45 4. 3 Solution o)f' Bogく）liUb()V-dC Gじones i三qしi a t iく1ris in tule
sしIpeに（niductor 、48 4.4 l1()UJ1daJy conditions at the iritci・（aじe べ5 4. 5 SeIf-corisistenじy e()flditinns べ（、
4 , () Numeiica I 'I'】・じ；itlucin of SoIutj(>ns (>1 'J刃ど肝学買CT OF AN 44費生!i:I> L>.（二 IqELI) i u 5.:i 'l'be reatation l)et"eじfl cul・に1u anしi ''1tt1ke ifl u,(111(1（、丁1
Limit 7!
5.2 Microscぐ〕pic calculation of inducじ(j CUFI・(flt LIndじ11111、9じ
densities 7(1
5、2.1 Cha】・ge and CしIfl・じnl J）じnsities 77
AJ'PENi)JX 8、1
A. I Self-consistency conditions for the noruliti part 83 A.1,I Self-consistency conditions for the 1 iorniai part
at X=-dN 糾ユ
A. i .2 Self-consistency conditions for the normal part at x=O
A .2 Self-consistency conditions for the superconductor A,2. I Se1fcousistency conditions foi・the supei・conductor
at x=ds
A . 2 . 2 Sel fconsistency cond it ions for the superconductor at the interface(x＝の
A.3 l3oundary Conditions at the Interface
88 92 93 つー ロ0 nツ ハソ
REFEREN(.' if S
CONCLUDiNG REA
組
RKS■ 11 IjJ nリ ハU dll 11血
