Journal of Low Temperature Physics, Vol. 117. Nos, 5/6, 1999

Magnetic and Pairing Correlation Functions andInterchain Coherence in Quasi-One-Dimensional

Dimerized Organic Conductors

Kenji Yonemitsu

Institute for Molecular Science, Okazaki 444-8585, Japan

We study how magnetic and pairing correlation evolves with an increasing in-terchain hopping integral and decreasing dimerization of intrachain hoppingintegrals, by applying the density matrix renormalization group (DMRG)method to a three-chain extended Hubbard model at quarter filling for quasi-one-dimensional organic conductors, (TMTTF)2X and (TMTSF)2X. Mag-netic correlation changes from weakly coupled chains of large-amplitude spindensity waves to an interchain-coherence-developed spin density wave. Pair-ing correlation increases, though it still decays exponentially owing to acharge gap for parameters considered here.

PACS numbers: 75.30 Fv, 74.70 Kn, 71.30 +h.

1. INTRODUCTION

Various electronic phases in quasi-one-dimensional organic conductors,(TMTTF)2X and (TMTSF)2X, have attracted much attention. As theapplied pressure increases, the ground state changes from a spin-Peierlsstate to a spin density wave (SDW). a superconductor, and finally to ametal.1 Above the phase transition temperatures, crossover from a one-dimensional Tomonaga-Luttinger liquid to a conventional Fermi liquid issuggested theoretically2.3 and experimentally.4 The superconductivity pos-sibly originates from spin fluctuations.5,6 Thus electron correlation plays amajor role in these organic conductors.

The NMR measurements have indicated that the wave number of theSDW in (TMTTF)2Br is commensurate with the reciprocal lattice vector.7while that in (TMTSF)2PF6. which is effectively located on the high-pressure

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side of the former, is incommensurate.8,9 The observed magnetic moment islarger in the former. The (TMTTF)2Br salt under pressure shows a tran-sition to the commensurate SOW.10,ll This commensurate-incommensuratetransition inside the SDW phase has been suggested to be correlated withthe charge localization-delocalization crossover above the SDW transitiontemperatures.

It is theoretically pointed out that interchain one-particle coherence issuppressed when a charge gap due to the dimerization of intrachain hop-ping integrals is large or the interchain hopping integral is small, based onperturbative renormalization-renormalization methods.3,12 When the inter-chain one-particle coherence is suppressed, the Fermi surface is absent sothat the order would be determined by the optimal real-space configurationof magnetic moments. Meanwhile, when the coherence is restored underpressure, the nesting of the Fermi surface would be the driving force.3 Inorder to directly observe the correlation between the interchain one-particlecoherence and the magnetic or pairing correlation function in the groundstate, we apply the DMRG method13 to a lattice fermion model.

2. THREE-CHAIN EXTENDED HUBBARD MODEL

Even-chain systems have a spin gap. The three-chain Hubbard andtJ models are well studied at and near half filling.14"16 Then, as a firststep toward quasi-one-dimensional systems, we use a three-chain extendedHubbard model,

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where ni,.,>=4J>cij>, n^^n^, and c\^a (ciji<r) creates (annihilates)an electron with spin <r on site (i, j). The alternating intrachain hoppingintegrals, t1 and t2, define the dimerization amplitude, S=(t1 — t 2 ) ( t 1 + t 2 ) .Here t = t1t2 \(t\ + i|)/2]~ ' is fixed at unity, tb represents the interchainhopping integral, U the on-site repulsion strength, and V the intrachainnearest-neighbor repulsion strength. We use the open boundary conditionfor the Lx x 3 lattice and consider quarter filling. In the DMRG calculations,the number of states kept. m. is taken up to 150 for Lx up to 20.

Magnetic and Pairing Correlation in Dimerized Organic Conductors

Site Site

Fig. 1. Spin density, (n^f - ^i,j,i), as a function of i for j=l (solid line),j=2 (dash-dotted line), j=3 (dashed line) and (a) tb-0.1, (b) tb=0.5. Otherparameters are (5=0.1, (7=4, V=l, Lx=20, and m=120.

3. RESULTS

We use U=4> 2V so that SDW correlation is dominant. The charge gapA is calculated from the ground state energies at and near quarter filling.In the Lx —> oc limit, A vanishes for 6=0 and becomes finite for finite S andsmall tb, increasing with 6 and V. For 6=0.1, U=4, V=l and V=2, which areused to draw the figures in this work, A is finite for tb>=0.1, but it vanishesfor tb=0.5 in the Lx —> oo limit. The interchain hopping correlation (forfinite Lx) is found to be sensitive to the ratio of A (for finite Lx) to tb- Forthe parameters used in Fig. 1, A is 0.5 for (a) tb=0.1, and 0.3 for (b) tb=0.5.The interchain hopping correlation (not shown) is strongly suppressed forthe parameters of Fig. 1 (a), but it is well developed for the parameters ofFig. 1 (b).

In the three-chain Hubbard and t J models near half filling,14 16 the spinexcitations in the odd (i.e., first-chain minus third-chain) channel and the d-wave pairing excitations have gapless spectra and asymptotically power-lawcorrelation. From the analogy to these models and the fact that the presentsystem has a charge gap for finite 6 and small tb. the SDW correlation inthe odd channel is expected to be the most dominant as far as tb, S and Vare small enough. In fact, such correlation appears dominant in Fig. 1 (a).Since m is not large enough here, the wave function converges to a statewith broken spin symmetry. Thus the spin density is shown instead of thespin-spin correlation function.

In Fig. 1 (a), the SDW in each chain is weakly coupled with those in theneighboring chains, so that the total energy is insensitive to a small mismatch

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in the relative SDW phase. However, compared with the strongly suppressed,interchain one-particle coherence, the interchain particle-hole coherence (inthe SDW channel) is well restored already at tb=0.1. In Fig. 1 (b), the centralregion has a domain wall since we used the inversion symmetry in the DMRGcalculations, but it is not essential. Here the SDWs in the neighboring chainsare out of phase and strongly coupled with each other. In other words, theinterchain SDW coherence is well developed. But the SDW amplitude issmaller than in Fig. 1 (a). These facts would correspond to a transitionor a crossover from a commensurate SDW to a Fermi-surface-nesting-drivenSDW which is generally incommensurate, although the present three-chainsystem cannot reproduce the experimentally observed, SDW patterns.

Similar changes occur in the spin density distribution and the inter-chain hopping correlation for larger V also, as shown in Fig. 2. In contrastto Fig. 1, both of Figs. 2 (a) and (b) show the out-of-phase SDW patterns.The analogy with the three-chain Hubbard and t J models is lost here. Inaddition, the spin density on two sites within a dimer tends toward dispro-portion into one site because the nearest-neighbor repulsion V favors chargedensity alternation.

Finally we show the pairing correlation function in the interchain singletchannel in Fig. 3. where ASiijtj+\ = (c,^j-Cj ij+li|-Cj ij ijCj ij+lij-)/\/2. Becauseof a charge gap. the pairing correlation decays exponentially with increasingintrachain distance. The magnitude of the pairing correlation is small, sothat these parameters would be far from the superconductor phase. Never-theless, it is found that the pairing is strongly suppressed when the interchainone-particle coherence is suppressed.

Fig. 2. Spin density, (n^f — n^j.), as a function of i for j=l (solid line),j=2 (dash-dotted line), j=3 (dashed line) and (a) £(,=0.1, (b) tb-0.5. Otherparameters are 5=0.1, (7=4, V=2, LX=20, and m=120.

Magnetic and Pairing Correlation in Dimerized Organic Conductors

Fig. 3. Singlet pairing correlation, <A^//I/2J,J.,+1As?L.I./2_ij-J-+1}, as a func-

tion of i for j'=l with j=l (solid line), j=2 (dash-dotted line) and (a) tb|,=0.1,(b) tb,=0.5. Other parameters are 5=0.1, U=4, V=l, LX=20, and m=120.

REFERENCES

1. D. Jerome, Science 252, 1509 (1991).2. C. Bourbonnais, Synth. Met. 84, 19 (1997); and references therein.3. J. Kishine and K. Yonemitsu, J.Phys.Soc.Jpn. 67, 2590 (1998); 68, No.8 (1999).4. J. Moser et al, Eur. Phys. J. B 1, 39 (1998).5. D.J. Scalapino, E. Loh, Jr. and J.E. Hirsch, Phys. Rev. B 34, 8190 (1986).6. H. Shimahara, J. Phys. Soc. Jpn. 58, 1735 (1989).7. T. Nakamura et al., Synth. Met. 70, 1293 (1995).8. T. Takahashi et al., J. Phys. Soc. Jpn. 55, 1364 (1986).9. J.M. Delrieu et al., J. Phys. (Paris) 47, 839 (1986).10. B.J. Klemme et al., J. Phys. I Prance 6, 1745 (1996).11. M. Hisano et al., Synth. Met. in press (1999).12. Y. Suzumura, M. Tsuchiizu and G. Gruner, Phys. Rev. B 57, 15040 (1998).13. S.R. White, Phys. Rev. Lett. 69, 2863 (1992).14. T. Kimura, K. Kuroki and H. Aoki, Phys. Rev. B 54, 9608 (1996).15. T.M. Rice et al., Phys. Rev. B 56, 14655 (1997).16. S.R. White and D.J. Scalapino, Phys. Rev. B 57, 3031 (1998).

ACKNOWLEDGMENTS

The author thanks J. Kishine and T. Nakamura for enlightening discus-sions. This research is supported by a Grant-in-Aid for Scientific Researchon Priority Area "Metal-Assembled Complexes" and for Encouragement ofYoung Scientists from the Ministry of Education, Science, Sports and Cul-ture, Japan.

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