low frequency dielectric spectroscopy of the peierls-mott insulating state in the deuterated...

Eur. Phys. J. B 13, 503–511 (2000) THE EUROPEANPHYSICAL JOURNAL Bc©

EDP SciencesSocieta Italiana di FisicaSpringer-Verlag 2000

Optical and photoemission evidence for a Tomonaga-Luttingerliquid in the Bechgaard salts

V. Vescoli1, F. Zwick2, W. Henderson3, L. Degiorgi1,a, M. Grioni2, G. Gruner3, and L.K. Montgomery4

1 Laboratorium fur Festkorperphysik, ETH Zurich, 8093 Zurich, Switzerland2 Institut de Physique Applique, Ecole Polytechnique Federale de Lausanne, 1015 Lausanne, Switzerland3 Department of Physics, University of California at Los Angeles, Los Angeles CA 90095-1547, USA4 Department of Chemistry, University of Indiana, Bloomington IN 47405, USA

Received 17 May 1999 and Received in final form 13 July 1999

Abstract. Combined optical and photoemission experiments on the quasi-one dimensional Bechgaard saltsreveal the non-Fermi liquid character of these prototype quasi-one dimensional interacting electron systems.We show that various aspects of the exotic normal state properties along the chains are consistent withthe predictions of the Tomonaga-Luttinger liquid theory. We also discuss the effect of interchain couplingon the insulator-metal transition, associated with the electron confinement-deconfinement crossover.

PACS. 78.20.-e Optical properties of bulk materials and thin films – 79.60.-i Photoemission and photo-electron spectra – 71.27.+a Strongly correlated electron systems; heavy fermions

1 Introduction

The Fermi liquid (FL) theory is extremely general and ro-bust, and has been one of the cornerstones of the theoryof interacting electrons in metals for the last half century.The theory is based on the recognition that the low-lyingexcitations of an interacting electron system are in a one-to-one correspondence with those of the noninteractinggas, only with renormalized energies. FL theory has beenthoroughly tested on a variety of materials and is usuallyvalid in higher than one dimension (1D). One possible no-table exception is the normal state of the two-dimensional(2D) copper oxide-based high-temperature superconduc-tors (HTSC). Recently, a great deal of interest has beendevoted to the possible breakdown of the FL frameworkin quasi-one dimensional materials.

In a strictly 1D interacting electron system, the FLstate is replaced by a state where interactions play a cru-cial role, and which is generally referred to as a Tomonaga-Luttinger liquid (TLL). The 1D state predicted by theTLL theory [1] is characterized by features such as spin-charge separation and the absence of a sharp edge in themomentum distribution function n(k) at the Fermi wavevector kF (i.e., by the fact that, in the Fermi liquid lan-guage, the renormalization factor Z → 0 at kF). The non-Fermi liquid nature of the TLL is also manifested by anabsence of single-electron-like quasiparticles and by thenon-universal decay of the various correlation functions.The first immediate consequence of the absence of the dis-continuity at kF in the momentum distribution function

a e-mail: [email protected]

is the powerlaw behaviour of the density of states (DOS)ρ(ω) ∼ |ω|α (ω = EF − E). The exponent in this expres-sion reflects the nature and strength of the interaction.Figure 1a compares the typical DOS near the chemicalpotential and at T = 0 for a FL and a TLL scenario (withα > 1).

The TLL, which describes gapless 1D fermion systems,may be unstable towards the formation of a spin or acharge gap [2,3]. Spin gaps are obtained in microscopic1D models including electron-phonon coupling, and arerelevant to the description of the normal state of super-conductors and Peierls (CDW) insulators [2]. The sec-ond instability, which concerns the linear chain Bechgaardsalts discussed below, is a more typical consequence ofelectronic correlations. At half filling, and more generallyat commensurate values of band filling n = p/q (withp and q integers), the long-range electron-electron inter-action together with Umklapp scattering (which ariseswhen the lattice periodicity is also involved) [3] drivethe system to a Mott insulator with a correlation gapin the charge excitation spectrum (i.e., in the real partσ1(ω) of the optical conductivity (Fig. 1b)). Strictlyspeaking, 1D systems with one gapped channel, eithercharge or spin, do not belong to the universality classof the Tomonaga-Luttinger model, but rather to that ofthe related Luther-Emery (LE) model [2]. Nevertheless,the two models exhibit several common, typically 1D fea-tures, like spin-charge separation. Of course, real materialsare only quasi-one-dimensional, and the interchain hop-ping integrals are finite in the two transverse directions.The electronic ground state is therefore determined by

504 The European Physical Journal B

Fig. 1. Comparison between the Fermi-liquid and Tomonaga-Luttinger liquid scenarios: (a) density of states, (b) opticalconductivity (Mott-insulator, doped Mott semiconductor andDrude behaviour), and (c) Top: FL and TLL spectral func-tions as obtained in the angle-integrated (PES) experiment;Bottom: angle-resolved (ARPES) spectra illustrating the dis-persion and the crossing of the chemical potential (“Fermi sur-face crossing”) by a quasiparticle peak [3,17].

a competition between the Mott gap (i.e., the 1D limit)and the interchain hopping. In a very crude way, the inter-chain hopping can be viewed as an effective doping, lead-ing to deviations from the commensurate filling (which isinsulating).

The spectral properties of both metallic and gapped1D systems reflect the unusual nature of correlations in1D. Therefore, optics and photoemission, especially on

single crystal samples, are powerful tools to address theabove fundamental issues. The optical response has beenalso calculated for a doped one-dimensional Mott semi-conductor and consist of a Mott gap (as reminder of theoriginal 1D limit) and a zero-energy mode (represent-ing the effective metallic contribution) for small dopinglevels (Fig. 1b) [3]. Of course for the low-energy mode,this is an oversimplified view, since the interchain hop-ping makes the system two-dimensional, and the low-energy feature is unlikely to be described by a simpleone-dimensional theory [3]. Such an interchain couplingbecomes ineffective at high enough temperatures or fre-quencies, and thus we would expect the 1D physics (i.e.,the Mott insulating state) to dominate in this regime,where a powerlaw behaviour in σ1(ω) is expected in bothlimits (Fig. 1b) [3]. While the high temperature dc con-ductivity has essentially a metallic character in most linearchain compounds [4], the finite frequency optical responseis distinctly non-Drude [5–7].

Non-Fermi liquid features should also be visible in thephotoemission spectra. The k-integrated spectrum of theLuttinger model vanishes at the chemical potential (EF)as a power law. By contrast, a normal metal is charac-terized by a finite intensity at EF, and by a temperature-and resolution-limited edge – the metallic Fermi step –(Fig. 1c). Distinct spectral features, the holon and thespinon, reflecting spin-charge separation, are also expectedto replace the dispersing quasiparticle peaks in the k-resolved (ARPES) spectra [8,9]. Correspondingly in angle-integrated (PES) spectra the intensity near the chemicalpotential is strongly renormalized (Fig. 1c) [10].

In this paper we show that the combined insightsfrom optics and photoemission support a TLL scenario inthe linear-chain organic Bechgaard salts. We also discussthe dimensionality crossover which progressively drivesthe systems from a 1D Mott insulator to a quasi-2D Fermiliquid metal, under the effect of increasing transverse (i.e.,perpendicular to the 1D chains) interactions. Parts of thiswork, and several technical details have been separatelypresented elsewhere [7,11,12]. After a short introductionon the Bechgaard salts and a reminder of the experimentaltechniques, we first illustrate the most relevant results. Wediscuss them by exploring possible scenarios, alternativeto the FL approach. The conclusion summarizes severalopen issues and gives an outlook on future research.

2 Experiment and results

2.1 Bechgaard salts

Since their first synthesis in the late 1970 [13], the(TMTSF)2X family of linear-chain organic conductors,and the closely related TMTTF family, have attractedcontinual attention. While the various broken symme-try ground states, including spin-density waves, charge-density waves, spin Peierls, and even superconductiv-ity have been extensively explored over the last twodecades [4,14,15], much of the current attention is now

V. Vescoli et al.: Optical and photoemission evidence for a Tomonaga-Luttinger liquid in the Bechgaard salts 505

Fig. 2. Temperature dependence of the resistivity for(TMTTF)2X and (TMTSF)2X measured along the chain axis.The data are taken on our samples and are in agreement withpreviously published results [4,13,20].

focused on the (metallic) normal state, because of the is-sues pointed out above [16,17]. These compounds havebecome one of the prototypical testing grounds for thestudy of the effects of electron-electron interactions inone-dimensional structures. In the Bechgaard salts, chargetransfer of one electron from every two TMTSF moleculesleads to a quarter-filled (or half-filled due to the dimer-ization of the TMTSF and TMTTF molecules along thechain axis [4]) hole band, thus making Umklapp scatteringrelevant [18].

Many of the measurements presented here were madepossible by our ability to grow large single crystals ofthe Bechgaard salts. The large single crystals used in thisstudy were grown by the standard electrochemical growthtechniques [13], but at reduced temperature (0 ◦C) andat low current densities. These conditions produce a slowgrowth rate and, over a period of 4–6 months, single crys-tals up to 4×2.5×1 mm3. These large, high-quality crys-tal faces in the a−b′ plane allowed us to perform reliablemeasurements of the electrodynamic response and pho-toemission spectra of these materials both parallel (E‖a)and perpendicular (E‖b′) to the highly conducting chainaxis down to low frequencies [19].

Figure 2 displays the resistivity ρ(T ) of the Bechgaardsalt compounds that we have measured along the linearchain axis. There is a good agreement with the literaturedata [4,13,20]. The (TMTSF)2X salts have a clear metal-lic behaviour down to TSDW of 12 and 6 K for X = PF6

and ClO4, respectively, where the SDW phase transitiontakes place. The TMTTF salts, on the other hand, have afirst metal-insulator phase transition at Tρ ∼ 100−200 K.Such an insulating phase was ascribed to charge lo-calization [4,21]. Below temperatures of about 10 K,

Fig. 3. Left: PES spectrum of (TMTSF)2PF6 (dashed line)showing no intensity at EF. The solid lines are ARPES spectraof (TMTSF)2ClO4, measured at the Γ point (bottom) andat the zone boundary (middle), in the chain direction (T =150 K). Right: Comparison of normal emission ARPES spectraof three Bechgaard salts. The extrapolation of the leading edgesdefines a material-dependent energy gap.

there is a spin-Peierls and a SDW phase transition for(TMTTF)2PF6 and (TMTTF)2Br, respectively [4,22].

2.2 Photoemission

For our photoemission measurements we used both polar-ized synchrotron radiation (at the Wisconsin SynchrotronRadiation Center), and unpolarized HeI radiation (hν =21.2 eV, at Lausanne). The experimental energy resolutionvaried between 10 meV and 30 meV, and the momentumresolution was ∆k ∼ 0.04 A−1 at 21.2 eV. We determinedthe Fermi level position with an accuracy of ±5 meV fromthe spectra of evaporated Au films.

Figure 3 illustrates representative PES and ARPESspectra of the Bechgaard salts. The angle integrated PESspectrum of (TMTSF)2PF6 exhibits a prominent featureat 1 eV, a binding energy which corresponds to the bot-tom of the conduction band [23]. Remarkably, the inten-sity is vanishingly small at the Fermi level, in apparentcontradiction with the metallic character of this material(see Fig. 1c). The strong spectral weight renormalizationis consistent with photoemission data on other quasi-1Dmaterials [10,11,24–29]. The leading edge of the spectrumcould be fitted over a broad energy range by a power-lawlineshape, with an exponent of order 1.

The unusual lineshape is confirmed by the ARPESspectra of (TMTSF)2ClO4, in the normal state. Withinour experimental accuracy, these data are also indistin-guishable from those of (TMTSF)2PF6. These spectraexhibit a strong polarization dependence: the intensitywithin 1.5 eV of EF is enhanced when the electric field vec-tor is parallel to the chains, as in Figure 3 [11]. At normalemission, corresponding to the Γ point in the Brillouin


zone (BZ), the spectrum exhibits a main peak at 1 eV,followed by a linear slope between 0.6 eV and EF. Asexpected, this band feature does not disperse in a direc-tion perpendicular to the chains. However, we did not ob-serve any dispersion even along the chain direction butonly slight intensity variations. In particular, we could notdetermine any Fermi surface crossing. These features arecommon to all the Bechgaard salts we have investigated, ofboth the (TMTSF) and (TMTTF) families, and indicatethe absence of dispersing quasiparticle peaks (Fig. 1c).

The only material-dependent changes are small rigidshifts of the spectral leading edges in the (TMTTF) salts.The high-resolution normal emission data of Figure 3b arerepresentative of the results obtained throughout the BZ.A linear fit of the leading edge defines a crossing of thebaseline near EF in (TMTSF)2PF6 (and ClO4). On theother hand, the baseline crossing is at ∆ ∼ 100 meV for(TMTTF)2PF6, and∆ ∼ 30 meV for (TMTTF)2Br. Sinceall spectra are referred to a common Fermi level, the shiftsindicate energy gaps (Egap ∼ 2∆) in the (TMTTF) salts.The smaller shift for (TMTTF)2Br is consistent with itsnarrower gap. This interpretation is supported by recentdata on (TMTSF)2ReO4. The spectra of that materialexhibit a transition from a “pseudogap-like” lineshape toa real gap, in correspondence of the anion ordering metal-insulator transition at 180 K (not shown) [4,30].

The null value for the TMTSF compounds is compat-ible with their metallic behavior but, taking into accountthe thermal and experimental broadening, we cannot defi-nitely exclude a small (up to ∼ 10 meV) gap. The spectraof Figure 3 unambiguously establish the insulating charac-ter of the TMTTF samples. However, ARPES only probesthe occupied states, and some care is necessary when themeasured shifts are used to estimate the gap values. Forinstance, if the Fermi level was pinned by impurities atthe bottom of the conduction band, our analysis wouldoverestimate the gap by a factor 2. On the other hand, itis likely that pinning defects will act in a similar way forall the members of the (TMTTF) family, so that all gapswill be similarly over- or underestimated.

2.3 Optics

By combining the results from different spectrometers inthe microwave, millimeter, submillimeter, infrared, visibleand ultraviolet ranges, we have obtained the electrody-namic response of these Bechgaard salts over an extremelybroad range (10−5−10 eV) [6,7]. At all frequencies up toand including the midinfrared, we placed the samples in anoptical cryostat and measured the reflectivity as a functionof temperature between 5 and 300 K [6,7]. In the opticalrange from 2 × 10−3 to 10 eV, the polarized reflectancemeasurements were performed, employing four spectrom-eters with overlapping frequency ranges; while in the mi-crowave and millimeter wave spectral range, the spectrawere obtained by the use of a resonant cavity perturbationtechnique [6,7,12].

Figure 4 summarizes the temperature dependence ofthe real part σ1(ω) of the optical conductivity in different

Fig. 4. On chain optical conductivity of (a) (TMTTF)2PF6,(b) (TMTTF)2Br, and (c) (TMTSF)2PF6 at temperaturesabove the transitions to the broken symmetry states. The ar-rows indicate the gaps observed by dielectric (ε) response, dcresistivity and photoemission (ph). A simple Drude componentis also shown in part (c). Note that photoemission measures thequantity Egap/2, assuming that the Fermi level is in the middleof the gap.

Bechgaard salts for E‖a, the chains direction. Part (a)and (b) show σ1(ω) for the PF6 and Br compounds ofthe TMTTF family, while part (c) displays σ1(ω) for(TMTSF)2PF6. We can immediately remark that the tem-perature dependence of σ1(ω) is quite important in allcompounds, except in (TMTTF)2PF6, which is basicallyin an insulating state at all temperatures. The data pre-sented here are in broad agreement with previous, less de-tailed studies [5,31], and they include frequencies belowthe conventional optical spectra.

The optical conductivity of the TMTTF salts displaysseveral transitions with large absorption features due tolattice vibrations (phonon modes), mainly due to the in-ter and intramolecular vibrations of the TMTTF (andTMTSF) unit. These vibrations can be even enhanced bythe electron-phonon coupling [31]. The phonon modes areparticularly observed in the TMTTF salts, because thescreening by free electrons is less effective. Although it isclear that the optical properties of the TMTTF salts are


those of a semiconductor, with a gap for the charge excita-tions, the evaluation of the magnitude of the gap, based onthe optical spectra, is not straightforward, because of thelarge phonon activity. Thus, the results of other measure-ments were used to evaluate the gap. The dc conductiv-ity as well as the low-temperature dielectric constant (ε)measured at 100 GHz are consistent with Egap = 87 and50 meV for (TMTTF)2PF6 and (TMTTF)2Br, respec-tively [12,32]. These results also suggest that the absorp-tion in σ1(ω) near 99 meV for (TMTTF)2PF6 is associ-ated with Egap; this is supported by the fact that thisfeature has the correct spectral weight [12]. Moreover, forthe (TMTTF)2Br below 90 K (i.e., at T < Tρ) there is theprogressive disappearance of the spectral weight, definedas∫ ωc

0dω σ1(ω) with ωc a cut-off frequency, in FIR (i.e.,

ω < 37 meV) with decreasing temperatures. The missingspectral weight mainly piles up at the gap feature around50 meV. The photoemission experiments suggest a gap of0.2 eV for (TMTTF)2PF6 and 60 meV for (TMTTF)2Br(see Fig. 3 and the discussion in Sect. 2a). The gap val-ues obtained for (TMTTF)2X with different techniquesare displayed in Figure 4. Because the band is partiallyfilled, the charge gap in both of the (TMTTF)2X salts isa correlation rather than a single-particle gap.

The optical properties of the (TMTSF)2X analogs,for which the dc conductivity gives evidence for metallicbehaviour down to low temperatures (to the transitionto the spin density wave state at TSDW), are markedlydifferent from those of a simple metal. A well-definedgap feature around 25 meV and a zero-frequencymode [6,7,12,33] are observed at low tempera-tures. The latter mode at low temperatures is nar-rower in (TMTSF)2ClO4 (not shown here) than in(TMTSF)2PF6 [12]. The combined spectral weight ofthe two modes is in full agreement with the knowncarrier concentration of 1.4 × 1021 cm−3 and a bandmass that is very close to the electron mass [4]. Forboth (TMTSF)2X salts, the zero-frequency mode hassmall spectral weight on the order of 1% of the total.Nevertheless, this mode is responsible for the largemetallic conductivity. Figure 4c also indicates thatthe two components of σ1(ω) clearly develop at lowtemperatures. In fact, there is a progressive narrowingof the effective metallic contribution to σ1(ω) withdecreasing temperatures. Moreover, the dc-limit of σ1(ω)is in fair agreement with σdc values from the transportdata, as also confirmed by the so-called Hagen-Rubensextrapolation of our original absorption or reflectivitymeasurements [12,34].

3 Discussion

Both photoemission and optical data indicate that thespectral properties of the metallic Bechgaard salts are in-compatible with those of a simple metal (Figs. 1b, c). Thephotoemission spectra reveal a strong suppression of spec-tral weight near the chemical potential and the absenceof dispersing quasiparticle features. The optical response

is complex, and cannot be described by a simple Drudecomponent.

A standard interpretation of the angle-integrated spec-trum of (TMTSF)2PF6 would suggests a deep pseudogap,with a vanishingly small DOS at the Fermi level. This,however, is incompatible with transport data (Fig. 2), andwith optics, which shows no evidence for such a broad(∼ 0.5 eV) pseudogap (Fig. 4 and discussion below). The1D properties of (TMTSF)2PF6 suggest to interpret thespectrum as the incoherent power-law background ρ(ω) =|ω|α of the Luttinger model (Figs. 1a, c). The exponent αreflects the strength of the interactions, and is related tothe fundamental charge correlation parameter Kρ of theLuttinger model by the expression α = (Kρ+K−1

ρ −2)/4.An analysis of the experimental data yieldsKρ ∼ 0.2, withrather large error bars due to the finite temperature, andthe uncertainties over the energy range where the asymp-totic Luttinger expression applies [24]. Anyway, Kρ is wellbelow the 1/2 limit of the standard Hubbard model. Thisindicates strong and long-range electronic correlations, inqualitative agreement with optics, and with the conclu-sions of NMR and transport investigations [17,20,35,36].

The ARPES data should be compared with the k-dependent spectral function A(k, ω) of the Luttingermodel [8,9]. The spectra of Figure 3 certainly do not ex-hibit the characteristic spinon and holon peaks. However,Voit [2] has shown that the appearance of the TLL spec-tral function is drastically modified for large values of theexponent α, which may be relevant here. In this parame-ter range the holon peak is reduced to a cusp singularity,and the spinon is replaced by a (k-dependent) low energytail. These aspects of a large-α TLL are qualitatively con-sistent with the experimental lineshapes.

The Luther-Emery model provides a more appropriatescenario for the insulating (TMTTF) salts. For moder-ately strong interactions (small α values) the LE spectralfunction exhibits separate spin and charge features, al-though the intensity distribution is not identical to thatof the TLL spectral function [2]. We may speculate that,with increasingly strong correlations, and larger α, theevolution of the LE and TLL lineshape will be similar,i.e. towards a strong suppression of intensity near EF.

A Luttinger (or Luther-Emery)-like interpretationfaces two main objections: the unexpectedly large valueof α, and the absence of any k-dependence in the ARPESspectra. α values of the order of 1 are incompatible withresults for the standard Hubbard model; for purely lo-cal interactions, in fact, Kρ > 1/2 (α < 1/8). SmallerKρ (larger α) values are possible for longer-range inter-actions. Lower limits are then set by Umklapp scattering,which becomes relevant at commensurate filling. Exactlyat quarter-filling the system is insulating for Kρ < 1/4(α > 9/16). This is indeed the parameter range suggestedby optics (see below). Slightly away from 1/4 filling, adoped 1D chain can still exhibit TLL behavior with Kρ

as small as 1/8, and α as large as 1.53 [37], within thecorrelation gap, on the energy scale of the dopant band.However, this energy scale is more than one order of mag-nitude smaller than the energy range (the pseudogap) over


which the photoemission spectra exhibit non-Fermi liquidbehavior. Moreover, at such low energies, the physics of areal system is likely to be anyway dominated by transverseinteractions.

The lack of dispersion in the ARPES spectra is equallypuzzling. Even for a large-αTLL, where the spectral peaksare considerably smeared, theory [2,9] predicts that theleading edge of the spectral function should exhibit a k-dependence. In this respect, it is interesting to comparethe present results with the data on the 1D organic con-ductor TTF-TCNQ [38]. Also in that case the ARPESspectra suggest non-Fermi liquid behavior, and an expo-nent close to 1, but the (anomalous) spectral features dis-perse with the periodicity of the lattice. Dispersing fea-tures have also been reported for the (half-filled) 1D Mottinsulators SrCuO2 and Sr2CuO3 [39,40].

The absence of dispersion suggest that, within theprobing depth of photoemission, the electronic states ofthe Bechgaard salts are localized. Localization could bedue to surface-specific defects like cleavage steps, or amodified surface stoichiometry, which do not affect thebulk of the sample. The peculiar lineshapes of the angle-integrated and angle-resolved spectra, and the absenceof dispersion, could be considered as an indirect man-ifestation of the TLL phenomenology (via the extremesensitivity to defect-induced localization) and strong 1Dcorrelations. Interestingly, in a TLL with impurities, thevalues of Kρ are not modified, but the usual criticalexponents are replaced by new, renormalized “boundaryexponents” [41,42]. In a 1/4 filled system, the criticalKρ = 1/4 for a Mott transition would yield α = 1.5.Therefore, in the presence of impurities, exponents as largeas 1.5 may be compatible with a small charge gap. Ifsuch large α values are actually realized, we can expectthem to smear any subtle differences between the vari-ous Bechgaard salts, and thus yield the observed material-independent lineshape. Of course, the relative rigid shiftreflecting overall variations of the chemical potential,would still survive.

Focusing now our attention on the optical response(Fig. 4), we note that it is mainly characterized bythe gap-like feature in all compounds and by the nar-row zero frequency mode in the (TMTSF) salts only. Inboth cases, due to full charge transfer from the organicmolecule to the counter ions, the TMTTF or TMTSFstacks have a quarter-filled hole band. There is also a mod-erate dimerization, which is somewhat more significant forthe TMTTF family [4]. Therefore, depending on the im-portance of this dimerization, the band can be describedas either half-filled (for a strong dimerization effect) orquarter-filled (for weak dimerization). Due to the com-mensurate filling, a strictly one-dimensional (Luttinger)model is expected to lead to a Mott insulating behaviour(Fig. 1b). Indeed, the (TMTTF)2X salts, with X = PF6 orBr, are insulators at low temperatures [4] with a substan-tial (Mott) charge gap (see Figs. 3 and 4). For these com-pounds the correlation gap is so large that the interchainhopping (defined by tb) is suppressed by the insulatingnature of the 1D phase and is not relevant.

It thus seems very natural to interpret the high fre-quency part of the optical conductivity in terms of a Mottinsulator (Fig. 1b). Due to the apparent contradiction ofhaving a rather large (Mott) correlation gap (∼ 12 meV)and a good metallic dc conductivity in the (TMTSF) fam-ily, it was proposed that the peak structure was due to thedimerization gap ∆dim [31,43]. This would indeed be thecase for an extremely strong (nearly infinite) repulsion,with the quarter-filled band being transformed into a half-filled band of (nearly noninteracting) spinless fermions. Itwas then argued that the real charge gap of the problemwas smaller, on the order of 50 K.

However, such an interpretation fails to reproducethe observed frequency dependence above the peak inconductivity. At frequencies greater than tb, the inter-chain electron transfer is irrelevant and calculations basedon the 1D Hubbard model should be appropriate. Suchcalculations result in a frequency-dependent conductiv-ity σ1(ω) ∼ ω−γ (where γ = 4n2Kρ − 5) for frequen-cies greater than tb and Egap but less than the on-chain bandwidth 4ta (Fig. 1b) [3]. Our results can bedescribed with an exponent γ = 1.3 for both (TMTSF)2Xcompounds [7,12]. Using the same type of analysis forthe conductivity as in reference [37], and attributing thepeak to the dimerization gap, results in σ1(ω) ∼ 1/ω3 forω � ∆, as in a simple semiconductor (corresponding tonearly free spinless fermions). The observed power law (seeFig. 4 in Ref. [12]) differs significantly from this prediction,making such an interpretation of the data very unlikely.The exponent γ can in principle be used to obtain theLuttinger liquid parameter Kρ, which controls the decayof all correlation functions [3,7]. From our value for γ andthe assumption that quarter-filled band Umklapp scatter-ing (i.e., with n = 2 then γ = 16Kρ − 5) is dominant inthe TMTSF family, we obtain Kρ ∼ 0.23 [7], which is inreasonable agreement with photoemission (Fig. 3) [10,11]and transport data [17,20].

We now turn to the issue about the apparent contradic-tion between a good metallic dc conductivity and a largeMott gap in the (TMTSF) family. As anticipated above,such a situation is realized when the system is dopedslightly away from commensurate filling (Fig. 1b) [3]. In-deed, this is what seems to be observed here (Fig. 4), withthe “Drude” peak in the TMTSF family containing only1% of the carriers (i.e., 1% of the total spectral weight ob-tained by integrating σ1(ω) up to ωc ∼ 1 eV). Althoughno real doping exists from a chemistry point of view, onecould attribute such a deviation from commensurability tothe effects of interchain hopping. If single-particle hopping(tb) between chains is relevant, small deviations from com-mensurate filling due to the warping of the Fermi surfaceexist, and should lead to effects equivalent to real dopingon a single chain. Of course, such a picture is only a poorman’s way of viewing the low-frequency structure. Sincethe interchain hopping is relevant, the low-frequency peakshould in principle be described by a full two-dimensionaltheory of interacting fermions [3].

The dimensionality crossover, induced by the increas-ing tb upon pressure or by changing the chemistry from


Fig. 5. The pressure dependence of the (Mott) correlationgap, as established by different experimental methods, and ofthe transfer integral, perpendicular to the chains, tb, for theBechgaard salts. The horizontal scale was derived with the re-sults of pressure studies [4,20].

the TMTTF to the TMTSF family, is one of the centralissues. There is a well-established order for tb among thefour salts investigated. The (TMTTF)2X analogs are moreanisotropic, and the transfer integrals are approximatelygiven by ta:tb:tc = 250:10:1 meV [4]. For the (TMTSF)2Xanalogs, the transfer integrals are about 250:25:1 meV.The values for both groups of salts are in broad agreementwith tight-binding model calculations and with the trendindicated by the plasma frequency [7,12,44]. To arrive ata scale for tb, we took the calculated values as averagesfor the (TMTSF)2X and (TMTTF)2X salts, respectively,and assumed that pressure changes tb in a linear fashion.The positions of the various salts along the horizontal axisof Figure 5 reflect this choice [12], with pressure valuestaken from the literature; such a scale has been widelyused when discussing the broken symmetry ground statesof these materials [4].

The solid line in Figure 5 represents the overall be-haviour of the correlation gap (see also Figs. 3 and 4).Various experiments give slightly different values of thegap. This is probably due to the differences in the cur-vature of the band which is scanned differently by dif-ferent experiments, or due to the different spectral re-sponse functions involved. The decrease going from the(TMTTF)2X to the (TMTSF)2X analogs may representvarious factors [45], such as the decreasing degree of dimer-ization and the slight increase in the bandwidth along thechain direction, as evidenced by the greater value of theplasma frequency measured along the chain direction inthe (TMTSF)2X salts [12,31]. The dotted line represent-ing 2tb (this is half the bandwidth perpendicular to thechains in the tight-binding approximation) crosses the full

line displaying the behaviour of Egap between the saltsexhibiting insulating and metallic behaviour, whereas thedotted line representing tb crosses the solid line betweenthe two metallic salts. Therefore, our experiments stronglysuggest that a crossover from a non-conducting to a con-ducting state occurs when the unrenormalized single par-ticle transfer integral between the chains exceeds the cor-relation gap by a factor A, which is on the order of butsomewhat greater than 1.

Additional evidence for a pronounced qualitative dif-ference between states with Atb < Egap and Atb > Egap

is given by plasma frequency studies along the b′ direc-tion (i.e., perpendicular to the chain). As shown in ref-erence [12], there is no well-defined plasma frequency forthe insulating state, and we regard this as evidence forthe confinement [46] of electrons on individual chains. Infact, the reflectivity has a temperature independent over-damped like behaviour. Conversely, the electrons becomedeconfined as soon as Atb ∼ Egap (Fig. 5). Such a decon-finement is manifested by the onset of a sharp plasmaedge in the low-temperature reflectivity spectra of the(TMTSF) salts along the b′ axis [12]. This conclusion isnot entirely unexpected: a simple argument (the same asone would advance for a band-crossing transition for anuncorrelated band semiconductor) would suggest that tocreate an electron hole pair with the electron and hole re-siding on neighbouring chains, an energy comparable tothe gap would be required.

Various theories [46–50] suggest a strong renor-malization of the relevant interchain transfer inte-gral teff

b = tb(tb/ta)(α/1−α) [48], substantially smallerthan tb, for coupled Luttinger liquids. Some of thesestudies [46–49], however, do not take into account the pe-riodicity of the underlying lattice and the resulting Umk-lapp scattering. Such a scattering has a marked influ-ence on the effect of interchain transfer. A renormalizationgroup treatment [49] of two coupled Hubbard chains pre-dicts a crossover between confinement (that is, no inter-chain single-electron charge transfer) and deconfinement,at Ateff

b = Egap, with the value of A estimated to be be-tween 1.8 and 2.3. A transition or crossover from an in-sulator to a metal has also been conjectured by Bourbon-nais [50], on the basis of studies of arrays of coupled chains,where also Umklapp scattering has been taken into ac-count. We notice that, for the large α exponents discussedpreviously, the above formula would yield unreasonablylow values of teff

b . Such small values are both incompatiblewith teff

b = Egap/A ∼ 10−20 meV estimated from exper-iment, and with the observed metallic behaviour in theTMTSF salts at low frequency [7].

Discrepancies between theoretical predictions and ex-perimental estimates are not totally surprising, if one con-siders that the experiment probes the transverse opticalresponse over an energy scale of about 0.1 eV. At theseenergies, self-energy effects at the origin of the renormal-ization of tb may be irrelevant. It follows that from optics,teffb can be closer to the bare tb. In that sense, the onset

of the transverse plasma edge as a function of (chemical)


pressure may not coincide with the one found from low-energy probes like dc transport [20] and NMR [35].

We also note that, in the absence of pressure-dependent optical studies, it remains to be determinedwhether the onset of the transverse plasma edge [12] whichwe observe going from the (TMTTF)2X to (TMTSF)2Xsalts, coincides with the insulator-to-metal transitionfound in transport [20] and nuclear magnetic resonance(NMR) measurements [35]. Although optical experimentsunder pressure are difficult to conduct, studies of the pres-sure dependence of the dielectric constant, combined withdc transport data, could clarify this issue.

The existence of a gap feature in the metallic state,containing nearly all of the spectral weight, is at firstsight similar to what is expected for a band-crossing tran-sition for simple semiconductors, which would result ina semimetallic state. However, the nearly temperature-independent magnetic susceptibility [4], which givesstrong evidence for a gapless spin excitation spectrum(this has often been interpreted as a Pauli susceptibility oras the susceptibility due to a large exchange interaction),demonstrates that the state is not a simple semimetal.The existence of a gap, or pseudogap in the charge exci-tations (Figs. 3 and 4) with the absence of a gap for spinexcitations, indicates charge-spin separation in the metal-lic state. This charge-spin separation is, however, distinctfrom that of a 1D TLL, in which both excitations are gap-less but have different velocities. Here, it is the Umklappscattering which leads to gapped charge excitations. Thenature of the metallic state may be close to that of a doped1D Mott-Hubbard semiconductor [3,51], where the inter-chain transfer results in deviations from half- (or quarter-)filling on each chain and therefore has an effect similar to(self-) doping [3,7,17,52].

4 Conclusion

Both photoemission and optical data reveal the pecu-liarity of the one-dimensional interacting electron gas re-sponse. The unusual spectral features of the Bechgaardsalts prove that these materials are certainly not simpleanisotropic band metals. Clear deviations from the Fermiliquid behaviour have been identified and several aspectshint to a possible manifestation of a Tomonaga-Luttingeror Luther-Emery liquid in the normal phases [16,17].Interestingly, optics and photoemission reveal such devi-ations on different energy scales. The characteristic en-ergy scale in the optical conductivity data is the Mott-Hubbard gap, of about ∼ 12 meV in (TMTSF)2PF6. Thesalient feature of the photoemission spectra is the muchlarger (∼ 102 meV) pseudogap. Both techniques, on theother hand, point to a characteristic Luttinger parameterKρ ∼ 0.2, and therefore to strong, long-range 1D cor-relations. Also, both the photoemission and optics datadiscriminate between the conducting (TMTSF) and theinsulating (TMTTF) salts, with a reasonable agreementon the gap size of the latter.

Several issues concerning the electronic structure ofthese materials are still open, and it is not yet clear

whether a comprehensive description is possible withinthe existing theoretical scenarios. The optical response inthe TMTSF salts has been interpreted in terms of a di-mensionality crossover induced by the interchain coupling.Nevertheless, an incipient 2D Fermi liquid behaviour atlow temperature and frequency [17,20] is de facto de-scribed starting from the 1D TLL theory, instead of atwo-dimensional approach. Even in a 1D framework, thereis no clear justification for using the results of the Lut-tinger model in the presence of a charge gap. It may beargued that, for small gaps, the typical correlations of theTLL liquid will still manifest themselves at frequencies(energies) larger than the gap. However, theoretical workis certainly necessary to put these speculations on firmerground. Also, it remains to be explained why theory pre-dicts the confinement-deconfinement crossover when Egap

is of the order of the renormalized transfer integral teffb ,

while experimentally the bare tb seems to be relevant. Itseems that a theory of the dimensionality crossover incoupled Luttinger liquid that would be completely con-sistent with the present data is still lacking. In fact, itis a common theoretical opinion that a large α exponentshould prevent any coherent transport, even though theMott gap can be overcome by a large tb. As far as pho-toemission is concerned, the absence of dispersion, whichis not a general feature of quasi-1D systems, is puzzling.The ARPES experimental results point towards localizedstates and renormalized exponents near the surface. Thereare indications that these surface effects are related to the1D nature of the materials, but no clear theoretical pic-ture is yet available. Such specific details may eventuallyprevent the development of a comprehensive frameworkfor the spectral properties of the Bechgaard salts. Furtherinvestigations of the effects of disorder, and of possibleanomalous effects in the photoexcitation process in 1D,not considered in a standard approach, could contributeto clarify these discrepancies.

The authors are very grateful to C. Bourbonnais, P.M. Chaikin,M. Dressel, T. Giamarchi, D. Jerome, F. Mila and J. Voit formany illuminating discussions. Research at ETH Zurich andEPF Lausanne was supported by the Swiss National ScienceFoundation. Research at UCLA by NSF grant DMR-9503009and at Indiana University by NSF grant DMR-9414268, andat SRC by NSF grant DMR-95-31009.

References

1. J. Luttinger, J. Math. Phys. 4, 1154 (1963); S. Tomonaga,Prog. Theor. Phys. 5, 554 (1950); for a review, see H.J.Schulz, Int. J. Mod. Phys. B 5, 57 (1991).

2. J. Voit, Eur. Phys. J. B 5, 505 (1998); in Proceedings ofthe NATO Advanced Research Workshop on The Physicsand Mathematical Physics of the Hubbard Model, San Se-bastian, October 3-8, 1993, edited by D. Baeriswyl, D.K.Campbell, J.M.P. Carmelo, F. Guinea, E. Louis (PlenumPress, New York, 1995).

3. T. Giamarchi, Physica B 230-232, 975 (1997).4. D. Jerome, H.J. Schulz, Adv. Phys. 31, 299 (1982).


5. C.S. Jacobsen et al., Phys. Rev. Lett. 46, 1142 (1981);Solid State Commun. 38, 423 (1981); Phys. Rev. B 28,7019 (1983).

6. M. Dressel et al., Phys. Rev. Lett. 77, 398 (1996).7. A. Schwartz et al., Phys. Rev. B 58, 1261 (1998).8. V. Meden, K. Schonhammer, Phys. Rev. B 46, 15753

(1992).9. J. Voit, J. Phys. Cond. Matter 5, 8305 (1993).

10. B. Dardel et al., Europhys. Lett. 24, 687 (1993).11. F. Zwick et al., Phys. Rev. Lett. 79, 3982 (1997).12. V. Vescoli et al., Science 281, 1181 (1998).13. K. Bechgaard et al., Solid State Commun. 33, 1119 (1980).14. G. Gruner, Rev. Mod. Phys. 60, 1129 (1988).15. G. Gruner, in Density Waves in Solids (Addison-Wesley,

Reading, MA, 1994).16. D.G. Clarke et al., Science 279, 2071 (1988).17. C. Bourbonnais, D. Jerome, cond-mat/9903101.18. V.J. Emery et al., Phys. Rev. Lett. 48, 1039 (1982).19. The b′ and c′ directions are perpendicular to the chain

direction a. These directions also define the faces of thesamples on which the optical experiments were conductedand are slightly different from the b and c directions ofthe unit cell because of the triclinic crystal structure. Thissmall difference does not influence the arguments advancedin this work.

20. J. Moser et al., Eur. Phys. J. B 1, 39 (1998).21. C. Coulon et al., J. Phys. France 43, 1059 (1982).22. J.P. Pouget et al., Mol. Cryst. Liq. Cryst. 79, 129 (1982).23. P.M. Grant, J. Phys. Colloq. France 44, C3-847 (1983).24. B. Dardel et al., Phys. Rev. Lett. 67, 3144 (1991).25. A. Sekiyama et al., Phys. Rev. B 51, 13899 (1995).26. T. Takahashi, Phys. Rev. B 53, 1790 (1996).27. Y. Hwu et al., Phys. Rev. B 46, 13624 (1992).

28. G.-H. Gweon et al., J. Phys. Cond. Matter 8, 9923 (1993).29. M. Grioni et al., Phys. Scr. T 66, 172 (1996).30. F. Zwick et al., Solid State Commun. 113, 179 (2000).31. D. Pedron et al., Phys. Rev. B 49, 10893 (1994).32. S.E. Brown (private communication).33. N. Cao, T. Timusk, K. Bechgaard, J. Phys. I France 6,

1719 (1996).34. W. Henderson et al., Eur. Phys. J. B 11, 365 (1999).35. P. Wzietek et al., J. Phys. I France 3, 171 (1993).36. C. Bourbonnais et al., J. Phys. Lett. France 45, L-755

(1984).37. T. Giamarchi, Phys. Rev. B 44, 2905 (1991).38. F. Zwick et al., Phys. Rev. Lett. 81, 2974 (1998).39. C. Kim et al., Phys. Rev. Lett. 77, 4054 (1996).40. H. Fujisawa et al., Solid State Commun. 106, 543 (1998).41. S. Eggert, H. Johanneson, A. Mattson, Phys. Rev. Lett.

76, 1505 (1996).42. Y. Wang, J. Voit, F.-C. Pu, Phys. Rev. B 54, 8491 (1996).43. F. Favand, F. Mila, Phys. Rev. B 54, 10435 (1996).44. L. Ducasse et al., J. Phys. C 19, 3805 (1986).45. K. Penc, F. Mila, Phys. Rev. B 50, 11429 (1996).46. P.W. Anderson, Proc. Natl. Acad. Sci. U.S.A. 92, 6668

(1995).47. F. Mila, D. Poilblanc, Phys. Rev. Lett. 76, 287 (1996).48. C. Bourbonnais, L.G. Caron, Int. J. Mod. Phys. B 5, 1033

(1998).49. Y. Suzumura et al., Phys. Rev. B 57, R15040 (1991).50. C. Bourbonnais, in Strongly interacting fermions and high

Tc superconductivity, edited by B. Doucot, J. Zinn-Justin(Elsevier, Amsterdam, 1995), p. 307.

51. H. Mori et al., J. Phys. Soc. Jap. 63, 1639 (1994).52. N. Bulut et al., Phys. Rev. Lett. 72, 705 (1994).

low frequency dielectric spectroscopy of the peierls-mott insulating state in the deuterated...

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