Brabetz, C.

Janowitz, C.

Manzke, R.

May, M.M.

English

Matthias M. May

Christine Brabetz

Christoph Janowitz

Recardo Manzke

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Physical Review Letters

Charge-Density-Wave Phase of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mi>T</mml:mi><mml:mtext mathvariant="normal">−</mml:mtext><mml:msub><mml:mi>TiSe</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>: The Influence of Conduction Band Population

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CDW phase of 1T -TiSe2: The influence of conduction band populationMatthias M. May,1, 2, ∗ Christine Brabetz,1 Christoph Janowitz,1 and Recardo Manzke11Department of Physics, Humboldt-University of Berlin, D-12489 Berlin, Germany2Institute for Materials for Photovoltaics, Helmholtz Centre Berlin, D-14109 Berlin, Germany(Dated: September 9, 2011)The charge-density wave (CDW) phase of TiSe2 was studied by angle-resolved photoelectronspectroscopy (ARPES) and resistivity measurements investigating the influence of the band gap sizeand of a varying population of the conduction band. A gradual suppression of the CDW-inducedelectronic superstructure is observed for a variation of the band gap in the ternary compoundsTiCxSe2−x with C=(S, Te) as well as for an occupation of only the conduction band by H2Oadsorption-induced band bending. These observations point to an optimum band gap and supportan excitonic driving force for the CDW.PACS numbers: 71.20.Nr, 71.35.Lk, 71.45.Lr, 79.60.-iSome of the transition-metal dichalcogenides(TMDCs) with their typical quasi-two-dimensionalstructure were among the first materials where CDWphase transitions have been discovered [1, 2]. TiSe2,one representative of the TMDCs exhibiting a CDWphase transition, is particularly interesting as the originof its CDW phase has been under discussion ever since.Amongst others, a Jahn-Teller effect [3, 4], an excitonicorigin [5–7] or a mixture of both [8, 9] were proposed,see also [10] for a comprehensive review. A competingsuperconducting phase was found on Cu intercalation[11] and pressure [12] emphasising the close relationshipbetween the collective charge carrier phenomena CDWand superconductivity. The question whether TiSe2 isa small-gap semiconductor [8] or a semi-metal [3] hasbeen a long-standing discussion which was answered byRasch et al. [13] in favour of the semiconductor with aband gap of Eg ≈ 150 meV. It is generally agreed thatthe CDW phase transition of TiSe2 is of second orderforming a commensurate 2x2x2 superstructure belowTc ≈ 200 K [2]. This results in a reduced Brillouin zone(BZ) as shown in Fig. 1(a). The two most prominentexperimentally seizable features of the CDW phaseare a peaking resistivity below Tc and the evolutionof backfolded bands due to the reduced BZ visible toARPES. Both signatures will be addressed in this Letter.The valence band maximum of TiSe2 derived from Se4p states is found at Γ while the minimum of the conduc-tion band of Ti 3d character is located at the BZ bound-ary at L as schematically shown in Fig. 1(c). In theCDW phase of TiSe2 both, conduction and valence bandshift to higher binding energies and a backfolded valenceband appears at L, which represents a new Γ point of theCDW superstructure, assigned Γ∗, as depicted schemat-ically in Fig. 1(d). Experimentally determined spectraat the high symmetric points A and L [15] well in theCDW phase (T=21 K) are shown in Fig. 2(a) and (b) ingood agreement with [6]. At low temperatures, a CDW-induced energy shift ∆ is observed and a distinct amountof spectral weight is transferred to the backfolded bands,FIG. 1. (Colour online) (a) BZ of TiSe2 of the normal phase(black) and in the CDW phase (red). High symmetric umk-lapp points of the reduced BZ are marked by a star. (b)Specific resistivities of different ternary compounds and ofpristine TiSe2 grown at different temperatures. (c) Schematicview of conduction band c and valence band v around theirminimum and maximum (with spanning vector ~ωi) at Γ andL, respectively, in the normal phase (c) and in the CDW phase(d). The backfolded valence band v∗ is shown in red with theCDW-induced energy shift ∆. Sketch similar to e.g. [14].see e.g. Monney et al. [14] for further discussion. In theexcitonic model, holes at Γ and electrons at L of Se 4pand Ti 3d character, resp., form excitons lowering theoverall energy of the system. Their different locations ink -space define the spanning vector ~ωi giving rise to theelectronic superstructure. Therefore, the driving forceof CDW formation is of electronic origin, followed by aperiodic lattice distortion. In contrast, for a phononicJahn-Teller like driven CDW, the energy is lowered by aspatial distortion of the crystal lattice. As both modelsshow deficiencies in explaining all experimental observa-tions, a combined model was proposed by van Wezel etal. [9, 16].2In this Letter we present ARPES and resistivity exper-iments probing the influence of the occupation of the va-lence and conduction bands on the strength of the CDWphase of the small-gap semiconductor TiSe2. At first, thesize of the band gap is varied changing the occupationof both, the topmost valence and the lowest conductionband. These results point to an optimal band gap size fora strong CDW, however a decrease of the gap size affectsthe CDW much stronger than an increase. At second,the occupation of the conduction band is increased bydecreasing the occupation of the valence band by an in-duced bending of these bands. It will be shown that theoccupation of the conduction band is the crucial param-eter for the CDW evolution.A variation of the size of the band gap Eg was re-alised via ternary compounds TiCxSe2−x with C=S andTe. TiS2 and TiTe2 are homologous crystallographicand electronic systems to TiSe2, but with a different en-ergy gap Eg. TiS2 is a semiconductor with a positiveband gap of about 300 meV [17]. TiTe2 on the otherhand is a semi-metal with a negative band gap of ap-proximately 800 meV [18]. For both, no CDW phasehas been reported. As a first approximation, the bandgap of ternary compounds TiCxSe2−x can be regardedto change its size linearly with the stoichiometric factorx similar as in other ternary TMDC series [19]. Hence,the ternary TiCxSe2−x series with small x values repre-sent a possibility to study in detail the influence of theband gap size on the CDW formation in TiSe2. The sin-gle crystals of TiSe2 and the derived ternary compoundsTiCxSe2−x were grown at a temperature Tg = 740 ◦Cby chemical vapour transport using iodine as transportgas. The resistivities in the plane perpendicular to the c-direction were determined using an alternating current of30 Hz and 20 mA varying the temperature between 2 and300 K at an alteration rate of 1 K/min. ARPES experi-ments were performed at the synchrotron source BESSYII (beamline BEST) at a photon energy of hν = 22 eVwith an energy resolution of 25 meV and an angle res-olution of 0.1 ◦. The samples were cleaved in situ andtheir temperature was varied between 20 K and 300 K ata temperature stability of < 1 K.Another way to manipulate the population of the con-duction band is rendered possible by the unit cell’s struc-ture of TiSe2 with its van der Waals sandwiches formingnatural cleavage planes free of surface states. Karschnicket al. [20] demonstrated the (reversible) enhancement ofthe Ti 3d photoemission by band-bending due to H2O ad-sorption. In a simple model, the water molecules of highdipole moment are physisorbed and create a Schottkycontact-like bending of the bands [13] and thus allowinga systematic increase of the population of the conductionband at the surface. For the H2O experiments, watervapour was used in the UHV chamber, its amount spec-ified by the unit Langmuir (L): 1L = 1.33 · 10−6 mbar·s.A saturation of the energy shift occurs around 30 kL andFIG. 2. (Colour online) ARPES intensity maps (hν = 22 eV )of pristine TiSe2 on the AL high symmetry line of the Bril-louin Zone. (a) Point A at 21 K (b) L at 21 K (c) L at 140 K.corresponds to one monolayer of H2O molecules on thesurface and an overall band bending of 130 meV [13].This technique was also previously used to determine thesize of the band gap of TiSe2 [13]. Although band bend-ing due to water adsorption is a typical surface effect,it should be mentioned that this is exactly the regionprobed by ARPES. As a purely electronic modificationof the population, this would probe the existence of anexcitonic driving force.Results of resistivity measurements are given in Fig.1(b). For pristine TiSe2 samples, two different growthtemperatures are given. The peak in resistivity is morepronounced at a lower growth temperature (Tg = 630◦C)as expected [2], presumably due to less intercalated ex-cess Ti [2, 21]. The experimental signature of a well-developed CDW, the strength of the backfolded bandsmonitored by ARPES, is however equally strong [22].Comparing the different stoichiometries for Tg = 740◦C,we find a weakening of the resistivity maximum and ashift towards lower temperatures with increasing sulphurcontent, similar to [2]. For an already very small contentof tellurium (stoichiometric factor x = 0.05) the maxi-mum disappears completely.ARPES intensity maps at L(Γ∗) are given in Fig. 2and 3. The gradual suppression of the CDW phase bytemperature can be seen comparing pristine TiSe2 wellin the CDW phase at 24 K [Fig. 2(b)] with the spectrumat 140 K [Fig. 2(c)]. For 140 K, the backfolded valenceband shifts back towards the Fermi level and becomes lessintense. The conduction band also changes with temper-ature, revealing at 140 K more spectral weight exactly atL. This is due to the fact that the backfolded valenceband and the conduction band repel each other deep inthe CDW phase, see e.g. [10]. A very similar effect is ob-served for an adsorption of 3.2 kL H2O due to a bendingof the conduction band in direction to the Fermi energy[Fig. 3(a)], intensity and binding energy of the back-folded valence band decrease and more spectral weightis observed at L. Intensity maps of ternary compounds3FIG. 3. (Colour online) ARPES intensity maps (hν = 22 eV )arount the high symmetric point L at low temperatures. (a)Pristine TiSe2 at 22 K, 3.2 kL H2O (b) TiS0.13Se1.87 at 31 K(c) TiTe0.05Se1.95 at 25 K.TiCxSe2−x in Fig. 3(b) and (c) show a well developedbackfolded band for a sulphur content of x = 0.13 anda weaker, but still clearly identifiable backfolded Se 4pband for a tellurium content x = 0.05.Energy distribution curves (EDCs) of the low-temperature spectra extracted at L are given in Fig. 4.The evolution of the EDCs with increasing adsorptionof H2O is shown Fig. 4(a) revealing a good analogywith the temperature evolution measured by Monney etal. [14]. The two peaks of the backfolded valence bandshift towards the Fermi level and loose spectral weight.The second contribution of the Ti 3d conduction band,i.e. the prominent peak at ∼ 80 meV binding energy inthe spectrum at 0 kL [Fig. 4(a)], shifts with more wateron the surface similarly towards the Fermi level reduc-ing its intensity. This reveals the gradual suppression ofthe CDW phase with increasing H2O-induced conductionband population. These findings are similar to those byRossnagel [23] who investigated the influence of Rb ad-sorption.For the different stoichiometries, EDCs are given inFig. 4(b), exhibiting an intense backfolded Se 4p bandfor a sulphur content of x = 0.13, which evidences anequally well-developed CDW phase as the pristine TiSe2.The backfolding is however weaker for both the telluriumsample as well as for the sulphur content x = 0.33.The experimental signatures of the peaking resistiv-ity, measuring a macroscopic property of the bulk, andthe ARPES spectra, mapping the microscopic electronicstructure, therefore seem to be not strictly correlated.While the resistivity peak quickly decreases for a highergrowth temperature and a variation of the stoichiome-try, the evolution of an electronic superstructure turnsout to be more robust [22], especially to an increase ofEg. Applying the model of a linearly changing bandgap with stoichiometry [19], the interpolated value forTiS0.13Se1.87, showing a well developed CDW phase,FIG. 4. (Colour online) EDCs extracted at L from the spectrain Fig. 2 and 3. Evolution with increasing H2O adsorption (a)at low temperatures (T= 25 K) and different stoichiometries(b). Solid lines indicate fits, (I) marks the Ti 3d derived band,(II) the Se 4p derived band.would be Eg ≈ 170 meV. A further increase to Eg ≈200 meV for TiS0.33Se1.67 suppresses the CDW phase aswell as a decrease to Eg ≈ 100 meV for TiTe0.05Se1.95indicating the existence of an optimal band gap between100 and 200 meV. A suppression of the CDW phase byH2O adsorption can be deduced by the backfolded bands’loss of spectral weight and their shift towards the Fermilevel, though the water-induced band bending shouldshift the bands into the opposite direction. So we find asuppression of the electronic superstructure upon a low-ering or a significant increase of the band gap size as wellas an additional population of the conduction band. Inthe following we will discuss which model for the CDWevolution in TiSe2 fits best to our findings.Fermi surface nesting has already been regarded as animprobable driving force for the CDW in TiSe2 due toanisotropic Fermi surface pockets [10]. Our results fur-ther emphasise this view as a small variation of the bandgap size and conduction band population is unlikely tochange the Fermi surface significantly. A Jahn-Teller ef-fect would not only lower the energy of the valence bandbut also that of the Ti 3d conduction band near EF[4]. Therefore an additional population of the conduc-tion band should not instantly lead to a suppression ofthe CDW phase. The suppression of the CDW phase by4the (purely electronic) population of only the conductionband due to H2O-induced band bending however seemsto be consistent with the existence of an excitonic driv-ing force. This is similar to the results of Rohwer et al.[7] who deduced an excitonic origin from an ultra-fast re-sponse of the CDW phase arguing that the speed of theresponse could only be achieved by an electronic effect.Regarding the interpretation of our results within theexcitonic model, the asymmetric population of only theconduction band due to band bending provides the keyfor further understanding of CDW formation in TiSe2.Obviously the conduction band occupation hinders theformation of excitons. This can be due to (i) a breakdownof the balance between electrons and holes in the conduc-tion and valence band, resp., (ii) an increased screeningof the Coulomb interaction between the electrons andholes, (iii) a softening of the well defined spanning vector~ωi, or (iv) a combination of several of these effects. Forthe latter effect (iii) the softening would result from theoccupation of the very flat conduction band minimumover a broad regime of ~k values. But in essence it seemsto be the self-assembling balance between electrons andholes what stabilises the CDW phase in the small-gapsemiconductor TiSe2 and its robustness against pertur-bations. Also our finding of an optimum band gap sizeis a clear hint for such a balance. The weak correla-tion of the peaking resistivity with the strength of theCDW-induced superstructures accompanied by the umk-lapp bands measured by ARPES is there again a sign ofonly weak phononic contributions.In summary, the stable regime of the CDW phase inTiSe2 regarding the energy gap and the conduction bandpopulation has been probed. While the characteristichump in the temperature dependent resistivity is verysensitive to small variations of the stoichiometry re-spectively the size of the energy gap realised by ternarycompounds of TiCxSe2−x (C=S, Te), the transfer ofspectral weight into the backfolded bands monitoredby ARPES is a much better indicator for the strengthand robustness of the CDW phase. The investigatedvariation of the occupation of the valence and conductionband by both, a symmetric population by changing theband gap size as well as an asymmetric population ofonly the conduction band minimum by band bending,are in favour of an excitonic insulator instability. Thismainly electronic force driving the CDW is however ac-companied by a finite electron-phonon coupling causingthe periodic lattice distortion in TiSe2 [10].The authors would like to thank Stephan Thu¨rmer andIsaak Unger for inspiring discussions and Dr. HelmutDwelk for his assistance with the resistivity measure-ments. Part of the work has been conducted at BESSYII. We thank the staff for assistance.∗ Matthias.May@helmholtz-berlin.de[1] J. A. Wilson, F. J. Disalvo, and S. Mahajan, Adv. Phys.24, 117 (1975).[2] F. J. Di Salvo, D. E. Moncton, and J. V. Waszczak,Phys. Rev. B 14, 4321 (1976).[3] O. Anderson, G. Karschnick, R. Manzke, and M. Ski-bowski, Solid State Commun. 53, 339 (1985).[4] K. Rossnagel, L. Kipp, and M. Skibowski, Phys. Rev. B65, 235101 (2002).[5] T. Pillo, J. Hayoz, H. Berger, F. Levy, L. Schlapbach,and P. Aebi, Phys. Rev. B 61, 16213 (2000).[6] H. Cercellier, C. Monney, F. Clerc, C. Battaglia, L. De-spont, M. G. Garnier, H. Beck, P. Aebi, L. Patthey,H. Berger, and L. Forro, Phys. Rev. Lett. 99, 146403(2007).[7] T. Rohwer, S. Hellmann, M. Wiesenmayer, C. Sohrt,A. Stange, B. Slomski, A. Carr, Y. Liu, L. M. Avila,M. Kalla¨ne, S. Mathias, L. Kipp, K. Rossnagel, andM. Bauer, Nature 471, 490 (2011).[8] T. E. Kidd, T. Miller, M. Y. Chou, and T. C. Chiang,Phys. Rev. Lett. 88, 226402 (2002).[9] J. van Wezel, P. Nahai-Williamson, and S. S. Saxena,Phys. Rev. B 81, 165109 (2010).[10] K. Rossnagel, J Phys.: Condens Matter 23, 213001(2011).[11] E. Morosan, H. Zandbergen, B. Dennis, J. Bos, Y. Onose,T. Klimczuk, A. Ramirez, N. Ong, and R. Cava, NaturePhys. 2, 544 (2006).[12] A. F. Kusmartseva, B. Sipos, H. Berger, L. Forro, andE. Tutis, Phys. Rev. Lett. 103, 236401 (2009).[13] J. C. E. Rasch, T. Stemmler, B. Muller, L. Dudy, andR. Manzke, Phys. Rev. Lett. 101, 237602 (2008).[14] C. Monney, E. F. Schwier, M. G. Garnier, N. Mariotti,C. Didiot, H. Beck, P. Aebi, H. Cercellier, J. Marcus,C. Battaglia, H. Berger, and A. N. Titov, Phys. Rev. B81, 155104 (2010).[15] Due to the wave vector perpendicular to the crystal sur-face at hν = 22.0 eV, the measurement is along the lineAL of the BZ. The upper bound of the binding energy dif-ference between the valence band at A and its maximumat Γ is (40±10) meV [13]. The conclusions of the presentpaper are not influenced by this small energy difference.[16] J. van Wezel, P. Nahai-Williamson, and S. S. Saxena,Phys. Rev. B 83, 024502 (2011).[17] C. H. Chen, W. Fabian, F. C. Brown, K. C. Woo,B. Davies, B. DeLong, and A. H. Thompson, Phys. Rev.B 21, 615 (1980).[18] R. Claessen, R. O. Anderson, G. H. Gweon, J. W. Allen,W. P. Ellis, C. Janowitz, C. G. Olson, Z. X. Shen,V. Eyert, M. Skibowski, K. Friemelt, E. Bucher, andS. Hufner, Phys. Rev. B 54, 2453 (1996).[19] M. Moustafa, T. Zandt, C. Janowitz, and R. Manzke,Phys. Rev. B 80, 035206 (2009).[20] G. Karschnick, O. Anderson, W. Drube, and M. Ski-bowski, Surf. Sci. 155, 46 (1985).[21] M. Wiesenmayer, S. Hilgenfeldt, S. Mathias, F. Steeb,T. 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Charge Density Wave Phase of 1T TiSe2  The Influence of Conduction Band Population

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Charge Density Wave Phase of 1T TiSe2 The Influence of Conduction Band Population

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