Theory of the Hall effect in the normal state of copper oxide superconductors

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Physica C 185-189 (1991) 1697-1698 North-Holland

THEORY OF THE HALL EFFECT IN THE NORMAL STATE OF COPPER OXIDE SUPERCONDUCTORS Hiroshi KAMIMURA, Tatsuo SCHIMIZU t and ttideki USttlO t i Dept. of Applied Physics, Faculty of Science, Science Univ. of Tokyo, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162 t Department of Physics, Faculty of Science, University of Tokyo Bunkyo-ku, Tokyo 113 t t Tokyo National College of Technology,Hachioji-shi,Tokyo ll3,Japan The anomalous temperature and concentration dependences of the Hall effect observed for La2_=Sr~CuO, are clarified theoretically, extending the electronic structure recently derived by Kamimura and Eto to a periodic system. The calculated results can explain satisfactorily all the observed anomalous behaviors of the Hall effect including the sign change. Furthermore the cotangent of the Hall angle is predicted to be proportional to T 2. It is shown that the origin of anomalous behaviors of the Hall effect is due to the warped shape of the Fermi surface.

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The origin of the anomalous behavior of the Hall effect observed for La2-xSrxCuOl are clarified. It has been observed by Ong et al. 1 and Takagi et al. ~ that the Hall coefficient follows the ~ behavior at low Sr concentration. Then, with increases of concentration it decreases more rapidly than the -~ behavior, changes its sign from positive to negative around x=0.3. It also shows anomalously large T-dependence. 2 Extending the recent results of the first-principles cluster calculations by Kamimura and Eto 3 to a periodic system we3'4 have recently showed that holes occupy the O p, band with their spins being antiparallel with those of the localized Cu dx2_~2 holes in the Sr concentration below the onset of superconductivity, while they occupy the Cu dz2 upper Hubbard band with their spins being parallel with those of Cu d~2_y2 holes in the superconducting and normal state phases.* On the basis of this result we have calculated

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Sr-concentration x Figure 1: The calculated concentration dependence of the Hall coefficient Rtx for T=80K and T=300K, together with experimental result by Takagi et al.1

the Sr concentration dependence and the temperature of "1"Lille ltr_u laU lt.,llglt~;llI'l,,,.ll~;Illll ...~m~:..-, i~'~ ,1.~ Itlii~ ~__#rrlll~__ll S llD't'l{:l ~.... o f depenaence !

paper we summarize these results and show that the ori-

La2_xSrxOuO4 and explained both the observed x and T

gin of the anomalous behavior of the Hall effect comes

dependences of the Hall effect successfully. In the present

from the warping of the Fermi surface. First, the calculated results of both the z- and T-dependences of Rtt 5 arc given in Fig.l, where the experimental data by Takagi et al2 are also shown for comparison. It is seen that

* Strictly speaking, immediately above the onset of superconductivity the hole states are the mixture of the Cu d,~ upper Hubbard band and 0 pc band. With increase of Sr concentration the latter character decreases and finally diminishes above x _> 0.1.

the calculated x-dependence of Rn for T=80K and 300K as well as the magnitude of RH coincide well with exper-

0921-4534/91/$03.f0 © 1991 - Elsevier Science Publishers B.V. All rights reserved.

1698

H. Kamimura

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T 2 ( 104 K 2 ) Figure 2: The calculated temperature-dependence of the Hall angle 9s- Here cot 8H is plotted against T 2. imental results by Takagi et al. In particular, in the case

Figure 3: The Fermi surface of the Cu d,2 upper Hubbard band for z -" 0.15 in the Brillouin zone for an ordinary unit cell of La2_~Sr~CuO4. This is the view from the (0,1,1) direction between y-axis and z-axis.

of T=300K the sign change of theoretical RH appears around x = 0.3, consistent with experimental results. As regards the temperature dependence we have also cal-

the Hal! coefficient decreases more rapidly than the 1_ behavior and then changes its sign. The increase of the

culated the Hall angle 8H defined by tan-l(a,~/ax~) as a function of temperature. On doing so we have used the theoretical results of a ~ calculated by Ushio and Kamimura, 6 based on the Fermi surface for the upper

electron-like contribution is also the origin of large temperature dependence of the Hall effect. The !x behavior of R s in the low Sr concentration is ascribed to a small Fermi surface of the O pc band. It is concluded from

Hubbard d~2 band. Fig.2 shows cot 0H vs T 2 theoretical

the present study that a general feature of the Hall ef-

curves for various values of x in La2_xSr~CuO4. From this we predict that cot 0s shoud be proportional to T 2

fect of the copper oxides depends critically on the shape of a Fermi surface, so that it may change from one kind

for LSCO, as has been observed for YBCO by Ong 7.

of copper oxide to the other, depending on the shape of their Fermi surfaces.

The anomalous temperature- and concentrationdependences of the Hall effect are due to a complicated shape of the Fermi surface of the Cu dz 2 upper Hub-

REFERENCES 1. N. P. Ong et al: Phys. Rev. B35 (1987) 8807.

bard band, which is shown in Fig.3, for example, for z=0.15. The Fermi surface has basically a nearly cylin-

2. H. Takagi et al: Phy. Rev. B40, (1989) 2254.

drical feature of a quasi-two-dimensional system but it

3. H. Kamimura and M. Eto: J. Phy. Soc. Japan 59,

shows a zig-zag shape, there are two kinds of contributions to the HA! effect. The one kSnd comes from the convex type of the curvature and it gives rise to a holelike character in Hall effect. While the other kind comes from the concave type of curvature and it gives rise to an electron-like character. The x - and T - dependenses of the Hall effect is determined by the competition of two kinds of contributions. The electron-like contribution increases with the increase of St-concentration, and thus

(1990) 3053. 4. T. Schim.iz- and H. Kamimura: 3. Phy. Soc. Jpn. 59, (1990) 3691. 5. H.Ushio, T.Schimizu and ll.Kamimura , J. Phys Soc. Jpn 60 (1991) 1445. 6. H.Ushio and H.Kamimura: Solid State Commun. 76 (1990) 1115. 7. N.P.Ong, 2nd ISSP Symposium of high T¢ superconductivity.