The role of the Fermi level position in high Tc superconductivity in the interband model

Volume 137, number

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THE ROLE OF THE FERMI LEVEL POSITION IN HIGH T, SUPERCONDUCTIVITY IN THE INTERBAND MODEL P. KONSIN, N. KRISTOFFEL and T. ORD Institute of Physics, Estonian SSR Academy ofSciences, Riia 142, 202400 Tartu, USSR Received 14 December 1988; revised manuscript received 21 March 1989; accepted for publication 30 March 1989 Communicated by A.A. Maradudin

The T~versus chemical potential curve obtained earlier in the interband model of the highT, superconductivity is compared with summarized experimental data on T~ as a function ofhole concentration in La 2 _~Sr~CuO4. The superconductive gaps in this model are calculated.

In ref. [lithe interaction of overlapping hole conduction bands at special points of the Brillouin zone has been considered as a possible interband mechanism for high-temperature superconductivity in metal-oxide systems. The interband model for superconductivity has first been considered in refs. [2,31. Concerning high T. superconductors, these ideas have been developed in refs. [4—9], see also ref. [1]. In ref. [1], the superconductivity arises in connection with the positive (repulsive) sign of the leading interband interaction constant (in which the interband Coulomb contribution dominates) and a remarkable volume of the Brillouin zone works in contrast to the BCS and the phonon interband attractive case. In this theory, the superconducting transition temperature T~shows rather a significant dependence on the position ofthe chemical potential (— ~) relives to the overlapping bands. In the most actual region, where E~>~> E0, i.e. ~ crosses both overlapping bands (—E0 is the top energy of the lower hole band and —E~the cut-off energy)

1/2 +K_1)

],

(1)

2p where ,c= W 1p2, W is the interband coupling constant and o~,P2 are the densities ofstates of the bands. 420

centration of the holes with Supposing the holes to be highly degenerate, one obtains ~.

~=

~

+

~1,

~<

E0,

L~p+~ö2E0+~fi1Ei~>E0. (2) Pi +P2 Here E,~p= p p~,where p is the hole concentration as a fraction of total copper and Po corresponds to the half-filled upper band (La2CuO4) of the width E1 (the ~ are analogous fractional quantities). For ~=E0 the exact relation is =

—

+~E~ — ~kBTln iol

kBT~= l.14[~’(~—E0)] ~‘~(E~_~)1/2

x ex~[_ ~ (~n~~

More details on the model can be found in ref [1] ~‘. In this report the summarized experimental data [10,111 on T~as a function of hole concentration in La2 _~Sr~CuO4,obtained by various experimental groups, will be compared with (1) and with eqs. (9) and (10) from ref. [1] by using adjustable values of the parameters of the theory. First, we need an expression connecting the con-

2,

but the contribution of the last term as well as the respective corrections in (2) are negligible. Our best-fit curve to the experimental data is pre~ Please note the misprint in eq. (9) of ref. [1] where a power (—

1) in the argument of the exp. function is missing.

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Volume 137, number 7,8

sented in fig. 1 (the triangles denote the results of ref. [11], the squares are the results of von Dover et al. [10], and the circles are the results of Torrance et al. [10]) and the corresponding parameter values are the following: p,=l; P2=2 (eV cell)’, ~, ~ P2=l (eV cell)’, E,=4; E 0.085 eV. These quantitative 0=2.14; characteristics seem to E~=2.3;W= be reasonable, at least they are ofthe order proposed in ref. [11 for high T~systems. Somewhat surprising is the small difference between E~and E 0. Keeping in mind the uncertainty in defining the effective bottorn of the bands E~it is difficult to comment this fact here. One possible reason may be the defect-induced band-splitting like stated for YBa2Cu3O7.~ [12] or a hole decoupling phenomenon connected with the small correlation length. The agreement of the curve in fig. 1 (containing practically three free parameters) with the experimental behaviour is surprisingly good. Considering the very rough and simple model nature of the theory, not too However, much meaning should be ascribed to this agreement. the authors hope that the interband theory describes the essential influence of the Fermi-level position in a distinct part of the valence conduction band totality characteristic ofmetaloxide superconductors. Next the gap order parameters satisfying the system E~—

4,

—

Wp 242

J S

_______

d.E

EO_~jE+42

th \/E+ 4~ 2kBT

E~ ~ —

Wp, 4

‘

______

JE ~JE2 +4~ ~ \/E + 4~th 2k~T

(3) ‘

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40

29 May 1989

in the two-band model of ref. [1] will be calculated. At T= 0 = Wp24201n E~—C+ [(E~ —C)2+ 4~o]”2 Eo—C+ [(E 2+4~o]”2

~

~20

0—C) 2+4~ 2 = Wp, 4101nEc~+— C+ [C2+ 4 ~ 11/2 0]” [(E~—C)

.

(4)

The number of superconductive gaps is determined by the number of electron bands intersecting the Fermi-level. In case C lies above the maximum of the band of heavy holes, only 4,~is a gap and the usual relation 24,0/k~TC= 3.5 holds for it. The quantity ~2o has the meaning of a band shift in this case. For the case corresponding to (1), where the Fermi level passes through both bands, 4~o \ 4 2(C—E 2exp — 2Wp 20=2(E~—C)” 0)” 242o)

(

4io =2(E~

f 2Wp, 420 ~ C)’~2C~2 exp~—

(5)

Now both order parameters must be observable as gaps and the 24/kBTC ratios are not of BCS universality. Numerical estimates with W= 0.06 eV and P1,2 ranging from 1 to 5 (eV cell)—‘lead to values of the ratio between 1 and 10. Such remarkable deviation is confirmed by experimental findings [13—18],and there are cases where a number of gaps have been observed simultaneously [19,20]. With C moving away from the region ofband overlap T~decreases rapidly. Simultaneously, with C approaching the centre of the highest band a favourable situation arises for the appearance of a dielectric gap in the spectrum and of the electronic antiferromagnetic ordering. A residual Knight shift in the low-temperature part of the superconducting phase has been found [21]. This must not be the case according to the usual BCS theory. If this finding may be explored as the par-

~ 30 ‘20

ticipation of only a distinct part of the carriers in the superconductivity it agrees with the role of special points of the Brillouin zone supposed in the present

10! 0

TT

0,1

0,2

0.3

Fig. 1. Theoretical dependence of T~on hole concentration (solid line) in comparison with the experimental data (see text) for La2_~Sr~CuO4.

theory. The authors are indebted to the Organizing Cornmittee of the Adriatico Research Conference: “Towards the theoretical understanding of high T~su421

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perconductors” for sending us some material of the Conference.

29 May 1989

[91K. Hanzawa and K. Yoshida, J. Phys. Soc. Japan 56 (1987) [10]K.A. MUller, Review report at the Adriatico Research Conference: Towards the theoretical understanding ofhigh T~superconductors, Trieste (1988).

References [l]P.Konsin, N. Kristoffel and T. Ord, Phys. Lett. A 129 (1988) 339. [2]V.A. Moskalenko, Fiz. Met. Metalloved. 8 (1959) 503. [3]H. SuhI, B.T. Matthias and L.R. Walker, Phys. Rev. Lett. 3 (1959)552. [4]V.P. Galaiko, Fiz. Nizk. Temp. 13 (1987) 1102. [5] D.H. Lee and J. Ihm, Solid State Commun. 62 (1987) 811. [6] K. Yamaji, Solid State Commun. 64 (1987)1157. [7] B.Ya. Shapiro, Phys. Lett. A 127 (1988) 239. [8] F.J. Ohkawa, J. Phys. Soc. Japan 56 (1987) 3017.

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[11] M.W. Shafer, T. Penney and B.L. Olson, Phys. Rev. B 36 [12] F. Herman, R.V. Kasowski and W.Y. Hsu, Phys. Rev. B 36 (1987) 6904. [13]J.R.Kirtleyetal.,Phys.Rev.B35(1987)7216. [14]P. Leidereretal., Z. Phys. B67 (1987) 25. [15]S. Pan et al., Phys. Rev. B 35 (1987) 7220. [16]Z. Schlesinger et al., Phys. Rev. Lett. 59 (1987)1958. [17]M.D. Kirk et al., Phys. Rev. B 35 (1987) 8850. [18] J.R. Kirtley et al., Phys. Rev. B 35 (1987) 8846. [19] I.K. Janson et al., Fiz. Nizk. Temp. 13 (1987)557. [20] V.1. Verkin et al., Fiz. Nizk. Temp. 13 (1987) 771. [21] E. Lippmaa et al., Physica C 153—155 (1988) 91.