~ Solid State Communications, Vol.43, No.8, pp.637-639, 1982. 0038-1098/82/320637-03503.00/0 Printed in Great Britain. Pergamon Press Ltd.

Band Structure of ( T M T S F ) 2 X

M . - H . Whangbo* W. M. Walsh. Jr.

R. C. Haddon F. Wudl

Bell Laboratories Murray Hill. New Jersey 07974

ARS'TRACT

The electronic structure of the organic conductors (TMTSF)2X has been explored in terms of the tight binding band structures calculated for a sheet of TSF molecules. The Se 4d-orbitals appear to be critical in enhancing the interstack Se---Se interaction to the point that (TMTSF)2X becomes pseudo two-dimensional. Based upon the present band structure study, it is discussed whether a normal metallic state or a spin density wave state provides the closed Fermi surface responsible for the Shubnikov-de Haas oscillations observed in (TMTSF)2 P F 6.

Unlike other organic charge transfer salts, the organic conductors (TMTSF) ~ [TMTSF -- tetramethyltetrasclenafulvalene] exhibit a number of interesting properties such as very high conductivity, a low metal-insulator transition temperature and superconductivity, j-s That these unusual properties of (TM'~F) iX are closely related to the importance of multi-dimensionality effects has recently been demonstrated by the pressure-dependence of the conductivity 6, by polarized reflectance measurements, 3 and by the observation of Shubnlkov-de Haas (S-dH) oscillations. 7 In fact the crystal structures of (TMTSF)2X suggest that these materials may be pseudo two-dimensional by virtue of interstack Se...Se interactions. 6's't In the present paper we report band structure calculations which were carried out in order to understand the dimensionality of these materials.

The tight-binding band calculations employed in our work are based upon the extended Huckel method, details of which have been described elsewhere, s°.li Since the interaction between TM'I~F molecules is expected to be negligible along the c-axis because of the intervening sheets of anions X-, we have considered only a two-dimensional sheet of TMTSF molecules in the a-b plane omitting the anions. Upon replacing the four methyl groups of TMTSF by hydrogen atoms, our computational task was further reduced to a sheet of TSF molecules, s.t which was constructed based upon the crystal structure of (TMTSF)2PF6. s The atomic orbital parameters used for C(2s,2p), H(ls) and Se(4s,4p) were the standard values taken from previous work. 12

Our initial calculations without the 4d-orbitals of Se led to a band structure with appreciable dispersion along the a'-axis (i.e., the stacking axis) but very little dispersion along the b*- axis. We therefore examined if the Sc 4d-orbitals, which are well oriented to enhance the interstack Se...Se overlap, would increase the dispersion along the bS-axis to make the band structure two-dimensional. The exponent of the Se 4d-orbitals was estimated to be 0.9 from Burns rule, .6 and a range of orbital energies (i.e., -7.0, -7.5 and -g.0 eV) was chosen for the Se 4d-orbital by analogy with the value used for the S 3d-orbital (i.e., -6.017 and -8.0 eV'S). The salient features of the band structures calculated for the three choices of the Se 4d-orbital parameters are summarized in Figure I. The band structures shown in Figure 1 are composed of the highest occupied molecular orbital (HOMO) of each TSF molecule. The HOMO in TSF is found to be of btu symmetry and takes a similar form

m

f

i - 1 2

V

(o

/ /

y P

(b)

! I" v

-12

Y - " l I '

F F v ( ~ ,

Figure I. The band structures of a two-dimensional sheet of TSF molecules for the three values of the Se 4d- orbital energy: (a) H,w (Se 4d) = -7.0. (b) H ~ (Se 4d) = -7.5, and (c) H,,~ (Se 4d) = -8.0 eV. The symbols r , X, Y and V refer to the points in the Brillouin zone, whose coordinates are expressed in fractions of the reciprocal vectors a* and b* as follows: r - (0.0, 0.0), x - (0.5, 0.0), Y = (0.0, 0.5), and V = (0.5, 0.5). The Fermi levels are indicated by the dotted lines.

to that calculated for related molecules. 19n° The important features of these band structures may be summarized as

• Camille and Henry Dreyfus Teacher-Scholar, 19g0-1985. Permanent address: Department of Chemistry, North Carolina State University, Raleigh, NC 2?650.

637

638

follows: (1) Since a repeat unit consists of two TSF molecules, there occur two bands which are respectively composed of the in-phase and the out-of-phase combinations of two HOMO's. These two bands overlap and hence lead to a semi-metallic character with a combined hand width of ~1.7 eV. (2) These aspects of the band structure remain essentially unchanged even if the slight dimerization of TMTSF molecules along the a-axis 4's'9 is taken into consideration. (3) The dispersion along the aS-axis is only slightly affected by Sc 4d-orhitals (e.g., the band width changes from i.0 to 1.2 eV on inclusion of Sc 4d- orbitals). However, the dispersion along the baxis is greatly enhanced by Sc 4d-orbitals, and is quite sensitive to the choice of the Se 4d-orbital energy with the greater dispersion resulting from the lower orbital energy.

Figure 2 shows the Fermi surfaces 21 corresponding to the band structures of Figure 1. Figure 2a depicts a situation in which the interstack Se...Se interaction is not strong enough to close the Fermi surface. In Figure 2b the interstack interaction is large enough to just close the Fermi surface, while in Figure 2c the interstack interaction is well developed hence leading to a closed Fermi surface less flattened along the aS-axis than that of Figure 2b. Figures 1 and 2 represent three possible situations that may arise depending upon the magnitude of the interstack S¢...Sc interaction, which was varied in our study by adjusting the Se 4d-orbital energy. All those Cases shown in Figures 1 and 2 may actually be applicable to experimental situations in which the magnitude of the interstack Sc--.Sc interaction is controlled by pressure s or by the nature of counlerion. 4

The S-dH data of Kwak et al.~ may now be examined in terms of the Fermi surfaces shown in Figure 2. (TMTSF) 2 PF 6 and (TMTSF) 2 AsF 6 are known to enter a spin density wave (SDW) state below ~ I 1.5K at atmospheric pressure. Provided that a SDW state persists at the conditions (7.5 kbar and I . I K ) of the S-dH experiment, the S-dH data may be interpreted as follows: (a) If the S-dH oscillation were to arise from the Fermi surface of a normal metallic (i.e., single-particle) state, the S- dH data are consistent with the closed Fermi surface shown in Figure 2b or 2c, though not with the fairly large cross-sectional area of the calculated Fermi surface. The requirement of high magnetic fields in excess of 60 kG to observe the S-dH oscillation may then be considered as an indication of a magnetically induced change from a SDW state, whose electronic structure is yet to bc determined, to a normal metallic state. (b) Alternatively, the Fermi surface responsible for the S-dH oscillation may be associated with a SDW state itself as suggested by Horovitz ct el. zs Any open Fermi surface of a normal metallic state such as shown in Figure 2a is not consistent with the S-dH oscillation. However, upon shifting one of the two sheets of the Fermi surface by an appropriate nesting vector, such a metallic state may lead to a SDW state which has a closed Fermi surface with sinai] electron and hole pockets.

BAND STRUCTURE OF (TMTSF)2X

, i i i : ; ii'::::,"i'i:~',i'~,':, ,:,,

Y

:i'": i ,,~,',, . . . . . .

(a)

Vol. 43, No. 8

x V

(b)

(c)

Figure 2. The Fermi surfaces of a two-dimensional sheet of TSF molecules for the three values of the ,Se 4d- orb/tel energy: (a) H ~ (So 4d) - -7.0, (b) H~, (So 4d) -- -7.5, and (c) H~,, (,S¢ 4(I) - -8.0 eV. The occupied regions are indicated by shading.

Of the two interpretations (a) and (b) considered above, the latter appears to be more consistent with the S-dH data of Kwak et el. ~ since the data indicate small electron and hole pockets of equal cross-sectional areas (about 1% of the Brillouin zone). Thus the one-electron band structure of (TMTSF)2X may be best described by Figures la and 2a. Namely, the interstack Sc...Sc interaction is not strong enough to close the Fermi surface, but significant enough to make the two sheets of the Fermi surface curved thereby deviating from the perfect nesting condition. The interpretation (b) asserts that it is not a normal metallic state but a SDW state that has a closed Fermi surface. Therefore if this interpretation is correct, we expect that (TMTSF)2 PF6 should exhibit no S-dH oscillation in the absence of the SDW state.

The authors are grateful to K. Ragavachari for help with the computations, to R. N. Bhatt, F. J. DiSalvo, P. A. Lee, P. B. Littlewood and T. M. Rice for discussions, and to H. Gutfreund for a preprint, zs

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Vo].. 43, No. 8

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x~ ~ H ~ (eV)

H Is 1.3 -13.6 C 25 1.625 -21.4 C 2p 1.625 -11.4 Se 48 2.44 -20.5 Se 4p 2.07 -14.4

13.

The parameters for the Se orbitals are those employed previously, 13 and were taken from CIementi and Roetti t4 and from Hinze and Jaffe. 15

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BAND STRUCTURE OF (THTSF)2X

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The density of states and hence the Fermi surface were calculated by employing the tetrahedron method. ~-24

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