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Submitted on 1 Jan 1978
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RESONANCES IN GENERALIZED
SUSCEPTIBILITY AND PHONON ANOMALIES IN
YS
M. Gupta
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, suppl6ment au no
8,
Tome 39, aolit 1978, page C6-1039RESONANCES IN GENERALIZED SUSCEPTIBILITY
AND
PHONON ANOMALIES IN YS
M. Gupta
Centre de Me'canique OnduZatoire AppZique'e du Centre NationaZ de Za Recherche Scaentifique, 23 m e du Maroc, Paris 75019, France
La FacuZtS.des Sciences drOrsay, 92405 Grsay, France
-f
R6sumb.- La susceptibilitb X(q) du sulfure d'yttrium, supraconducteur qui posssde 9 dlectrons de valence est obtenue, dans l'approximation des dldments de matrice constants au moyen d'un calcul ab- initio des bandes d'bnergie par la mdthode APW. De fortes rdsonances dans la contribution intraban- de de la susceptibilit6 apparaissent dans les directions [loo],
D
101 etc
I l] aux valeurs de<
05 des anomalies des branches acoustiques longitudinales du spectre de phonons ont Qtd rdcemment mesu- rbes par Roedhammer et coll..Bien que l'importance d'autres facteurs B l'origine des anomalies ne puisse Gtre exclue, les remarquables propridtds de nesting des surfaces de Fermi des chalcog6nures de mdtaux de transition possddant 9 dlectrons de valence tels que NbC, TaC, TiN, YS, renforcentsans nu1 doute les rdsonances qui sont P l'origine des modes "mous". Le prssent calcul montre que, con- trairement aux carbures de mdtaux de transition, l'hybridation p-d au niveau de Fermi est n6gli- geable pour YS ; ce resultat pourrait expliquer P la fois l'absence d'anomalies dans les branches acoustiques transversales et la faible valeur de la tempsrature critique pour YS.-+
Abstract.- The generalized susceptibility X(q) of the 9 valence electrons superconductor YS is ob- tained, within the constant matrix elements approximation, by means of an ab-initio augmentes plane wave determination of the ener bands. Large resonanc$s in the intraband contribution of ~ ( q ) are
found in the [100], [l 101 and B 1 l] directions at the q values where phonon anomalies have recently been measured by Roedhammer et al. in the longitudinal acoustic branches. Although the importance of other factors in producing anomalies is not excluded, the remarkable nesting features of the Fermi surfaces of the 9 valence electrons transition metal chalcogenides such a NbC, TaC, TiN and
YS, surely enhance the resonant screening which brings about the anomalies. Contrary to the transi- tion metal carbides, the p-d hybridization at the Fermi level is negligible for YS ; this result could have implications for the lack of anomalies in the transverse acoustic branches and the lower value of the superconducting transition temperature in YS.
The origin of phonon anomalies observed / l / in the 9 and 10 valence electrons (ve) transition metal chalchogenides (TMC) such as NbC, TaC, NbN and YS has been recently a matter of debate 121. A full understanding of this phenomenon seems parti- cularly important in view of its link to supercon- ductivity since an empirical correlation has been found between the occurrence of soft phonons and high superconducting transition temperature T
.
As the relative importance of the different factors which contribute to the existence of soft modes intransition metals and compounds has not yet been fully ruled out, it is important to report the in- formations, although partial, obtained from first principles calculations. With such a motivation, I studied the Fermi surface geometry and the genera-
-+
lized susceptibility X(q) of YS from an augmented plane wave (APW) determination of the energy bands. It is well known that divergences in the response function of the conduction electrons due to Fermi surface nesting features can lead through the re- normalization of the phonon frequencies, to a soft mode behaviour. Such resonances in the susceptibi-
lity of YS are due to intraband scattering and oc- cur at the values where soft modes have been recen- tly measured by Roedhammer et al. / l / . This striking correlation, which, as I found previously, exists for a full class of rocksalt structure 9ve TMC like NbC, TaC, TiN, and YS suggests that these resonances play an important role in producing the soft modes although the influence of other factors cannot be discarded. ~ndeed, recent calculations of Weber / 3 /
on NbC based on the formulation of lattice dynamics of Varma and Weber / 2 / confirm the importance of the intraband scattering in producing the anomalies of the 9ve TMC, while for other compounds and tran-
-h sition metals, the anomalies arise from the q de- pendence of the electron
-
ion matrix elements.The present results show that contrary to TaC and NbC, the p-d hybridization at the Fermi le- vel is negligible fox YS. This result is consistent with the conclusion of Hanke et al. /2/ about the origin of anomalies in the transverse acoustic branches, these branches being "normal" for YS.
Using the formalism of Gaspari-Gyorffy / 4 / for the calculation of the electron-phonon coupling constant,
which is .based upon the rigid ion approximation, the lack of p-d hybridization could also explain, in part, the lower value of T which is 2.8 K for YS while it reaches 10 and 1 1 K respectively for TaC and NbC.
The details of the electronic structure ob- tained from an APW calculation with warped muffin- tin potential will be reported elsewhere /5/, I indicate here briefly the salient features. The "3p" bands of sulphur form a complex of 2.7 eVwidth centered 4.1 eV below the bottom of the metal "4d" states ana well separated form it. Thus contrary to the carbides NbC and TaC, there is no overlap between the p bands of the chalcogen and the metal d band complex. The Fermi energy EF falls at the bottom of the metal d bands just above the
ri5
point, in a region where the density of states (DOS) is rather low with N(EF) = 13.47 states of both spin/Ry unit-cell. This feature also common to all superconducting TMC cannot be invoked to explainthe quite high values of Tc measured for some of them. The three lowest metal "d" bands belonging to the t manifold are found to cut the Fermi level. If2g
we label them by increasing order of energy asbands 4, 5, 6, band 4 contains the majority of electrons while bands 5 and 6 form only two small electron pockets around
r
; these pockets can be describedas deformed cubes of dimension % 0.23 (2 E) with stret- ched corners in the TK and rL directions respecti- vely for bands 5 and 6. The surface of interesthere is formed by band 4 ; it is a junglegym with multi- ply connected arms joining around and displaying flat parallel portions connected by nesting vectors. Qualitatively these features are similar to those I obtained /2/ for the band 4 Fermi surface of the transition metal carbides, but with slightly dif- ferent dimensions. As shown in figure 1, these geo- metrical properties lead to resonances in the in-+
traband 4 contribution of the susceptibility x(q)in all the three symmetry directions Eoo],
D
101 and[
l 1 ,]l which correlate very well with the positions of the soft modes measured in these directions in the longitudinal acoustic branches by Roedhammer et
+
a1 /l/. The peaks in X(q) are broad, so are the ob- served phonon anomalies. As the response function was obtained in the constant matrix elements (ME) approximation it is important to discuss separately the intraband and interband values as these contri- butions are known to be affected in a very different way by the M.E. I have indicated previously /2/that
the introduction of M.E. will not affect the con- clusions of the present work as the strong intra- band peaks will be multiplied by a slowly varying
+
function of q while the structureless interband band will be largely suppressed. This prediction is supported by the results of Weber 131 on NbC.
Fig. 1 : Th$ generalized susceptibility function X(q) along several symmetry directions :
(a) the intraband contribution of band 6 ;
(b) the intraband contribution from band 5 (c) the intraband contribution from band 4 and (d), the total interband contribution from bands 4, 5, 6.
References
/l/ Smith, H.G. and ~lzser, W., Phys. Rev. Lett.
2
(1970) 1611. ; Kress, W,, Roedhammer, P - , Bilz, H., Teuchert, W.D. and Christensen, A.N., Phys. Rev. B17
(1978) 1 1 1 ; Roedhammer, P., Reichardt, W. and Holtzberg, F., Phys. Rev. Lett.60
(1978) 465/2/ Weber,W., Phys. Rev. B8 (1973) 5082 ; Sinha,S. K. and Harmon,B.N.,
PFS.
Rev. Lett.35
(1975)1515 ; Gupta,M. and Freeman,A.J., Phys. Rev. Lett.
2
(1976) 364 ; Hanke,W., Hafner,J. and Bilz,H., Phys. Rev. Lett. 37 (1976) 1560 ; Var- ma,C.M. and Weber,W., ~ h ~ s r ~ e v . Lett.2
(1977)1094
/ 3 / Weber, W., Private communication and to be pu- blished
/h/ Gaspari, G.D. and Gyorffy, B.L., Phys. Rev. Lett.
