Low Field Galvanomagnetic Properties of Graphite Acceptor Compounds and Their Relation to Trigonal Warping
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KO SUGIHARA* Materials Research Laboratory, Moriguchi, Osaka 570 JAPAN.
Matsushita Electric Industrial Co.,
Ltd.,
ABSTRACT In first stage graphite intercalation compounds with cylindrical Fermi surfaces and isotropic relaxation times, no magnetoresistance occurs. Holzwarth pointed out that trigonal band warping provides a finite magnetoresistance in first stage compounds. A calculation of the galvanomagnetic coefficients of stage-2 acceptor compounds is performed including the effect of trigonal warping on the bands. In the present problem a perturbation calculation provides a good approximation. Without trigonal warping, the stage-2 compounds exhibit a finite magnetoresistance since they have 2 two kinds of holes. Retaining terms up to order (0 3 /y 0 ) , the weak field magnetoresistance is calculated2 in limit H•O; 2 2 2 2 2 (e/h c) (¶/EF) (3YOb/2)4{1/4(YI/EF) +57/2(Y 3 /Y0) } Ap/poH where b = 1.42 A is the nearest C-C distance, EF the Fermi energy and T the carrier relaxation time. The first term in curly brackets is due to the existence of the two kinds of holes. This formula indicates that the term due to trigonal warping is much larger than the other term.
INTRODUCTION In rirst stage graphite intercalation compounds (GIC) with a single cylindrical Fermi surface, a finite magnetoresistance AP/Po in the weak field limit is not expected, in contradiction to the observed results [1,21. In this connection, Holzwarth [31 presented a theory of the magnetoresistance and Hall effect which considered band warping and explained the qualitative features of the observed results without requiring two or more equivalent carriers [4]. Therefore, low field magnetoresistance measurements in the first stage GIC 1 provide not only a carrier mobility 1 M + c(Ap/poH2)1/2 in the limit R + 0 but also useful information on the band warping of the cylindrical Fermi surfaces. Accordingly, it is expected that the band warping might play an important role in the galvanomagnetic properties of higher stage compounds. In this paper we calculate the low field magnetoresistance and Hall coefficient of the second stage acceptor compounds, including the effect of trigonal warping of the bands. Existence of two kinds of holes makes the low field magnetoresistance finite even if the warping of the bands is absent. However, the effect of the trigonal warping dominates the two carrier effect. Assuming 73/Io = 10-1, we find that the warping contribution to the magnetoresistance is one order larger than the two carrier contribution. A similar situation should be realized in the higher stage compounds. The effect of trigonal warping on the Hall coefficient is not as large, but nevertheless cannot be neglected. *Present address: MA 02139,
Mat.
Res.
Center for Materials Science and Engineering,
MIT Cambridge,
USA.
Soc.
Symp.
Proc. Vol.
20 (1983) OElsevier Science Publishing Co.,
Inc.
180 We can thus get information on the ratio (Y3 /Yo)
by measuring •M/LO, where io
denotes the conductivity mobility.
EFFECTS OF THE TRIGONAL BAND WARPIN
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