We report a Raman scattering study of low-temperature, pressure-induced
melting of the CDW phase of 1T-TiSe2. Our Raman scattering measurements reveal
that the collapse of the CDW state occurs in three stages: (i) For P<5 kbar,
the pressure dependence of the CDW amplitude mode energies and intensities are
indicative of a ``crystalline'' CDW regime; (ii) for 5 < P < 25 kbar, there is
a decrease in the CDW amplitude mode energies and intensities with increasing
pressure that suggests a regime in which the CDW softens, and may decouple from
the lattice; and (iii) for P>25 kbar, the absence of amplitude modes reveals a
melted CDW regime.Comment: 5 pages, 4 figure

C. S. Snow

C. S. Lue

E. Dagotto

J. F. Karpus

S. L. Cooper

S. Sugai

S. V. Zaitsev-Zotov

S. Yasuzuka

T. E. Kidd

T.-C. Chiang

English

arXiv

C. S.  Snow

Crossref

We report a Raman scattering study of low-temperature, pressure-induced melting of the charge-density- wave (CDW) phase of 1T-TiSe2. Our measurements reveal that the collapse of the CDW state occurs in three stages: (i) For P\u3c5 kbar, the pressure dependence of the CDW amplitude mode energies and intensities are indicative of a ‘‘crystalline’’ CDW regime; (ii) for 5\u3cP\u3c25 kbar, there is a decrease in the CDW amplitude mode energies and intensities with increasing pressure that suggests a regime in which the CDW softens, and exhibits enhanced fluctuations; and (iii) for P \u3e 25 kbar, the absence of amplitude modes reveals a metallic regime in which the CDW has melted

Snow, C. S.

Karpus, J. F.

Cooper, S. L.

Kidd, T. E.

Chiang, T.-C.

Name not available

Quantum Melting of the Charge-Density-Wave State in 1T-TiSe2

University of Northern Iowa

University of Northern Iowa UNI ScholarWorks Faculty Publications Faculty Work 9-2003 Quantum Melting of the Charge-Density-Wave State in 1T-TiSe2 C. S. Snow University of Illinois at Urbana-Champaign J. F. Karpus University of Illinois at Urbana-Champaign See next page for additional authors Let us know how access to this document benefits you Copyright ©2003 C.S. Snow, J.F. Karpus, S.L.Cooper, T.E. Kidd, and T.-C. Chiang. The copyright holder has granted permission for posting. Follow this and additional works at: https://scholarworks.uni.edu/phy_facpub  Part of the Physics Commons Recommended Citation Snow, C. S.; Karpus, J. F.; Cooper, S. L.; Kidd, T. E.; and Chiang, T.-C., "Quantum Melting of the Charge-Density-Wave State in 1T-TiSe2" (2003). Faculty Publications. 16. https://scholarworks.uni.edu/phy_facpub/16 This Article is brought to you for free and open access by the Faculty Work at UNI ScholarWorks. It has been accepted for inclusion in Faculty Publications by an authorized administrator of UNI ScholarWorks. For more information, please contact scholarworks@uni.edu. Authors C. S. Snow, J. F. Karpus, S. L. Cooper, T. E. Kidd, and T.-C. Chiang This article is available at UNI ScholarWorks: https://scholarworks.uni.edu/phy_facpub/16 Quantum Melting of the Charge-Density-Wave State in 1T-TiSe2C. S. Snow, J. F. Karpus, S. L. Cooper, T. E. Kidd,* and T.-C. ChiangDepartment of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign,Urbana, Illinois 61801, USA(Received 8 April 2003; published 24 September 2003)We report a Raman scattering study of low-temperature, pressure-induced melting of the charge-density-wave (CDW) phase of 1T-TiSe2. Our measurements reveal that the collapse of the CDW stateoccurs in three stages: (i) For P< 5 kbar, the pressure dependence of the CDWamplitude mode energiesand intensities are indicative of a ‘‘crystalline’’ CDW regime; (ii) for 5< P< 25 kbar, there is adecrease in the CDW amplitude mode energies and intensities with increasing pressure that suggests aregime in which the CDW softens, and exhibits enhanced fluctuations; and (iii) for P > 25 kbar, theabsence of amplitude modes reveals a metallic regime in which the CDW has melted.DOI: 10.1103/PhysRevLett.91.136402 PACS numbers: 71.30.+h, 71.45.Lr, 78.30.–jThere has been a great deal of interest in the relation-ship between various diverse and exotic low-temperaturephases of strongly correlated systems, including theantiferromagnetic insulating and unconventional super-conducting phases of the high Tc cuprates [1], the charge-ordered insulating and ferromagnetic metal phases of themanganites [2], the orbital-ordered and ferromagneticmetal phases of the ruthenates [3–5], and the charge-density-wave (CDW) and superconducting phases oflayered dichalcogenides such as 2H-NbSe2 [6]. Of par-ticular interest is the exotic phase behavior that is ex-pected between fully ordered (crystalline) and disordered(isotropic) phases as one tunes the interactions in thesesystems using some control parameter other than tem-perature. These include electronically phase-separatedregimes [2], and ‘‘quantum liquid crystal’’ phases, whichare expected to be observed between charge-ordered in-sulating and ‘‘disordered’’ metallic or superconductingphases as one increases the interactions between thecharge stripes [7]. Clearly, therefore, it is of great interestto carefully explore the manner in which 2D and 3Dquantum ordered phases collapse, or ‘‘melt,’’ into quan-tum disordered phases as a function of some controlparameter — such as pressure — that tunes the competinginteractions in the material at low temperatures.In this Letter, we report a pressure-dependent low-temperature Raman scattering study of the CDW sys-tem 1T-TiSe2, in which we are able to explore the mannerin which a quasi-2D CDW state melts with increasingpressure near T  0 K. Because of its layered structureand simple commensurate CDW phase, 1T-TiSe2 is anideal system for such an investigation. 1T-TiSe2 is also ofinterest because the CDW transition is not driven by con-ventional Fermi surface nesting, but rather by an uncon-ventional mechanism involving electron-hole couplingand an ‘‘indirect’’ Jahn-Teller effect [8]. Our pressure-dependent light scattering approach allows us to exploreunique details associated with quantum mechanical melt-ing of the CDW in 1T-TiSe2. In particular, this studyreveals that the CDW state evolves with increasing pres-sure in a manner reminiscent of classical 2D melting,with crystalline and disordered CDW regimes, as well asan intermediate ‘‘soft’’ CDW regime in which the CDWexhibits strong fluctuations and loses its stiffness.The 1T-TiSe2 samples used in this study were grownby iodine vapor transport with a temperature gradient of570–640 C [8]. The sample stoichiometry was verifiedby x-ray and resistivity measurements. The Raman spec-tra were taken in a true backscattering geometry with647.1 nm incident photons. Variable low-temperature,high-pressure measurements were obtained with a modi-fied SiC-anvil cell inserted into a flow-through heliumcryostat, allowing continuous adjustment of both thetemperature (3.5–300 K) and pressure (0–100 kbar) [5].Argon was used as the pressure transmitting medium, andthe pressure inside the cell was determined from the shiftof the ruby fluorescence line; argon is quasihydrostatic inthe temperature and pressure range of interest [9].Figure 1 shows the temperature-dependent Raman scat-tering spectrum below the CDW transition temperatureat TC  200 K. Several new modes develop in the CDWphase. Of particular interest are an Eg mode near75 cm1 and an A1g mode near 115 cm1. These twomodes are CDW-coupled ‘‘amplitude’’ modes associatedwith the zone-boundary transverse acoustic phononsfrom the L point in the Brillouin zone, which are foldedto the zone center due to the formation of the CDW super-lattice [10,11]. That these two modes are indeed coupledto the CDW mode is confirmed by their temperature de-pendence in Fig. 2: Both the 75 cm1 Eg and 115 cm1A1g amplitude mode energies soften dramatically as thetemperature is increased toward the CDW transition tem-perature. By contrast, the 134 cm1 Eg and 203 cm1 A1gzone-center optical phonon energies are nearly tempera-ture independent, indicating that they are not stronglyinfluenced by the development of the CDW state.The CDW amplitude modes are excitations of theCDW ground state, involving fluctuations of the CDWstate that modulate the amplitude of the charge-densitywave. In particular, the A1g amplitude mode nearP H Y S I C A L R E V I E W L E T T E R S week ending26 SEPTEMBER 2003VOLUME 91, NUMBER 13136402-1 0031-9007=03=91(13)=136402(4)$20.00  2003 The American Physical Society 136402-1115 cm1 involves fluctuations of the CDW amplitudethat preserve the symmetry of the CDW ground state(Fig. 1 inset), while the Eg amplitude mode involvesout-of-phase fluctuations of the CDW amplitude awayfrom the ground state symmetry. These two amplitudemodes serve as ideal ‘‘probes’’ with which to study thestability and stiffness of the CDW state as it evolves andmelts as a function of increasing pressure.Figure 3 shows the pressure-dependent Raman spectraof TiSe2 at 3.5 K. The energy and intensity of the115 cm1 A1g and 75 cm1 Eg CDW amplitude modes,along with both the 134 cm1 Eg and 203 cm1 A1g opti-cal phonon modes, are summarized in Fig. 4. One of thechief effects of pressure on the low-temperature Ramanspectrum of 1T-TiSe2 is the gradual suppression of the 75and 115 cm1 CDW amplitude mode intensities withincreasing pressure, and the complete collapse of theCDWstate near a T  0 critical pressure of approximatelyP  25 kbar. Notably, the dramatic increase in the A1goptical phonon linewidth near P  25 kbar [Fig. 3(c)inset] betrays increased damping of this phonon by freecarriers, indicative of a pressure-induced CDW-metaltransition near P. This value of the critical pressure issimilar to that observed in pressure-induced CDW-to-metal transitions in NbSe3 (P  24 kbar) [12] andLu5Ir4Si10 (P  21 kbar) [13].More interesting than the pressure-induced collapse ofthe CDW phase is the manner in which this collapseoccurs. This process can be carefully studied by examin-ing the energies and intensities of the 75 cm1 Eg and115 cm1 A1g amplitude modes as a function of pressure,summarized in Figs. 4(c) and 4(d), respectively. For com-parison, Fig. 4 also summarizes the pressure-dependentenergies of both the (a) 203 cm1 optical phonon and(b) 134 cm1 optical phonon modes.Notably, Fig. 4 reveals several regimes of behaviorassociated with the pressure-induced (T  0) quantummelting of the CDW state in 1T-TiSe2:(i) Crystalline CDW regime.—From P  0 to 5 kbar,the A1g CDW amplitude mode’s intensity decreasesslightly, but its energy increases at a rate of approximatelyd!o=dP1 cm1=kbar. This behavior is consis-tent with increased stiffening of the CDW state withincreased pressure, indicative of a ‘‘crystalline’’ regime.Significantly, the manner in which the A1g amplitudemode energy increases with pressure is similar to thatof the 203 cm1 [Fig. 4(a)] and 134 cm1 [Fig. 4(b)]optical modes, providing evidence that the CDW remainscommensurate with the lattice in this regime.(ii) Soft CDW regime.—Between roughly P 5 to25 kbar, the A1g amplitude mode exhibits a number ofinteresting and anomalous changes as a function of in-creasing pressure: its energy softens—revealing ananomalous, slightly negative Grüneisen mode parameterd!o=dP in this regime [14] — its intensity decreases rap-idly, and its linewidth increases substantially [Fig. 3(c)inset]. By contrast, neither the 134 cm1 Eg nor the203 cm1 A1g optical phonon modes show an appreciableFIG. 2. Temperature dependence of the peak energies of(a) the A1g optical mode, (b) the Eg optical mode, (c) theA1g CDW mode, and (d) the Eg CDW mode.FIG. 1. Temperature dependent Raman scattering spectra ofTiSe2. The inset shows the displacement pattern associatedwith the CDW distortion, for Ti atoms (solid circles), Se atomsabove a Ti layer (open circles), and Se atoms below a Ti layer(shaded circles).P H Y S I C A L R E V I E W L E T T E R S week ending26 SEPTEMBER 2003VOLUME 91, NUMBER 13136402-2 136402-2change in either intensity or linewidth throughout thispressure regime. The behavior of the A1g CDW mode inthis regime is consistent with a distinct softening of theCDW state to breathing-mode fluctuations of the CDWamplitude, and with an increase in CDW fluctuations nearP. Equally interesting is the fact that the energy of theA1g CDW amplitude mode exhibits a distinctly differentpressure dependence than the Eg or A1g optical phononmodes in this regime, suggesting that the CDW becomesincommensurate with the lattice [15,16]. Importantly, theEg amplitude mode also exhibits a particularly anoma-lous pressure dependence in this regime, including adecrease in energy and a rapid reduction in intensitywith increasing pressure. The rapid disappearance of theEg mode, in particular, indicates that out-of-phase fluc-tuations of the CDW amplitude are not well-defined ex-citations above roughly P 5 kbar, even though there isclearly some vestige of the A1g CDW mode at thesepressures. This may indicate a breakdown of long-rangeCDW order in this phase regime; indeed, calculations of1D CDW systems show that a softening of the CDW toshear deformations, and a consequent breakdown of long-range translational order, occurs when the coupling be-tween CDW stripes reaches a critical value [17]. In sum,the behavior of the CDW modes in the ‘‘soft CDW’’regime is characteristic of a regime in which the CDWhas begun to soften, or melt, as well as exhibit increasingCDW fluctuations.(iii) Disordered CDW regime.—Finally, above roughlyP  25 kbar, both the Eg and A1g CDWamplitude modesare completely suppressed; consequently, there is no evi-dence in the spectra for long- or short-range CDW order,indicating that the CDW state has melted completely intoa metallic or semimetallic phase.It is interesting to compare the pressure-induced‘‘melting’’ process described above for 1T-TiSe2 to melt-ing in other 2D systems [18,19]. Calculations of classicalmelting in 2D solids suggest the presence of a ‘‘hexatic’’phase — in which long-range orientational order is pre-served, but long-range translational order is lost — inter-mediate between the crystalline and disordered phases.This topological phase arises because dislocations causetranslational order to decay exponentially, but cause amuch weaker suppression of orientational order. Such ahexatic-like phase has indeed been observed as a func-tion of increasing disorder (x) in the layered NbxTa1xS2FIG. 4 (color). Pressure dependence of the peak energies(circles) and normalized intensities, IP=IP  0 (squares)at T  3:5 K for (a) the A1g optical mode, (b) the Eg opticalmode, (c) the A1g CDW mode, and (d) the Eg CDW mode. Thehatched lines denote rough boundaries between crystallineCDW, soft CDW, and disordered CDW regimes.FIG. 3 (color). Pressure dependence of the Raman spectra ofTiSe2 at T  3:5 K for (a) the Eg CDW mode, (b) the A1g CDWand Eg optical phonon modes, and (c) the A1g optical phononmode (P  0 spectrum not shown for clarity). The intensemode near 143 cm1 in (b) is an anvil phonon mode. Theinset shows the pressure dependence of the A1g optical phonon(red circles) and A1g CDW mode (blue squares) linewidths(FWHM).P H Y S I C A L R E V I E W L E T T E R S week ending26 SEPTEMBER 2003VOLUME 91, NUMBER 13136402-3 136402-3system using scanning-tunneling microscopy (STM):these measurements reveal a system that is, in turn,crystalline (0< x< 0:04), hexatic (0:04 	 x 	 0:07),and amorphous (x > 0:07), as a function of increasingdisorder (x).While classical melting in 2D systems is reminiscentof the phase behavior we observe as a function of pressurein 1T-TiSe2, an important qualification should be madewith respect to this comparison. In contrast to the ex-amples above, the melting process we observe in1T-TiSe2 is quantum mechanical in nature, in that it isdriven near T  0 K by pressure tuning the competinginteractions in this system. To understand the nature ofthis competition, note first that the zero-pressure CDWstate in 1T-TiSe2 is unconventional, arising from an in-direct Jahn-Teller–type interaction that splits and lowersthe unoccupied conduction band [8]: as a result of theelectron-hole interaction between the conduction and va-lence bands, the lowering of the split conduction band‘‘repulses’’ and flattens the valence band, resulting in alowering of the system’s energy, and the formation of asmall gap CDW state. Upon applying pressure to thisCDW state, one expects several regimes of behavior: atlow applied pressures, increasing pressure will increasethe matrix element associated with the Jahn-Teller inter-action; this is expected to result in a further lowering ofthe conduction band, and via the electron-hole coupling,to cause a lowering of the valence band and a consequentstiffening of the CDW state. This behavior is similar tothat observed in the ‘‘crystalline CDW’’ regime of Fig. 4.As the pressure is increased beyond a critical pressure,however, the increasing strength of the Jahn-Teller inter-action is expected to overwhelm the electron-hole inter-action between the conduction and valence bands, leadingto a collapse of the CDW gap, and a pressure-inducedtransition to a metallic phase in which the CDW distor-tion is completely suppressed. Again, the dramatic in-crease in the linewidth of the A1g optical phonon above P[Fig. 3(c) inset], as well as the disappearance of the CDWmode intensities, is indicative of such a pressure-inducedmetallic phase above P in 1T-TiSe2. Most significantly,our results indicate that, prior to the complete collapse ofthe CDWgap above P in 1T-TiSe2, there is a distinct softCDW phase regime in which the CDW loses its stiffness;this appears to result from increased fluctuations of theCDW near P, likely caused by an increase in free car-riers as the CDW gap collapses. In theoretical support ofthis, Zaitsev-Zotov et al. have shown that increased cou-pling between CDW stripes leads to an increase in dy-namic fluctuations and a decreased CDW stiffness [17].Interestingly, such long wavelength lattice fluctuationsare expected to destroy long-range translational orderbut preserve long-range orientational order [20].In summary, Raman scattering studies of T  0pressure-induced melting of the CDW state in 1T-TiSe2reveal a low-pressure (P< 5 kbar) crystalline CDW re-gime, a high-pressure (P > 25 kbar) metallic regime,and an intermediate pressure regime (5<P< 25 kbar)in which the CDW loses its stiffness, exhibits increasedfluctuations, and may have only short-range order. Thispressure-induced melting of the CDW state in 1T-TiSe2is noticeably different from classical 3D melting, whichoccurs via an abrupt first-order transition, and insteadappears to occur in a manner more akin to classical 2Dmelting.We thank E. Dagotto, E. Fradkin, M.V. Klein, andM. Rübhausen for useful discussions. This work wassupported by the National Science Foundation underGrant No. DMR-0244502 and by the Department ofEnergy under Grant No. DEFG02-91ER45439.*Present address: Brookhaven National Laboratory,Upton, NY.[1] Physical Properties of High-Temperature Supercon-ductors I-V, edited by D. M. Ginsberg (World Scientific,Singapore, 1989).[2] E. Dagotto, Nanoscale Phase Separation and ColossalMagnetoresistance: The Physics of Manganites and Re-lated Compounds (Springer, Berlin, Heidelburg, 2003).[3] G. Cao et al., Phys. Rev. B 67, 060406 (2003).[4] S. Nakatsuji and Y. Maeno, Phys. Rev. Lett. 84, 2666(2000).[5] C. S. Snow et al., Phys. Rev. Lett. 89, 226401 (2002).[6] D. E. Moncton, J. D. Axe, and F. J. DiSalvo, Phys. Rev.Lett. 34, 734 (1975).[7] S. A. Kivelson, E. Fradkin, and V. J. Emery, Nature(London) 393, 550 (1998).[8] T. E. Kidd et al., Phys. Rev. Lett. 88, 226402 (2002).[9] U. Venkateswaran et al., Phys. Rev. B 33, 8416 (1986).[10] J. A. Holy et al., Phys. Rev. B 16, 3628 (1977).[11] S. Sugai et al., Solid State Commun. 35, 433 (1980).[12] S. Yasuzuka et al., J. Phys. Soc. Jpn. 69, 3470 (2000).[13] C. S. Lue et al., Physica (Amsterdam) 364C, 243 (2001).[14] Similar behavior has also been observed in quasi-1DCDW systems, e.g., N. Kuroda et al., Phys. Rev. Lett.68, 3056 (1992); G. S. Kanner et al., Phys. Rev. B 50,18 682 (1994).[15] An incommensurate CDW state should result in addi-tional ‘‘phase’’ modes in the spectrum, although suchmodes will likely be too weak to observe due to theexperimental conditions and the intensity of the CDWmodes in this pressure regime.[16] Evidence for a pressure-induced transition to an incom-mensurate CDW phase has also been observed in2H-TaSe2 by high-pressure x-ray scattering, D. B.McWhan et al., Phys. Rev. Lett. 45, 269 (1980).[17] S. V. Zaitsev-Zotov et al., Phys. Low-Dim. Struct. 1–2,79 (2002).[18] B. I. Halperin and D. R. Nelson, Phys. Rev. Lett. 41, 121(1978).[19] H. Dai, H. Chen, and C. M. Lieber, Phys. Rev. Lett. 66,3183 (1991).[20] N. D. Mermin, Phys. Rev. 176, 250 (1968).P H Y S I C A L R E V I E W L E T T E R S week ending26 SEPTEMBER 2003VOLUME 91, NUMBER 13136402-4 136402-4

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Quantum Melting of the Charge Density Wave State in 1T-TiSe2

Quantum Melting of the Charge Density Wave State in 1T-TiSe2

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