Probing charge density wave phases and the Mott transition in 1T-TaS_2 by inelastic light scattering
S. ?ur?i? Mijin, A. Baum, J. Bekaert, A. ?olaji?, J. Peši?, Y. Liu, Ge He, M. V. Miloševi?, C. Petrovic, Z. V. Popovi?, R. Hackl, N. Lazarevi?
PProbing charge density wave phases and Mott transition in T -TaS by inelastic lightscattering S. Djurdji´c Mijin, A. Baum, J. Bekaert, A. ˇSolaji´c, J. Peˇsi´c, Y. Liu, ∗ Ge He, M. V. Miloˇsevi´c, C. Petrovic, Z. V. Popovi´c,
1, 5
R. Hackl, and N. Lazarevi´c Center for Solid State Physics and New Materials, Institute of Physics Belgrade,University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia Walther Meissner Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium Condensed Matter Physics and Materials Science Department,Brookhaven National Laboratory, Upton, NY 11973-5000, USA Serbian Academy of Sciences and Arts, Knez Mihailova 35, 11000 Belgrade, Serbia (Dated: February 10, 2021)We present a polarization-resolved, high-resolution Raman scattering study of the three consec-utive charge density wave (CDW) regimes in 1 T -TaS single crystals, supported by ab initio cal-culations. Our analysis of the spectra within the low-temperature commensurate (C-CDW) regimeshows P3 symmetry of the system, thus excluding the previously proposed triclinic stacking of the“star-of-David” structure, and promoting trigonal or hexagonal stacking instead. The spectra of thehigh-temperature incommensurate (IC-CDW) phase directly project the phonon density of statesdue to the breaking of the translational invariance, supplemented by sizeable electron-phonon cou-pling. Between 200 and 352 K, our Raman spectra show contributions from both the IC-CDW andthe C-CDW phase, indicating their coexistence in the so-called nearly-commensurate (NC-CDW)phase. The temperature-dependence of the symmetry-resolved Raman conductivity indicates thestepwise reduction of the density of states in the CDW phases, followed by a Mott transition withinthe C-CDW phase. We determine the size of the Mott gap to be Ω gap ≈ −
190 meV, and trackits temperature dependence.
I. INTRODUCTION
Quasi-two-dimensional transition metal dichalco-genides (TMDs) have been in the focus of various sci-entific investigations over the last 30 years, mostly dueto the plethora of charge density wave (CDW) phases.Among all TMD compounds 1 T -TaS stands out becauseof its unique and rich electronic phase diagram [1–4]. Itexperiences phase transitions at relatively high temper-atures, making it easily accessible for investigation and,mainly for the hysteresis effects, attractive for potentialapplications such as data storage [5], information pro-cessing [6] or voltage-controlled oscillators [7].The cascade of phase transitions as a function oftemperature includes the transition from the normalmetallic to the incommensurate CDW (IC-CDW) phase,the nearly-commensurate CDW (NC-CDW) phase andthe commensurate CDW (C-CDW) phase occurring ataround T IC = 554 K, T NC = 355 K and in the temper-ature range from T C ↓ = 180 K to T C ↑ = 230 K, respec-tively. Recent studies indicate the possibility of yet an-other phase transition in 1 T -TaS at T H =80 K, namedthe hidden CDW state [8–10]. This discovery led to anew boost in attention for 1 T -TaS .Upon lowering the temperature to T IC = 554 K, thenormal metallic state structure, described by the spacegroup - P¯3m1 (D d3d ), [11] transforms into the IC-CDW ∗ Present address: Los Alamos National Laboratory, Los Alamos,New Mexico 87545, USA state. As will be demonstrated here, the IC-CDW do-mains shrink upon further temperature reduction untilthey gradually disappear, giving place to the C-CDWordered state. This region in the phase diagram between554 K and roughly 200 K is characterized by the coexis-tence of the IC-CDW and C-CDW phases and is oftenrefereed to as NC-CDW. At the transition temperature T C IC-CDW domains completely vanish [12] and a newlattice symmetry is established. There is general consen-sus about the formation of “star-of-David” clusters within-plane √ a × √ a lattice reconstruction, wherebytwelve Ta atoms are grouped around the 13 th Ta atom[13, 14]. In spite of extensive investigations, both ex-perimental and theoretical, it remains an open questionwhether the stacking of “star-of-David” clusters is tri-clinic, trigonal, hexagonal or a combination thereof [13–17]. The C-CDW phase is believed to be an insulator[1, 18–20] with a gap of around 100 meV [11]. Very re-cent theoretical studies based on density-functional the-ory (DFT) find an additional ordering pattern along thecrystallographic c -axis which renders the material three-dimensional metallic. The related has a width of approx-imately 0.5 eV along k z and becomes gapped at the Fermienergy E F in the C-CDW phase [21, 22].Nearly all of the previously reported results for opticalphonons in 1 T -TaS are based on Raman spectroscopy onthe C-CDW phase and on temperature-dependent mea-surements in a narrow range around the NC-CDW toC-CDW phase transition [11, 13, 15–17]. In this articlewe present temperature-dependent polarization-resolvedRaman measurements in the temperature range from 4 K a r X i v : . [ c ond - m a t . s t r- e l ] F e b to 370 K covering all three CDW regimes of 1 T -TaS .Our analysis of the C-CDW phase confirms the symme-try to be P3, while the NC-CDW phase is confirmedas a mixed regime of commensurate and incommensu-rate domains. The spectra of the IC-CDW phase mainlyproject the phonon density of states due to breaking oftranslation invariance and sizeable electron-phonon cou-pling. The growth of the CDW gap upon cooling, fol-lowed by the opening of the Mott gap is traced via theinitial slope of the symmetry-resolved spectra. The sizeof 170-190 meV and the temperature dependence of theMott gap are directly determined from high-energy Ra-man data. II. EXPERIMENTAL AND NUMERICALMETHODS
The preparation of the studied 1 T -TaS single crystalsis described elsewhere [23–26]. Calibrated customizedRaman scattering equipment was used to obtain the spec-tra. Temperature-dependent measurements were per-formed with sample attached to the cold finger of a He-flow cryostat. All measurements were performed under ahigh vacuum of approximately 5 · − Pa. The 575 nmlaser line of a diode-pumped Coherent GENESIS MX-SLM solid state laser was used as an excitation source.Additional measurements with the 458 nm and 514 nmlaser lines were performed with a Coherent Innova 304CArgon ion laser. All spectra shown are corrected for thesensitivity of the instrument and the Bose factor, yield-ing the imaginary part of the Raman susceptibility Rχ (cid:48)(cid:48) where R is an experimental constant. The linear polar-izations of the incident and scattered light are denotedas e i and e s , respectively, and are always perpendicu-lar to the c -axis. Low energy data up to 550 cm − wereacquired in steps of ∆Ω = 1 cm − with a resolution of σ ≈ − . The symmetric phonon lines were mod-elled using Voigt profiles where the width of the Gaussianpart is given by σ . For spectra up to higher energies thestep width and resolution were set at ∆Ω = 50 cm − and σ ≈
20 cm − , respectively. The Raman tensors for theD point group are given in Table I. Accordingly, par-allel linear polarizations project both A g and E g sym-metries, while crossed linear polarizations only project E g . The pure A g response then can be extracted bysubtraction.We have performed DFT calculations as implementedin the ABINIT package [27]. We have used the Perdew-Burke-Ernzerhof (PBE) functional, an energy cutoff of 50Ha for the planewave basis, and we have included spin-orbit coupling by means of fully relativistic Goedeckerpseudopotentials [28, 29], where Ta-5d and S-3s states are treated as valence electrons. The crystal struc-ture was relaxed so that forces on each atom were below10 µ eV/˚A and the total stress on the unit cell below 1bar, yielding lattice parameters a = 3 .
44 ˚A and c = 6 . TABLE I. Raman tensors for trigonal systems (point groupD ) A g = a a
00 0 b E g = c − c d d E g = − c − d − c − d coupling (EPC) were obtained from density functionalperturbation theory (DFPT) calculations, also withinABINIT [30]. Here, we have used an 18 × × k -pointgrid for the electron wave vectors and a 6 × × q -pointgrid for the phonon wave vectors. For the electronic oc-cupation we employed Fermi-Dirac smearing with broad-ening factor σ FD = 0 .
01 Ha, which is sufficiently highto avoid unstable phonon modes related to the CDWphases.
III. RESULTS AND DISCUSSIONA. Lattice dynamics of the charge-density waveregimes
1. C-CDW phase
At the lowest temperatures 1 T -TaS exists in the com-mensurate C-CDW phase. Here, the atoms form so called“Star-of-David” clusters. Different studies report eithertriclinic stacking of these clusters leading to P¯1 unit cellsymmetry [14], or trigonal or hexagonal stacking andP3 unit cell symmetry [13, 15–17]. Factor group anal-ysis predicts 57 A g Raman-active modes with identicalpolarization-dependence for P¯1 unit cell symmetry, andalternatively 19 A g + 19 E g Raman-active modes forP3 unit cell symmetry. Our polarized Raman scatter-ing measurements at T = 4 K, measured in two scatter-ing channels, together with the corresponding cumula-tive fits are shown in Figure 1. As it can be seen, wehave observed modes of two different symmetries in therelated scattering channels. This result indicates trigo-nal or hexagonal stacking of the “Star-of-David” clusters.The symmetric phonon lines can be described by Voigtprofiles, the best fit of which is shown as blue (for par-allel light polarizations) and red (crossed polarizations)lines. After fitting Voigt profiles to the Raman spectra,38 phonon modes were singled out. Following the selec-tion rules for A g and E g symmetry modes, 19 wereassigned as A g and 19 as E g symmetry, meaning all ex-pected modes could be identified. The contribution fromeach mode to the cumulative fit is presented in Figure 1as green lines, whereas he complete list of the correspond-ing phonon energies can be found in the Table II of theAppendix A. R c '' ( W ,T ) (counts s-1 mW -1) T = 4 K e i | | e s i ^ e s R a m a n S h i f t W ( c m - 1 ) R c '' ( W ,T ) (counts s-1 mW -1) W ( c m - 1 )E g R a m a n S h i f t W ( c m - 1 )A FIG. 1. Raman spectra at T = 4 K, i.e. in the C-CDW phase,for parallel and crossed light polarizations. Red and bluesolid lines represent fits of the experimental data using Voigtprofiles. The exact energy values are presented in Table II.
2. IC-CDW phase
At the highest experimentally accessible temperatures1 T -TaS adopts the IC-CDW phase. Data collected byRaman scattering at T = 370 K, containing all symme-tries, is shown as a blue solid line in Figure 2. As 1 T -TaS is metallic in this phase [31] we expect the phonon linesto be superimposed on a continuum of electron-hole ex-citations which we approximate using a Drude spectrumshown as a dashed line.[32, 33]Since the IC-CDW phase arises from the normal metal-lic phase, described by space group P¯3m1,[11, 34] it is in-teresting to compare our Raman results on the IC-CDWphase to an ab initio calculation of the phonon dispersionin the normal phase, shown as inset in Fig. 2. Four dif-ferent optical modes were obtained at Γ: E u at 189 cm − (2 × degenerate), E g at 247 cm − (2 × degenerate), A u at342 cm − and A g at 346 cm − . Factor group analysisshows that two of these are Raman-active, namely E g and A g [11].We observe that the calculated phonon eigenvalues of e i || e s R c '' ( W , T ) ( c oun t s s - m W - ) T = 0 K PDOS Ta PDOS SRaman Shift W (cm -1 ) T = 370 K P D O S ( a r b . un i t s ) FIG. 2. Raman response for parallel light polarizations in theIC-CDW phase at 370 K (blue line). The dashed line depictsthe possible electronic continuum. The contributions of theTa- (dark brown) and S atoms (light brown) to the calcu-lated PDOS are shown below. The inset shows the calculatedphonon dispersion of 1 T -TaS in the simple metallic phase,with the electron-phonon coupling ( λ ) of the optical branchesindicated through the color scale. the simple metallic phase at Γ do not closely match theobserved peaks in the experimental spectra of the IC-CDW phase. Rather, these correspond better to the cal-culated phonon density of states (PDOS), depicted inFig. 2. As the momentum transfer by light scatteringis negligible, the projection of the PDOS requires a wayto transfer momentum. We rule out chemical impurityscattering, expected to exist at all temperatures, as thelow-temperature spectra (Fig. 1) show no signs thereof.The additional scattering channel may come from theelectron-phonon coupling (EPC). The calculated EPC, λ ,in the optical modes (inset of Fig. 2) is limited, yet notnegligible, reaching maxima in the lower optical branchesof ∼ . T -TaS is furthermore supported byexperimental results linking a sharp increase in the resis-tivity above the IC-CDW transition temperature to theEPC [34]. It also corroborates calculated [12] and experi-mentally obtained [11] values of the CDW gap, which cor-respond to intermediate to strong EPC [34]. Although,
01 02 03 04 003 06 09 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 001 0 02 0 03 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0T e m p e r a t u r e T K 3 6 0 K A g ( a ) I C - C D W 3 5 2 K 3 3 0
K 2 7 0
K 2 3 5 K R c '' ( W ,T ) (rel. units) ( c ) N C - C D W 2 0 0 K 1 6 5
K 1 0 0
K 4 K R a m a n S h i f t W ( c m - 1 )( e ) C - C D W E g - T a S ( b ) ( d )( f ) FIG. 3. Symmetry-resolved Raman spectra at temperaturesas indicated. Both C-CDW (blue lines) and IC-CDW (redlines) domains yield significant contributions to the Ramanspectra of the NC-CDW phase (green lines).
EPC certainly contributes we believe that the majorityof the additional scattering channels can be traced backto the incommensurate breaking of the translational in-variance upon entering IC-CDW. Thus the ”weighted”PDOS is projected into the Raman spectrum (see Fig. 3(a) and (b)). These ”weighting” factors depend on thespecific symmetries along the phonon branches as well asthe ”new periodicity” and go well beyond the scope ofthis paper.
3. NC-CDW phase
The nearly-commensurate phase is seen as a mixedphase consisting of regions of commensurate and incom-mensurate CDWs [35, 36]. This coexistence of high andlow-temperature phases is observable in our temperaturedependent data as shown in Fig. 3. The spectra for theIC-CDW (red curves) and C-CDW phase (blue curves)are distinctly different, as also visible in the data shownabove (Figs. 1 and 2). The spectra of the NC-CDW phase(235 K < T <
352 K) comprise contributions from bothphases. As 352 K is the highest temperature at which the contributions from the C-CDW phase can be observedin the spectra, we suggest that the phase transition tem-perature from IC-CDW to NC-CDW phase is somewherein between 352 K and 360 K. This conclusion is in goodagreement with experimental results regarding this tran-sition [2–4].
B. Gap evolution
The opening of a typically momentum-dependent gapin the electronic excitation spectrum is a fundamentalproperty of CDW systems which has also been observedin 1 T -TaS [11, 34, 37]. Here, in addition to the CDW, aMott transition at the onset of the C-CDW phase leads toan additional gap opening in the bands close to the the Γpoint [38, 39]. Symmetry-resolved Raman spectroscopycan provide additional information here using the mo-mentum resolution provided by the selection rules.As shown in Fig. 4(a-c), different symmetries projectindividual parts of the Brillouin zone (BZ). The A g ver-tex mainly highlights the area around the Γ point whilethe E g vertices predominantly project the BZ bound-aries. The opening of a gap at the Fermi level reducesthe density of states N F , leading to an increase of theresistivity in the case of 1 T -TaS . This reduction of N F manifests itself also in the Raman spectra which, to ze-roth order, are proportional to N F . As a result the initialslope changes as shown Figs. 4(d-e), which zooms in onthe low energy region of the spectra from Fig. 3. The ini-tial slope of the Raman response, R lim Ω → ∂χ (cid:48)(cid:48) ∂ Ω ∝ N F τ ,where R incorporates all experimental factors. The elec-tronic relaxation Γ ∗ ∝ ( N F τ ) − is proportional to the dcresistivity ρ ( T ). The black lines in Fig. 4(d-g) representthe initial slopes and their temperature dependences ofthe low-energy spectra. The lines comprise carrier relax-ation and gap effects, and we focus only on the relativechanges.Starting in the IC-CDW phase at T = 370 K [Fig. 4(d)]the initial slope is higher for the E g spectrum than for A g symmetry. While the CDW gap started to open al-ready at 554 K around the M points [38], which are high-lighted by the A g vertex, the Fermi surface projected bythe E g vertex continues to exist. Thus, we may interpretthe different slopes as a manifestation of a momentumdependent gap in the IC-CDW phase and assume over-all intensity effects to be symmetry-independent for alltemperatures. At T = 352 K [Fig. 4(e)] the slope for E g symmetry is substantially reduced to below the A g slopedue to a strong increase of the CDW gap in the commen-surate regions [38] which emerge upon entering the NC-CDW phase. Further cooling also decreases the slope forthe A g spectrum, as the Mott gap around the Γ pointstarts to open within the continuously growing C-CDWdomains[35, 36]. Below T = 270 K the initial slopes areidentical for both symmetries and decrease with temper-ature. Apparently, the Mott gap opens up on the entireFermi surface in direct correspondence with the increase FIG. 4. Evolution of the gaps. (a-c) Raman vertices andFermi surface of 1 T -TaS for the indicated symmetries. (d-g)Low energy Raman spectra for A g symmetry (blue) and E g symmetries (red) at temperatures as indicated. The spectrashown are zooms on the data shown in Fig. 3. The blacklines highlight the initial slope of the spectra. (h) High en-ergy spectra at 4 K. Vertical dashed lines and colored barsindicate the approximate size and error bar of the Mott gapfor the correspondingly colored spectrum. (i) Temperaturedependence of the Mott gap ∆ µ ( µ = A g , E g ) of the resistivity by approximately an order of magni-tude [1]. Finally, at the lowest temperature close to 4 Kthe initial slopes drop to almost zero [Fig. 4(g)] indicat-ing vanishing conductivity or fully-gapped bands in theentire BZ.Concomitantly, and actually more intuitive for theopening of a gap, we observe the loss of intensity inthe Raman spectra below a threshold at an energyΩ gap . Below 30 cm − the intensity is smaller than0.2 counts(mW s) − [Fig. 4(g)] and still smaller than0.3 counts(mW s) − up to 1500 cm − [Fig. 4(h)]. For asuperconductor or a CDW system the threshold is givenby 2∆, where ∆ is the single-particle gap, and a pile-upof intensity for higher energies, Ω >
2∆ [40]. A pile-upof intensity cannot be observed here. Rather, the overallintensity is further reduced with decreasing temperatureas shown in the Appendix in Figs. 5 and 6. In partic-ular, the reduction occurs in distinct steps between the phases and continuous inside the phases with strongesteffect in the C-CDW phase below approximately 210 K[Fig. 5]. In a system as clean as 1 T -TaS the missingpile-up in the C-CDW phase is surprising and argues foran alternative interpretation.In a Mott system, the gap persists to be observablebut the pile-up is not a coherence phenomenon and hasnot been observed yet. In fact, the physics is quite dif-ferent, and the conduction band is split symmetricallyabout the Fermi energy E F into a lower and a upper Hub-bard band. Thus in the case of Mott-Hubbard physicsthe experimental signatures are more like those expectedfor an insulator or semiconductor having a small gap,where at T = 0 there is a range without intensity andan interband onset with a band-dependent shape. At fi-nite temperature there are thermal excitations inside thegap. For 1 T -TaS at the lowest accessible temperature,both symmetries exhibit a flat, nearly vanishing elec-tronic continuum below a slightly symmetry-dependentthreshold (superposed by the phonon lines at low en-ergies). Above the threshold a weakly structured in-crease is observed. We interpret this onset as the dis-tance of the lower Hubbard band from the Fermi energy E F or half of the distance between the lower and theupper Hubbard band, shown as vertical dashed lines at1350 − − ≡ −
190 meV [Fig. 4(h)]. The en-ergy is in good agreement with gap obtained from thein-plane ARPES[38] and infrared spectroscopy[11] whichmay be compared directly with our Raman results mea-sured with in-plane polarizations. Upon increasing thetemperature the size of the gap shrinks uniformly inboth symmetries [Fig. 4(i)] and may point to an onsetabove the C-CDW phase transition, consistent with theresult indicated by the initial slope. However, we can-not track the development of the gap into the NC-CDWphase as an increasing contribution of luminescence (seeAppendix B) overlaps with the Raman data.Recently, it was proposed on the basis of DFT cal-culations that 1 T -TaS orders also along the c -axis per-pendicular to the planes in the C-CDW state [21, 31].This quasi-1D coupling is unexpectedly strong and theresulting metallic band is predicted to have a width ofapproximately 0.5 eV. For specific relative ordering of the“star of David” patterns along the c -axis this band de-velops a gap of 0.15 eV at E F [22] which is intriguinglyclose to the various experimental observations. However,since our light polarizations are strictly in-plane, we haveto conclude that the gap observed here (and presumablyin the other experiments) is an in-plane gap. Our ex-periment can not detect out-of-plane gap. Thus, neithera quasi-metallic dispersion along the c -axis nor a gap inthis band along k z may be excluded in the C-CDW phase.However, there is compelling evidence for a Mott-like gapin the layers rather than a CDW gap. IV. CONCLUSIONS
We have presented a study of the various charge-density-wave regimes in 1 T -TaS by inelastic light scat-tering, supported by ab initio calculations. The spec-tra of lattice excitations in the commensurate CDW (C-CDW) phase determine the unit cell symmetry to be P T NC ≈ −
360 K, in good agree-ment with previously reported values. At the lowest mea-sured temperatures, the observation of a virtually cleangap without a redistribution of spectral weight from lowto high energies below T C argues for the existence ofa Mott metal-insulator transition at a temperature oforder 100 K. The magnitude of the gap is found to beΩ gap ≈ −
190 meV and has little symmetry, thus mo-mentum, dependence in agreement with earlier ARPESresults [34]. At 200 K, on the high-temperature end ofthe C-CDW phase, the gap shrinks to ∼
60% of its low-temperature value. Additionally, the progressive filling ofthe CDW gaps by thermal excitations is tracked via theinitial slope of the spectra, and indicates that the Mottgap opens primarily on the parts of the Fermi surfaceclosest to the Γ point. Our results demonstrate the potential of using inelas-tic light scattering to probe the momentum-dependenceand energy-scale of changes in the electronic structuredriven by low-temperature collective quantum phenom-ena. This opens perspectives to investigate the effect ofhybridization on collective quantum phenomena in het-erostructures composed of different 2D materials, e.g.,alternating T and H monolayers as in the -TaS phase.[41] ACKNOWLEDGEMENTS
The authors acknowledge funding provided by the In-stitute of Physics Belgrade through the grant by theMinistry of Education, Science and Technological Devel-opment of the Republic of Serbia. The work was sup-ported by the Science Fund of the Republic of Serbia,PROMIS, No. 6062656, StrainedFeSC, and by ResearchFoundation-Flanders (FWO). J.B. acknowledges supportof a postdoctoral fellowship of the FWO, and of the Eras-mus+ program for staff mobility and training (KA107,2018) for a research stay at the Institute of Physics Bel-grade, during which part of the work was carried out.The computational resources and services used for thefirst-principles calculations in this work were provided bythe VSC (Flemish Supercomputer Center), funded by theFWO and the Flemish Government – department EWI.Work at Brookhaven is supported by the U.S. DOE underContract No. DESC0012704. A. B. and R. 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Figure 5 shows Raman spectra at temperatures rang-ing from T = 4 K to 370 K for parallel [panel (a)] andcrossed [panel (b)] in-plane light polarizations. The spec-tra were measured in steps of ∆Ω = 50 cm − and a reso-lution of σ ≈
20 cm − . Therefore neither the shapes northe positions of the phonon lines below 500 cm − may beresolved. All spectra reach a minimum in the range from500 to 1600 wn. At energies above 500 cm − the overallintensities are strongly temperature dependent and de-creasing with decreasing temperature. Three clusters ofspectra are well separated according to the phases theybelong to.In the C-CDW phase ( T ≤ K , blue lines) the spec-tra start to develop substructures at 1500 and 3000 cm − .The spectra at 200 K increase almost linearly with en-ergy. The spectra of the NC- and IC-CDW phases ex-hibit a broad maximum centered in the region of 2200-3200 cm − which may be attributed to luminescence (seeAppendix B). For clarification we measured a few spectrawith various laser lines for excitation. Appendix B: Luminescence
Figure 6 shows Raman spectra measured with parallellight polarizations for three different wavelengths λ i ofthe incident laser light. Panels (a-b) depict the measured
051 01 5 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 0051 0 C - C D WN C - C D W e i | | e s T e m p e r a t u r e T ( K ) 4 2 3 5 3 6 0 1 0 0 2 7 0 3 7 0 1 6 5 3 3 0 2 0 0 3 5 2 I C - C D W( a ) R c '' ( W ,T ) (counts s-1 mW -1) R a m a n S h i f t W ( c m - 1 ) e i ^ e s - T a S ( b ) FIG. 5. Raman spectra up to high energies for (a) paralleland (b) crossed polarizations of the incident and scatteredlight at temperatures as given in the legend.
14 16 18 20020406080100 14 16 18 20 220 2000 4000 60000510152025303540 0 2000 4000 6000 8000 l i = 458 nm l i = 514 nm l i = 575 nm(a) I n t en s i t y I ( W , T ) ( c oun t s s - m W - ) Energy w (10 cm -1 ) T = 330 K e i || e s (b) T = 4 K T = 330 K R c '' ( W , T ) ( c oun t s s - m W - ) Raman Shift W (cm -1 )(c) T = 4 K (d) Metallic Upper HubbardLower Hubbard
T>210 K T~ 0 Ks
FIG. 6. Luminescence contribution to the Raman data. (a-b) Intensity as a function of the absolute frequency for (a) T = 330 K and (b) T = 4 K. The approximate peak maxi-mum of the contribution attributed to luminescence is high-lighted by the gray shaded area. (c-d) Raman susceptibilitycalculated from panels (a) and (b), respectively, shown as afunction of frequency (Raman) shift. The luminescence peakappears at different Raman shifts depending on the wave-length of the laser light. At T = 4 K the spectra are identicalup to 1600 cm − for all laser light wavelengths. intensity I (without the Bose factor) as a function of theabsolute frequency ˜ ν of the scattered light.At high temperature [ T = 330 K, panel(a)] a broadpeak can be seen for all λ i which is centered at a fixedfrequency of 15200 cm − of the scattered photons (greyshaded area). The peak intensity decreases for increas-ing λ i (decreasing energy). Correspondingly, this peak’scenter depends on the laser wavelength in the spectrashown as a function of the Raman shift [panel (c)]. Thisbehaviour indicates that the origin of this excitation islikely to be luminescence where transitions at fixed ab-solute final frequencies are expected.At low temperature [Fig. 6(b)] we cannot find a struc-ture at a fixed absolute energy any further. Rather, asalready indicated in the main part, the spectra developadditional, yet weak, structures which are observable inall spectra but are particularly pronounced for blue ex-citation. For green and yellow excitation the spectralrange of the spectrometer, limited to 732 nm, is not wideenough for deeper insight into luminescence contributions(at energies different from those at high temperature) andno maximum common to all three spectra is observed. If these spectra are plotted as a function of the Raman shiftthe changes in slope at 1500 and 3000 cm − are found tobe in the same position for all λ i values thus arguing forinelastic scattering rather than luminescence. Since wedo currently not have the appropriate experimental toolsfor an in-depth study our interpretation is preliminaryalthough supported by the observations in Fig. 6(d).As shown in the inset of Fig. 6(d) we propose a sce-nario on the basis of Mott physics. In the C-CDW phasethe reduced band width is not the largest energy any fur-ther and the Coulomb repulsion U becomes relevant [19]and splits the conduction band into a lower and upperHubbard band. We assume that the onset of scatteringat 1500 cm − corresponds to the distance of the highestenergy of the lower Hubbard band to the Fermi energy E F . The second onset corresponds then to the distancebetween the highest energy of the lower Hubbard bandand the lowest energy of the upper Hubbard band. Animportant question remains open: Into which unoccupiedstates right above E F the first process scatters electrons.We may speculate that some DOS is provided by themetallic band dispersing along k zz