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Dynamical Properties of the One-Dimensional Band Insulator ���NbSe4���3I

V. Vescoli,1 F. Zwick,2 J. Voit,3 H. Berger,2 M. Zacchigna,2 L. Degiorgi,1 M. Grioni,2 and G. Grüner4

1Laboratorium für Festkörperphysik, ETH Zurich, CH-8093 Zurich, Switzerland2Institut de Physique Appliquée, Ecole Polytechnique Fédérale, CH-1015 Lausanne, Switzerland

3Fakultät für Physik, Albert-Ludwigs-Universität, D-79104 Freiburg, Germany4Department of Physics, University of California, Los Angeles, California 90095-1547

(Received 15 July 1999)

Optical and photoemission experiments reveal unexpected spectral signatures of one-dimensional bandinsulators. In the model compound �NbSe4�3I the optical conductivity decays as a power law s1�v� �v24.25 above a sharp gap edge. Photoemission observes both the valence and a shadow band, producedby a commensurate superstructure. We identify an optical and photoemission band gap consistent withother measurements but much smaller than the energy scale defined by the dispersion of the band peakin the photoemission spectra.

PACS numbers: 71.10.Pm, 71.20.Ps, 78.30.Hv, 79.60.– i

One-dimensional metals have been a fascinating topic ofresearch, both theoretically and experimentally. Much ofthe interest stems from the theoretical prediction that Fermiliquid theory breaks down in one dimension (1D), and thata novel quantum liquid is formed, the Tomonaga-Luttingerliquid [1]. It carries no quasiparticles, but only collectiveexcitations: the charge and spin of the electron separate,and, in addition, correlation functions decay with powerlaws of space and time variables �x, t� with anomalousexponents.

Experimental evidence for Luttinger liquid (LL) corre-lations has been collected in several classes of materials:(i) organic conductors such as the Bechgaard salts, whereNMR, photoemission, optics, and interchain transport sup-port a LL state [2], or TTF-TCNQ where angle resolvedphotoemission spectra (ARPES) [3] and diffuse x-ray scat-tering [4] are consistent with a LL; (ii) the inorganic chaincompound Li0.9Mo6O17 where a recent ARPES experi-ment apparently has observed LL line shapes [5], althoughthis is disputed by others [6]; (iii) semiconductor quantumwires where there is supporting evidence from transport[7]; (iv) carbon nanotubes, again with transport evidence[8]. There are other states possible for 1D electrons: Mottinsulators, spin-gapped Luttinger liquids, and fluctuatingPeierls insulators. Unusual spectral properties have beenobserved and interpreted in materials thought to fall intothese categories [9–11].

Here, we explore the possibility that even 1D band in-sulators, considered to be of little interest to date, maydeviate significantly—at least in their dynamical proper-ties—from standard preconceptions. By band insulator,we mean a system which is insulating on the basis of crys-tal periodicity and electron counting at all temperatures.We present a high-resolution investigation of optical andphotoemission properties at 300 K of the prototypical 1Dband insulator �NbSe4�3I [12]. The combination of bothexperiments is crucially important in obtaining a completepicture of the dynamical properties. Optical spectroscopyis a bulk probe of the total charge density, while ARPES

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is sensitive to the lattice periodicity and to the individualquasiparticles. Moreover, while for nearly free electronsthere is a direct relation between single-particle propertiesprobed by ARPES and two-particle properties measured byoptics, no general relation exists for correlated systems.

Nb chains, surrounded by Se4 rectangles, running alongthe c axis, give this material a strong 1D character, dueto the directional overlap of Nb 4dz2 orbitals [13]. If theSe4 units are ignored, the elementary unit cell of the roomtemperature structure comprises three Nb ions per chainwith distances of 3.25, 3.25, and 3.06 Å, and contains twochains. Iodine ions, located between the chains, act ascharge reservoirs, and determine the band filling. The va-lence band, which extends between 6p�c �c � 9.56 Å�,is completely filled and separated by a finite gap from theempty conduction band. The transport properties indicatea gap in the range of 0.2 to 0.4 eV [14]. The 1D bands aresplit by 2t� if the two chains in the unit cell are coupledby t�. If the 45± rotation of subsequent Se4 rectanglesaround the chain axis is included explicitly, the unit cell istwice as large, and the valence bands will be folded backat 6p�2c.

For a 1D band insulator, we expect the following opticaland photoemission properties: the optical conductivity willstart at the gap edge with a sharp singularity as s�v� ��v 2 2D�21�2 and decay, towards high frequencies, ass�v� � v23 if the lattice is assumed to be rigid and onlyumklapp scattering off the single-period lattice potentialis possible [15,16], or as s�v� � v22 when coupling tophonons is included [16,17]. Thermal and quantum lat-tice fluctuations can smear out the gap-edge singularityand produce subgap absorption [18]. In photoemission,one expects a spectral function A�k, v� � d���v 2 E�k����,where E�k� is the dispersion of the occupied valence band.No theory for the line shapes is available for 1D band in-sulators but, by analogy with the 3D case, it is expectedthat finite lifetimes, phonon broadening, as well as finiteexperimental angular resolution, will nearly symmetricallybroaden the line. This is not what we observe, nor do the

© 2000 The American Physical Society

VOLUME 84, NUMBER 6 P H Y S I C A L R E V I E W L E T T E R S 7 FEBRUARY 2000

dynamical properties conform to any published theory, orto the properties of other known classes of materials. Onthe other hand, we show the optical transitions to be con-sistent with the binding energies of the dispersing featuresobserved by photoemission. This highlights the unusualline shapes observed in both experiments, and the absenceof an adequate theoretical framework for their description.

Single crystal samples of �NbSe4�3I were grown, as inRef. [14], in the form of shiny platelets of typical dimen-sions 4 3 1 3 0.2 mm3. The optical reflectivity was ob-tained from the far infrared up to the ultraviolet with ourvariety of spectrometers, described elsewhere [15]. Theoptical conductivity was calculated by a Kramers-Kronigtransformation of the reflectivity spectra. We measuredARPES by a hemispherical electrostatic analyzer, usingthe HeI line �hn � 21.2 eV� of a resonance lamp. Theinstrumental experimental energy and momentum resolu-tion were 10 meV and 0.02 Å21. Clean surfaces for theARPES experiments were prepared by cleavage at a basepressure of 1 3 10210 torr and measured at 300 K. Thepossibility of spurious effects due to sample charging wascarefully investigated, and excluded.

Figure 1 shows the optical reflectivity and the real parts1�v� of the optical conductivity of �NbSe4�3I at 300 K,for light polarized along �E k c� and perpendicular �E�c�to the chains. The far-infrared spectral range is character-ized by several sharp phonon modes for both polarizationdirections (see also inset). For E k c, we observe a first op-tical transition between 0.5 and 1 eV. Further transitionsabove 1 eV are rather independent of polarization. Thefar-infrared part of our spectra agrees with previous resultsin the restricted spectral range where those were collected[12]. The reflectivity spectra and even more clearly s1�v�demonstrate the strong (optical) anisotropy of this material.Both the phonon spectrum and the spectral range aroundthe gap excitation are different along or perpendicular tothe chain axis, giving clear evidence for the low dimen-sionality of the crystal structure in �NbSe4�3I.

Figure 2 summarizes the photoemission results. Theintensity map, which illustrates the valence band disper-sion, was extracted from ARPES spectra collected as afunction of emission angle along the 1D chain direction.Spectra measured in a direction perpendicular to the chains(not shown) do not reveal dispersion, as expected fromthe quasi-1D character of the band states. The valenceband disperses upwards from the G point, the center of theBrillouin zone (BZ), attaining a minimum binding energyof 0.75 eV at k1,2 � 60.33 6 0.02 Å21 � p�c, in ex-cellent agreement with the calculated band structure [13].The dispersing feature recedes from the chemical potentialbeyond these points, into the second BZ, with a stronglyreduced intensity. The intensity map also shows a weakerfeature, with a maximum at G, intersecting the main bandat k � 60.17 Å21 � 6p�2c.

We identify the optical transition at 0.5 � 1 eV withthe fundamental gap. This assignment is due to the 1D

FIG. 1. Reflectivity and real part of the optical conductivity of�NbSe4�3I at 300 K and for light polarized along and perpendic-ular to the c axis. The inset is an enlargement of the far-infraredspectral range, showing the phonon modes.

nature of the excitation, and to a strong similarity with afeature in the closely related material �TaSe4�2I. There,an unambiguous identification is possible by following itsevolution through a Peierls metal-insulator transition [19].The transitions above 1 eV then are interband transitionsinto higher-lying electronic bands, consistent with theirrather isotropic oscillator strength.

The determination of the valence band maximum fromphotoemission is less straightforward. In three- andtwo-dimensional semiconductors it is usually made fromthe ARPES peak positions, reflecting the quasiparticleenergies. This approach yields gap values consistentwith optics, as in a recent high-resolution photoemission-inverse photoemission study of the layered compoundWSe2 [20]. In �NbSe4�3I, however, the highest peakposition is at 0.75 eV below EF , incompatible with theoptical gap 2Dopt � 0.5 eV (Fig. 1). If the leading edgeof our ARPES spectrum at k � p�c is extrapolated tothe baseline (inset in Fig. 4), the intersection occurs atan energy D� � 0.3 eV. While 2D� cannot be directlyinterpreted as the gap size, this energy is close to the

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Wave vector (Å-1)

2

1

0B

indi

ng E

nerg

y (e

V)

0 0.25-0.25

EF=0

FIG. 2. ARPES intensity map �hn � 21.2 eV; T � 300 K�of �NbSe4�3I. Each column represents the intensity of an ARPESspectrum collected at the indicated wave vector along the 1D�GZ� chain direction.

optical gap. Both values are larger than gap estimatesfrom transport [14]. A determination of (pseudo)gapsizes based on peak positions, previously suggested [21]for �TaSe4�2I, is apparently not permissible in 1D. Thediscrepancy between gap and peak position is surprisingin a quasiparticle perspective and inconsistent with anybroadening mechanism. Nevertheless, it emerges as ageneral feature of 1D materials. Even in 1D metals, thepeak of the dispersing line shape is well removed from theFermi energy. Only the extrapolation of the leading edge,intersecting the baseline at EF , shows that the excitationsare indeed gapless. This is observed both in �TaSe4�2I [10]above the Peierls transition, and in organic conductors [3].

The inverted band around G has the same line shape(not shown), and extends up to the same binding energy asthe main band. The two bands intersect at the boundariesof the reduced BZ associated with the doubled periodic-ity induced by the Se4 groups. Other Nb bands are ruledout by band structure calculations [13], and detailed cal-culations for �TaSe4�2I show that I 5p bands should havemuch smaller dispersions [22], incompatible with our data.We interpret the second dispersive feature as an umklappshadow of the main band, from the potential of the Se4units. As will be discussed elsewhere, the ratio of inten-sities of the shadow and the main bands directly reflectsthe ratio of the corresponding lattice potentials. To thebest of our knowledge, this is the first clear observation ofshadow bands outside the high-Tc cuprate family. Unlikethe cuprates, where they may be associated with antifer-romagnetic fluctuations, in the present case the origin isstructural. Our data imply that the potential of the Se4

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rectangles must not be ignored in band structure calcula-tions [13], and confirm that ARPES is sensitive to intrinsicbulk features of the electronic structure.

The line shapes of the optical and ARPES transitions areunusual and cannot be linked by a quasiparticle picture, orother theories. For the optical gap edge absorption at about0.5 eV, we do not observe clearly the predicted squaredroot singularity, although the data come rather close andcertainly show a sharper feature than in any other 1D ma-terial studied to date [23]. There may still be some thermalbroadening, or smearing from lattice fluctuations. The op-tical gap has a high frequency tail following the power laws1�v� � v2g with g � 4.25, as shown in Fig. 3. The fitcan be refined and extended to higher energies by model-ing the transitions above the fundamental gap by Lorentzoscillators (not shown), and subtracting them from the to-tal optical conductivity. This yields g � 4.4 6 0.2. Thisexponent is distinctly different from what has been mea-sured or predicted in other 1D systems. In typical 1D Mottinsulators like the organic Bechgaard salts, g � 1.3 is ob-served, in line with the theoretical predictions [15]. Impor-tantly, our g is also larger than the values g � 3, predictedfor a rigid 1D band insulator, or g � 2 when phonons areincluded [17], as observed in charge density wave (CDW)systems [24]. We have checked that the discrepancy tostandard models for s1�v� is outside experimental uncer-tainties. That our observed g value is larger than thosepredicted suggests that current relaxation involves a lessefficient mechanism in �NbSe4�3I than those treated theo-retically hitherto.

Figure 4 shows a superposition of line shapes forp�2c , k , p�c, and demonstrates that the line shapeis independent of k. It is certainly not a Lorentzian,nor Gaussian, nor any other standard shape. The total

FIG. 3. Log-log plot of the optical conductivity of �NbSe4�3I at300 K in the midinfrared spectral range, showing the powerlawbehavior (dashed straight line) at the high frequency tail of theoptical gap.

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FIG. 4. ARPES spectra of �NbSe4�3I for wave vectorsp�2c , k , p�c. The peak intensities and energy positionshave been normalized to those of the k � p�c spectrum toillustrate the k-independent line shape. A satisfactory fit istentatively obtained by two Gaussian peaks of equal width�FWHM � 0.29 eV� and 5:2 intensity ratio, separated by0.20 eV. Inset: a linear extrapolation of the k � p�c spectrumidentifies a baseline intersection D� � 0.3 eV.

linewidth of 300 meV is much larger than the experimen-tal resolution or the expected phonon broadening. The lineis asymmetric, and its leading edge is broader. A closeinspection reveals two different slopes on the leading edgesuggesting, together with the important width, that theline is composed of two underlying peaks dispersing inparallel. An excellent fit to the spectrum can be obtained,for instance, by two Gaussian peaks of identical widthand different intensity, as indicated in the figure. Contraryto fits with a phenomenological asymmetric line shapewhose theoretical underpinning would remain obscure,the two peaks emerging from the Gaussian fit may beassociated with the splitting of the two Nb 4dz2 bands inthe unit cell due to interchain coupling. This has beenestimated from band structure calculation to be about0.25 eV [13], and is consistent with the data. Spectraclose to p�2c exhibit a low energy tail which is visible inFig. 4 and which is due to the inverted band centered atG. The symmetric shapes of the two lines underlying oursignal are apparently inconsistent with proposed extrinsiceffects (energy losses) giving broad high-energy tails[25]. Moreover, such mechanisms cannot explain thedisplacement of the peak of the signal to binding energiesmuch larger than the gap.

In summary, our high-resolution data on �NbSe4�3I showunexpected spectral signatures in a 1D band insulator.Specifically, the optical conductivity exhibits very inef-ficient current relaxation, described by s1�v� � v24.25.Photoemission shows shadow bands, and a complex lineshape. The comparison of the two spectroscopies allowsa consistent identification of the gap around the chemi-cal potential, and shows that the extrapolation of the lead-

ing edge of the ARPES line determines the valence bandmaximum. However, there is a major discrepancy betweenthe gap energy scale ��0.3 eV� identified in this way, andthe ARPES peak position ��0.75 eV� whose origin is ob-scure. Apparently, 1D band insulators are not so well un-derstood as might be assumed. To make progress, it couldbe interesting to perform similar correlated experiments onother well-understood 1D insulators. Obvious candidatesare the insulating phases of Peierls systems, but also poly-mers, e.g., polyacetylene, or especially polydiacetylene,for which single crystals are available.

We would like to acknowledge discussions with R.Claessen, L. Forró, T. Giamarchi, P. Monceau, andA. Painelli. This work has been supported by theSwiss National Science Foundation, and by DeutscheForschungsgemeinschaft (J. V.).

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