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ELECTRONIC STRUCTURE, ELECTRON-PHONON
INTERACTIONS AND LOW-TEMPERATURE
ANOMALIES IN A 15 COMPOUNDS
B. Klein, L. Boyer, D. Papaconstantopoulos
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C6, supplément au n" 8, Tome 39, août 1978, page C6-416
ELECTRONIC STRUCTURE, ELECTRON-PHONON INTERACTIONS AND LOW-TEMPERATURE ANOMALIES
IN A 15 COMPOUNDS
B.M. K l e i n , L . L . Boyer and D.A. P a p a c o n s t a n t o p o u l o s
U.S. Naval Research Laboratory, Washington, D.C. 20375, U.S.A.
Résumé.- En nous servant de nos calculs ab initio de la structure de bande par la méthode APW self-consistante, nous discutons la structure fine dans la densité des états électro-niques près du niveau de Fermi, et l'interaction êlectron-phonon pour les composés A15 v3X et Nb3X, avec X = Al, Ga, Si, Ge et Sn.
Abstract.- Using our ab initio self-consistent APW band calculations,, we discuss fine structure in the electronic density of states near the Fermi level, and the electron-phonon interac-tions for the A15 compounds V3X and Nb3X, with X = Al, Ga, Si, Ge and Sn.
Theoretical work on the A15 materials has centered on relating the low-temperature anomalies and the high values of T in many of these com-pounds IM. Following the work of Clogston and Jaccarino /2/ who postulated the existence of a sharply peaked electronic density of states (DOS) near the Fermi energy (E„), there have been
seve-r
ral models of the band structure /3-7/ which have yielded such peaks. Most of these models make use of the quasi-one-dimensionality of the A15 struc-ture. Several ab initio band structure calculations have been done for A15 materials /8-10/ which have not verified the underlying assumptions of the model calculations, but they have lacked suffi-cient accuracy to study the fine structure in the DOS near E_.
More recently /ll/ we have done highly accurate AFW calculations for ten different A15 compound's : v3X and Nb3X, with X = Al, Ga, Si, Ge
and Sn, covering the range of high and low-T . The purpose of this work is to examine the Fermi sur-faces and related properties of these compounds in some detail. The techniques used, self-consis-tency, relativistic, warped muffin-tins,etc..., are fully described elsewhere /ll/. Here we will discuss some aspects of these results, namely the electron-phonon interactions (e-p-i) and sharp DOS structure of these materials.
Figure 1 shows the DOS near E_ for two
r
A15 compounds, Nb3Sn and V3Ge respectively, in a
very narrow energy range + 3 mRy (1 mRy ^ 150 K ) . It is clear from figure 1 that Nb3Sn which has rather drastic low-temperature electronic proper-ties (contrary to V3Ge) also has a very rapid DOS
variation near E_, while the behavior of the DOS (N) of V3Ge is nearly constant in the range + 300 K, around E . F — J 1 r~ UJ F o ' t; Nb=Sn !
§200- ^ J \ i
^ ^ \ ^*SJ £ 100- V3Ge ! ^ ^ ^ _ U- I • j >• I h~ I CO , •z i UJ J Q I I I I I I - 2 - 1 0 1 2 ENERGY CmRy)Fig. 1 : Electronic density of states near E„ for Nb3Sn and V3Ge.
The behavior of Nb3Sn, (AN/N)E„ is of order unity in a range AE < 100 K, is of the right magnitude to explain the observed anomalous low-temperature behavior. Our calculations, also show that results similar to Nb3Sn arise for V3Si, V3Ga, and to a somewhat lesser extent for Nb3Al and Nb3Ga /ll/. On the other hand the relatively "normal" mate-rials (e.g. V3A1 and V3Sn) behave similarly to
V3Ge. We should emphasize two additional points :
1) the DOS fine structure arises from a fully ab initio APW calculation; and 2) the unusually flat bands giving rise to the DOS fine structure comes
+
from t h e r e g i o n around t h e T12 p o i n t (k = 0) 1 9 , w i l l be g i v e n i n s u b s e q u e n t p a p e r s .
1 1 1 .
C a l c u l a t i o n s o f t h e e-p-i, q = N < I ~ > , a r e R e f e r e n c e s shown i n t a b l e I u s i n g t h e method of G a s p a r i and
G y o r f f y
/
21. In table I we see that r, correlates/
1/
S e e t h e f o l l o w i n g r e v i e w a r t i c l e s : T e s t a r d i ,L.R.. " P h v s i c a l Acoustics". W.P. Mason. e d . w e l l w i t h T and N(E ) w i t h t h e e x c e p t i o n o f Nb3
F
/
19731, c h a p t e r 10; Weger, .M. and ~ o l d b e r ~ , Ge and Nb3Si which we w i l l d i s c u s s s e p a r a t e l y . I.B. S o l i d S t a t e Phys.28
(1973) 1 ; Izyumov,Y.A. and Kurmaev, Z . Z . , Sov. Phys. Usp.
M
(1974) 193.Table I / 2 / C l o g s t o n , A.M. and J a c c a r i n o , V . , Phys. Rev. 121 (1961) 1357.
-
C a l c u l a t e d e l e c t r o n i c d e n s i t i e s of s t a t e s N(EF); 131 Weger, M . , Rev. Mod. Phys.
2
(1965) 175. electron-phonon i n t e r a c t i o n s of A-atoms, qA =N ( E ~ ) < I ~ > ~ ; and measured T c ' / 4 / Labb6, J. and F r i e d e l , J . , J . P h y s i q u e Radium 27 (1966) 153 ;
3
(1966) 303-
A3B N (EF)
n~
T,(exp-) / 5 / Cohen, R.W., Cody, G.D. and H a l l o r a n , J.J., Phys. Rev. L e t t .2
(1967) 840.-
(states/Ry-unit c e l l )(,V/j22)
/6/ Gor'Kov, L.P.,Zh. ETP P i s . Red
17
(1973) 525;V A 1 3 189 6.9 9.6 Zh. Edsp. Teor. F i z . 65 (1973) 1658.
-
15.4 / 7 / Lee, T.K., Birman, J . L . and Williamson, S . J . , Phys. Rev. L e t t . (1977) 839.
17.0
/8/ M a t t h e i s s , L.F. Phys. Rev.
138
(1965) A112; 6.1-
12B (1975) 2161.3.8 / 9 / K l e i n , B.M., P a p a c o n s t a n t o p o u l o s , D.A. and Boyer, L.L., F e r r o e l e c t r i c s
2
(1977) 299. 18.8/ l o / J a r l b o r g , T. and Arbman, G . , J.Phys. F: Metal 20.3 Phys.
5
(1976) 189;L
(1977) 1635.1 4 ~ / 1 1 / K l e i n , B.M., Boyer, L.L. and Papaconstantopou-
l o s , D.A., J.Phys. F:Metal Phys. (1978) i n 23.2b p r e s s ; and u n p u b l i s h e d .
8.5 18.2 1121 G a s p a r i , G.D. and Gyorffy, B.L., Phys. Rev. L e t t .
28
(1972) 801.=sputtered films Ref. /13/; bsputtered films Ref. /14/ 1131 G a u a l e r , J.R., Appl. Phys. L e t t .
3
(1973) 480; T e s t a r d i , L.R., Wernick, J.H. and Royer, W.A., S o l i d S t a t e Commun.15
(1974) 1 .We emphasize t h a t q f o r t h e B s i t e i s a l m o s t z e r o , 1141 Somekh, R.E. and E v e t t s , J.E., S o l i d S t a t e w i t h t h e prepondence o f e-p s c a t t e r i n g coming from Commun.
2
(1977) 733.t h e t r a n s i t i o n m e t a l s i t e (N(EF) i s 2. 90 % from t h e A-atoms a l s o ) . It i s a t f i r s t p u z z l i n g t h a t r, f o r Nb3Ge and Nb3Si a r e so s m a l l , e s p e c i a l l y i n l i g h t of t h e Tc = 23 K f o r t h e s p u t t e r e d f i l m s o f t h e former /13/ and t h e p r e d i c t e d h i g h Tc of t h e l a t t e r . Our r e s u l t s a p p e a r t o i n d i c a t e t h a t t h e s p u t t e r e d f i l m s have some s p e c i a l c h a r a c t e r i s t i c such a s soft phonon modes, o r s p e c i a l s u r f a c e s t r u c t u r e conduci- v e t o r a i s i n g T i n t h e A15 m a t e r i a l s . F u r t h e r e v i - dence f o r t h i s comes from t h e r e c e n t work of Somekh and E v e t t s /14/ who o b t a i n e d a Tc o f 1 1 K f o r V3Ge
