EFFECT OF NON-MAGNETIC IMPURITIES ON THE RAMAN SCATTERING BY SUPERCONDUCTING GAP EXCITATIONS IN LAYERED COMPOUNDS

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EFFECT OF NON-MAGNETIC IMPURITIES ON THE RAMAN SCATTERING BY

SUPERCONDUCTING GAP EXCITATIONS IN LAYERED COMPOUNDS

S. Behera

To cite this version:

S. Behera. EFFECT OF NON-MAGNETIC IMPURITIES ON THE RAMAN SCATTERING BY SUPERCONDUCTING GAP EXCITATIONS IN LAYERED COMPOUNDS. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-292-C6-294. �10.1051/jphyscol:1981684�. �jpa-00221620�

JOURNAL _{DE PHYSIQUE}

ColZoque C6, suppZdment au n012, Tome 42, d6cembre 1981 page C6-292

EFFECT OF NON-MAGNETIC I M P U R I T I E S ON THE RAMAN SCATTERING BY SUPERCONDUCTING GAP E X C I T A T I O N S I N LAYERED COMPOUNDS

S.N. Behera

I n s t i t u t e of Physics, Bhubaneswar-751007, India

Abstract.- The e f f e c t of small c o n c e n t r a t i o n s o f s u b s t i t u t i o n a l non-magnetic i m p u r i t i e s , on t h e o b s e r v a b i l i t y of superconducting gap e x c i t a t i o n s , i s considered. I t i s shown t h a t t h e presence of heavy mass i m p u r i t i e s t e n d s t o i n c r e a s e t h e s t r e n g t h of t h e Raman peak due t o t h e gap e x c i t a t i o n s , w h i l e lowering i t s frequ- ency. On t h e otherhand t h e l o c a l mode due t o l i g h t mass impuri- t i e s s p l i t s i n t o two because of i t s coupling t o t h e gap e x c i t a - t ions.

1. I n t r o d u c t i ~ . - Recently f o r t h e f i r s t time superconducting gap e x c i t a t i o n s have been observed i n t h e l a y e r e d compound 2H-NbSe2 throu- gh phonon Raman s c a t t e r i n g 1 . A t room temperature 2H-NbSe2 h a s two Raman l i n e s a t 234 om" and 248 cm-l. Below 3 3 O ~ t h e system undergoes a charge d e n s i t y wave (cDW) t r a n s i t i o n which induces a d d i t i o n a l Raman peaks around 40 cm". On f u r t h e r c o o l i n g it becomes superconducting

( S C ) a t 7 . ~ O K , r e s u l t i n g i n t h e appearence of s t i l l more Raman peaks a t approximately 16 cm", which i s c l o s e t o t w i c e t h e superconducting energy gap 2 (2 4 S 17.2 cm-I). C r u c i a l t o t h i s o b s e r v a t i o n i s t h e a v a i l a b i l i t y 3 of t h e CDW phonon c l o s e i n energy t o 2 A

.

2. Theory.- The system is described by t h e model Hamiltonian

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981684

H = HBF + ^HI ( 1 1 where HBF is t h e Balseiro-Falicov Hamiltonian and t h e c o n t r i b u t i o n due t o non-magnetic s u b s t i t u t i o n a l i s o t o p i c i m p u r i t i e s is given by

with ( 3 )

and i ( 8 + ^{9 ' W i}

u'~\%,~',

MI and M being t h e masses of t h e impurity and h o s t atoms respectively.

The impurity concentration ( c ) i s assumed t o be small. The phonon s e l s energy f o r t h i s system t u r n s o u t t o be

where

= i . + ~

dz (32q,(ti2-uirJ'

% ^{t (6 )}

(7 and2FF (W) i s t h e phonon s e l f energy i n t h e absence of t h e imputi- ties. Cc Since, we are i n t e r e s t e d i n Raman s c a t t e r i n g , eqn. ( 5 ) is evalua- t e d i n t h e l i m i t q = 0, with t h e E i n s t e i n model f o r t h e h o s t phonon,

B F

assuming t h a t i n eqn, ( 7 ) (a) is independent of ql. Thus, t h e ex&-

B ¹

t a t i o n spectrum i s given by t h e s o l u t i o n s of t h e equation

where F ( A ^{,x) =} h / ^{(x2 -1} + A ) ( 9 )

g y ( y ) ⁼ 4s y-1(i-y2)-1'2 tano1 [Y (1-Y 2 - 1 / 2 1 , ~ o r ~ ~ ~ with s ⁼ <p2f(ej> /%, x = O/U, and y = x ( q 2A 1 (11)

ma being t h e frequency o f t h e h o s t phonon, A is t h e superconduct- i n g energy gap, g is t h e electron-phonon coupling constant i n t h e SC s t a t e and 9 ~ 4 ) i s t h e e l e c t r o n d e n s i t y of s t a t e s a t t h e Fenni surface.

I n this c a l c u l a t i o n t h e e f f e c t o f t h e i m p u r i t i e s on t h e CDW s t a t e h a s been ignored.

3, R e s u l t s and Discussions.- F i r s t of a l l , we s h a l l assume t h a t % i s t h e CDW phonon and t h e impurity rode arises from ^{W o} , Hawever, i n s t e a & of appearing a t me u s u a l frequency of do ci - ^{)J'z t h e}

C6-294 JOURNAL DE PHYSIQUE

impurity mode s p l i t s i n t o two, because of its coupling to t h e SC gap e x c i t a t i o n s , a s i s obvious from eqn.(8). A heavy mass impurity giving rise t o a mode below 2 A , increases t h e strength of t h e gap excita- t i o n mode and pushe$ it towards zero frequency, which i s equivalent t o increas%the coupling s t r e n g t h s. On t h e o t h e r hand a l i g h t mass impurity giving r i s e to a l o c a l mode decreases t h e s t r e n g t h and in- creases t h e frequency of t h e 2 h excitation. Features s i m i l a r t o t h i s p r e d i c t i o n had been observed i n 22H.Nb5e2 samples c o n t a i 9 impurities 3

.

In t h e absence of t h e C&J phonon, d o w i l l ^be t h e Raman a c t i v e mode i n t h e nonnal s t a t e which being of high frequency W o >> ² h decreases t h e coupling strength$) considerably; r e s u l t i n g i n t h e

impossibility of observing t h e SC gap e x c i t a t i o n . However, i f t h e mode due t o a heavy impurity f a l l s near where t h e CDW mode e x i s t e d then because of its coupling t o t h e gap e x c i t a t i o n s , it i s possible t o observe t h e same under s p e c i a l conditions.

It i s worth mentioning t h a t s u b s t i t u t i o n of heavy mass impuri- t i e s i n place of N b i n 2H-NbSe2 may not be f e a s i b l e experimentally.

However, even a l i g h t mass i n p u r i t y atom can produce low frequency modes provided its s u b s t i t u t i o n causes nearest neighbour force con- s t a n t softening, S i m i l a r l y it is a l s o p o s s i b l e t h a t an impurity phonon can oouple r a t h e r strongly t o t h e SC e l e c t r o n s giving rise t o t h e i t s bound s t a t e with SC gap e x c i t a t i o n s , These f e a t u r e s a r e being

investigated c u r r e n t l y 5

.

Acknowledqement

.-

References

.-

1. Sooryakumar,R. and Klein,fi.V.,Phys. Rev. L e t t . 45, 660 (1980)

.

2 , Clayman,B.P. andFrindt,R.F, S o l i d s t a t e Comnun.2, 1881 (1971).

3. Sooryakumar, R. Klein, M.V. and Frindt,R.F. p r e p r i n t (1981)

.

4, Balseiro,C.A, and Falieov,L.M, Phys. Rev. Lett. 45, 662 (1980).

5. Behera,S .N . and Mohanty,G .C, (1981) unpublished calculations.