Perturbation of charge density waves in 1T-TiSe_2
Imrankhan Mulani, Umashankar Rajput, Luminita Harnagea, Aparna Deshpande
PPerturbation of charge density waves in T -TiSe Imrankhan Mulani, Umashankar Rajput, Luminita Harnagea, and Aparna Deshpande
Indian Institute of Science Education and Research (IISER) Pune,Dr. Homi Bhabha Road, Pashan, Pune 411008, India (Dated: February 19, 2021)In this study, using low-temperature scanning tunneling microscopy (STM), we focus on under-standing the native defects in pristine 1 T -TiSe at the atomic scale. We probe how they perturb thecharge density waves (CDWs) and lead to local CDW modulated region formation. These defectsinfluence the correlation length of CDWs. We establish a connection between suppression of CDWs,Ti intercalation, and show how this supports the exciton condensation model of CDW formation in1 T -TiSe . I. INTRODUCTION
Transition metal dichalcogenides (TMDCs) are versa-tile materials that exhibit phenomena like strongly cor-related phases to multifaceted tunable properties for ap-plications in flexible electronics, optoelectronics, spin-tronics, and energy harvesting [1–4]. Many exotic phys-ical phenomena, like spin-valley interaction, exciton-polariton states, charge density wave (CDW) states, areobserved in the TMDCs. TMDCs have a characteris-tic layered structure, tunable bandgap, and strong spin-orbit coupling favoring such applications. The chemicalcomposition of TMDCs is of the form
M X where M denotes transition metal (like T i , M o , W ) and X rep-resents chalcogen (like S , Se , and T e ). Despite havinga similar structure, these materials can be categorizedas insulating, semiconducting, semi-metallic, metallic, orsuperconducting, depending on their chemical composi-tion. The non-bonding d band and the extent of its elec-tron filling endow these compounds with diverse proper-ties. Bulk crystals of TMDCs consist of two-dimensional(2D) layers bonded by weak van der Waals interactions,rendering them easy to exfoliate. Depending on the ar-rangements of atoms, structural polytypes of 2D TMDCscan be categorized as 1 T (tetragonal symmetry with oc-tahedral coordination), 2 H (hexagonal symmetry withtrigonal prismatic coordination), and 3 R (rhombohedralsymmetry with trigonal prismatic coordination). Thelayer degree of freedom provides an additional parameterto tune the properties of TMDCs [5].One of the group IV TMDCs hosting interesting prop-erties is 1 T -TiSe . It is a semimetal with a small in-direct bandgap [6]. At temperature T CDW ∼ K T -TiSe undergoes a second-order phase transition tothe charge density wave (CDW) phase [7]. Chargedensity wave is a many-body, correlated electrons phe-nomenon, where a periodic distortion modulates electrondensity. CDWs, depending on the ratio of their wave-length and lattice parameters, are classified as commen-surate (CCDW), nearly commensurate (NCCDW), or in-commensurate (ICDW) [8, 9]. Pristine 1 T -TiSe showsCCDW order below 200 K [7]. Charge carrier doping viaelectrochemical ionic gating in 1 T -TiSe leads to suppres-sion of CCDW, emergence of ICDW and superconduct- ing phase at lower temperature [10]. The CDW transi-tion temperature drops significantly for 1 T -TiSe dopedwith copper. Superconductivity emerges in Cu x TiSe for x ∼ .
04, maxima of superconducting transition temper-ature reaches at x ∼ .
08 [11]. ICDW phase coexistswith superconducting phase under applied pressure [12]and copper doping [13]. The mechanism of formation ofCDWs in 1 T -TiSe is still a matter of debate. The two fa-vored mechanisms are excitonic insulator phase [14] andband type Jahn-Teller effect [15]. Excitons are boundstates of electrons and holes. Excitons are bosons and canform a Bose-Einstein condensate [16–19]. The excitonicinsulator phase can arise in a small gap semiconductor orsemimetal, where excitons form spontaneously because oflow carrier density to screen the attractive Coulomb in-teraction between electrons and holes. In the Jahn-Tellereffect, the lattice spontaneously distorts to lift the de-generacy and reach the lower symmetry state because ofthe interaction between phonons and degenerate electronstates. Jahn-Teller like mechanism is independent of freecarrier concentration.1 T -TiSe is a nonstoichiometric compound. The con-centration of T i in a crystal depends on the tempera-ture at which the crystal is grown. Commonly usedmethod for TMDC crystal growth is chemical vapourtransport (CVT). Higher growth temperature generateshigher chalcogen pressure resulting in a crystal with in-tercalation of metal [20]. An indirect inference of pres-ence of excess
T i can be carried out through temperature-dependent resistivity measurements. 1 T -TiSe showsanomalous resistivity peak near CDW phase transition.As the growth temperature increases, the crystal becomesmore metallic due to excess T i and hence suppresses theanomalous resistivity peak [7, 21]. 1 T -TiSe shows asmall indirect band gap above the transition temperature T CDW ∼ K [22, 23]. Angle resolved photo emissionspectroscopy (ARPES) experiments show a small bandgap below CDW transition [24]. Recent experimentalevidence suggests excitonic insulator mechanism [25–30].Theoretical investigations suggest that excitonic conden-sation can be either superfluid [31] or an insulator [32].Chiral nature of CDWs in pristine and Cu-doped 1 T -TiSe has been reported using polarized optical reflec-tometry and STM [33–35]. Suppression of CDW resultsin superconducting phase transition with application of a r X i v : . [ c ond - m a t . m t r l - s c i ] F e b pressure[36] via electrostatic gating [10] or with Cu inter-calation [11] or Pd intercalation [37]. 1 T -TiSe becomesinsulating after Pt doping[38]. This implies that dopingaffects the nature of CDWs and electronic properties of1 T -TiSe .A correlated phenomenon, like CDWs, is sensitive tothe presence of defects. Here, using low-temperatureSTM, we focus on the behavior of CDWs at the atomicscale in the presence of intrinsic defects. We investigatedthe relationship between growth conditions and intrinsicdefects in crystals grown by different synthesis routes.We referred to them as sample A (crystal was grown bychemical vapor transport (CVT) using iodine (I )) andsample B (crystal was grown using Se as self-flux) in thesubsequent discussion. II. METHODS
The experiments were performed by using an Omicronultra-high vacuum (UHV) low temperature(LT) scanningtunneling microscope (STM) at 77 K with a base pressureof 5 · –11 mbar. Two 1 T -TiSe crystals were studied.Sample A was grown using CVT with I as the transportagent. Sample B synthesized using the flux zone methodby 2D semiconductors, USA [39]. For STM studies ofboth the samples, 1 T -TiSe single crystal surface wasprepared by cleaving it in the UHV sample preparationchamber. The surface quality was checked with STM at77 K . A clean surface at the atomic level was inferredfrom several STM images of different scan sizes. Elec-trochemically etched tungsten( W ) tips used for imaging.Several trials of imaging were performed with differenttips. Topography measurements were taken in constantcurrent mode. In our set up bias voltage is applied tothe sample. The images were processed using the imageanalysis software SPIP 6.0.9 (Image Metrology). MAT-LAB (by The MathWorks Inc.) was used for numericalcalculations. III. RESULTS AND DISCUSSION T -TiSe crystal is a stack of monolayers bonded byvan der Waals interaction. Each monolayer consists oftitanium ( T i ) atoms sandwiched between two sheets ofselenium ( Se ) atoms (Fig.1 (a) ). Each T i atom is sur-rounded by six Se atoms in octahedral coordination,as shown in Fig.1 (a) . The space group of 1 T -TiSe is P m no. Se atoms in a hexagonal symmetric pat-tern. In constant current topography images, STM tipprobes the topmost Se atoms [40, 41]. The tunneling cur-rent is mainly due to the contribution from the 4 p orbitalof Se atoms. The preferred site for T i atom intercalationis schematically shown in Fig.1 (b) , whereas O substitu-tion site shown in Fig.1 (c) . Iodine is used as a transportagent in CVT method of crystal growth. Substitution of Se atom by I is another defect commonly found in CVTgrown samples. I substitution occupies same sites as O substitution. Defects in the STM topography image ofsample A in Fig.1 (d) and sample B Fig.1 (e) show up aslocalized bright regions. Note that the defects are less insample B than in sample A. FIG. 1. (a)
Schematics of 1 T -TiSe unit cell viewed from anangle, T i atoms in octahedral coordination, Se atoms form atriangular lattice. (b) Schematics of
T i intercalation site (c)
Schematic of O substitution site (d) Empty-states constantcurrent STM image of 30 nm × nm area of sample A, En-larged view of T i intercalation sites are in yellow rounded rect-angle inset and that of O substitution sites are in blue roundedrectangle inset. V bias = 300mV and I set = 300pA. (e) Empty-states constant current STM image of 20 nm × nm area of sample B , V bias = 300mV and I set = 500pA. In Fig.1 (d) the inset in yellow rounded rectangle showsthe enlarged atomic-scale image of the defect, which canbe identified as
T i intercalation site. Intercalated atomsoccupy octahedral sites or tetrahedral sites in the van derWaals gap. For
T i , favorable sites are octahedral sites be-cause of their more significant coordination number, andspacing between two nearby octahedral sites is more con-siderable than tetrahedral sites [42]. The characteristicappearance of intercalated
T i sites can be attributed tochange in the local density of states [43]. These defectsappear bright in filled-states STM images (at negativebias voltages).There were defects with a strongly localized density ofstates at the topmost Se atoms surrounded by depletedregion in empty-states STM images (at positive bias volt-ages). Those defects can be identified with oxygen ( O )substitution of the Se atom in the lower layer. I sub-stitution sites are hard to recognize as they appear veryfaint compare to O sites [41]. Substitution of Se by O or I on topmost layer is not favored energetically [41].Oxygen, present as an impurity in iodine and seleniumprecursor during growth, acts as a native dopant. Sam-ple A has been observed to possess more T i intercalationsites than sample B (Fig.1 (d) and 1 (e) ). Using STMimages taken in different regions of both samples, theaverage number of intercalation sites were counted. Em-ploying this method, we found that the average count of
T i intercalation sites per unit cell for sample A is 0 .
6% ascompared to 0 .
2% sites per unit cell for sample B. Thisobservation supports the dependence of
T i intercalationsites’ concentration on sample growth conditions [7].
FIG. 2. (a)
Filled-states constant current STM image of30 nm X 30 nm area of sample A grown by CVT method, V bias = −
400 mV I set = 300 pA.Areas marked by red areCDW modulated regions, separated by non-modulated re-gions induced by Ti intercalation sites. (b) Fourier transformof topography image in (a) . (c) An enlarged image showing2 X 2 superstructure with CDW peaks marked by yellow cir-cles (d)
Selective inverse Fourier transform of CDW peaksin (b) , (e) Empty-states constant current STM image of 30nm X 30 nm area of sample B grown by flux zone method, V bias = − I set = 400pA, (f ) Fourier transform of to-pography image in (e) . (g) Selective inverse Fourier trans-form of CDW peaks in (f )
Intercalation and substitution change the material’scarrier concentration, leading to a change in the mate-rial’s electronic properties. Correlated states like CDWsare sensitive to external factors like mechanical stress,external pressure, and carrier concentration. Point de-fects can affect CDWs by changing carrier density lo-cally and introducing localized distortions in lattice [20].STM topography images were obtained at different biasvoltages, spatially resolving the CDWs. Fig.2 (a) and2 (e) shows STM images of sample A and B with differ-ent
T i intercalation and O substitution densities. Realspace topography shows the clear 2 × (c) is an enlarged image with atomic res-olution showing CDWs forming superstructure (markedby yellow circles). Fourier transform (FT) of topography images (Fig.2 (b) and 2 (f ) ) yields contributions of latticeand CDW superlattice as six-fold symmetry peaks. Peaksin FT images affirm that the wavelength of CDW is twicethe lattice spacing (first-order Bragg peak). To reducebackground noise and understand the spatial variation ofCDW amplitude, we performed an inverse transform ofCDW FT peaks. Inverse Fourier transform (IFT) imageclearly shows diminishing CDW amplitudes in the pres-ence of T i defects in Fig.2 (d) and 2 (g) . In the presenceof a large number of defects, CDW modulated regions canbe easily visually identified from IFT images (Fig.2 (d) ).In 1 T -TiSe with more T i intercalation density, domainsof CDWs are formed by the presence of defects. 2 X 2superstructure of CDWs changes to 1 X 1 modulationnear intercalation sites, which forms the boundaries ofCDW modulated region (Fig.2 (a) and 2 (c) ). Also, theIFT image is used as a guide to locate these boundaries.Different CDW modulated regions are marked in red inFig.2 (a) . CDW modulated regions separated by bound-aries was not observed in Fig.2 (e) containing fewer inter-calation sites. IFT in Fig. (g) shows the reduced ampli-tude of CDWs in the presence of intercalation sites butno formation of separate regions. 1 T -TiSe thin flakesare reported to oxidise quickly in the atmospheric con-ditions and disrupt the CDW phase [44]. The oxidationof 1 T -TiSe was minimised by cleaving the crystals inour UHV sample preparation chamber(refer to sectionII. METHODS). O and I substitution sites increases thedensity of states in the unoccupied states away from theFermi energy [41]. The CDW gap near Fermi level re-mains unaffected by O or I substitution.Metal intercalation of 1 T -TiSe at certain doping con-centration shows phase shift of CDW modulation acrossthe domain walls [26, 45]. Cu intercalation in 1 T -TiSe re-sults in incommensurate CDW phase with localized com-mensurate CDWs separated by domain walls at criticaldoping concentration [46]. T i , like Cu , is electroposi-tive and suppresses the CDW phase. Cu intercalationinto van der Waals gap of 1 T -TiSe was stabilized bytransfer of charge from Cu to Se atoms in the adjacentlayers [47]. Similarly, the T i intercalant gets stabilizedby charge transfer. A significant overlap between theatomic orbitals of intercalated
T i and Se atoms in thelayer results in the intercalant sites’ peculiar appearancein the STM images. To better understand phase shiftof CDWs across domain boundaries, IFT of both latticeBragg peaks and CDW peaks of Fig.2 (a) were obtained,as shown in Fig.3 (a) . A line section of electron den-sity indicates the suppression of CDW modulation at theboundary (Fig.3 (b) ).Interestingly we observed no phase shift in the CDWmodulation across the boundaries. We can infer that theincreased concentration of T i intercalation leads to thedisruption of CDW and reduces long-range order to smallregions [48].The electropositive nature of
T i intercalation defectand formation of CDW modulated regions and non-modulated boundaries in excess
T i intercalation may pro-
FIG. 3. (a)
Inverse Fourier transform image of Bragg peaksand CDW peaks of STM image shown in Fig.2 (a) of sampleA. Line sections 1 and 2 passing through domain boundary(marked by red region) plotted in (b)
Red part of line sec-tion indicates no CDW modulation. No phase shift observedacross the domain wall. vide some insight into the mechanism of formation ofCDWs. Considering the results as mentioned above, weoffer a hypothesis for suppression of CDWs by
T i interca-lation. Semimetals or small gap semiconductors at lowertemperatures can undergo CDW phase transition by exci-tonic condensation mechanism. Exciton is a bound stateof electrons and holes, mediated by Coulomb interaction,a composite boson. For 1 T -TiSe a small carrier densityand a weakly screened Coulomb interaction can result inexciton formation. Excitons are formed from electronsin the pocket at the L point in the Brillouin zone (BZ)and holes from the pocket at Γ point in the energy bandstucture of 1 T -TiSe . Being a composite boson, it un-dergoes condensation at T CDW ∼ K as the numberof excitons increases. Excitonic condensation leads toa periodic modulation of charge density, a CDW state.The extent to which CDWs are modulated in 1 T -TiSe is intercalation dependent. If we assume excitonic con-densation as the mechanism of CDW state in 1 T -TiSe then the suppression of CDWs and formation of domainboundaries can be explained by the electropositive natureof T i intercalation.The first-principles energy band calculations show thatthe electron pocket at L point in BZ is derived mainlyfrom T i d states. Hole pockets at Γ are derived from Se p states hybridized with T i d states [49]. At Fermi energy, more than half the density of states (DOS) re-sults from T i states, and the rest comes from Se [47]. As T i intercalation’s character is electropositive, the addi-tion of
T i results in the acquisition of electrons. Becauseof
T i ’s larger DOS, electrons added to the system go to
T i derived states around the Fermi level.
T i intercalationnow causes the enhancement of electronic states at Fermienergy, resulting in the strong screening of Coulomb in-teraction between electrons and holes. This screeningresults in the reduction of excitonic pair and suppressionof charge density waves.
FIG. 4. (a)
Autocorrelation of 30 nm x 30 nm area of sampleA , (b)
Autocorrelation of 30 nm x 30 nm area of sample B, (c) and (d)
Line section of autocorrelation of sample A shownin (a) and autocorrelation of sample B shown in (b) alongthe CDW direction respectively, red curve indicates the rateof decay of CDW amplitude.
To further characterize the CDW order, we have calcu-lated the translational correlation. Calculating the corre-lation length of CDWs using topographic images can shedlight on the interplay between CDWs and intercalantdensity. Non modulated boundaries of CDW modulatedregions can be easily identified visually from STM topog-raphy images of areas with large defect concentration asin Fig.3 (a) . Correlation length can be used to gauge thedisruption of CDW order because of intercalation. Cor-relation length measurement can pick up the change inCDW order where it is not easily discernible from STMimages visually. The presence of intercalants dispruptsthe CDW order hence results in a reduced translationalcorrelation length.CDW peaks in the Fourier transform of topographyimages were selected and IFT was performed. IFT im-age displays CDW amplitudes as function of position (asin Fig.2 (d) and 2 (g) ). Autocorrelation of this imageprovides information about the translational correlationlength. The correlation length was obtained by calculat-ing the change in amplitude of CDW from line sectionsin the auto correlation of IFT images, using followingequation [50], A ( x ) = A e − x/ξ cos( k cdw x ) + B (1)Where A ( x ) is CDW amplitude, ξ is correlation length, k cdw wave vector of CDW in x direction, B is averagerandom noise in autocorrelation obtained from IFT and A = 1 − B . The finite correlation length is a conse-quence of the in-homogeneity and finite scanning area[50]. Autocorrelation of STM topography image of areawith more defects in Fig.2 (a) is shown in Fig.4 (a) andarea with less number of defects in Fig.2 (e) is shown inFig.4 (b) . Line section along the axis in autocorrelationimage that is the amplitude of CDW as a function of x was plotted. Correlation length was calculated by afitting curve to the decay rate of amplitude in the linesection. In Fig.4 (b) and (d) blue curve is line sectionalong CDW direction indicates its amplitude and redcurve fitted using (1) shows rate of change of CDW am-plitude. The correlation length obtained from fitting in-dicates that the correlation length is smaller for imageswith more intercalant sites than images with fewer in-tercalant sites. This implies the long-range coherence ofCDWs has broken into small domains because of inter-calation. A sharp decline of CDW amplitudes means asmaller correlation length, which is a sign of the reducedlong-range order. FIG. 5. Correlation length obtained by fitting the CDW am-plitudes for topography images of different Ti intercalationconcentration. Sample A contains more intercalation sitesthan sample B. (The average density of intercalation sites forsample A is 0 .
6% and for sample B is 0 . The correlation length of CDW is a function of theconcentration of Ti intercalation. A better picture ofthe exact dependence of correlation length on Ti inter-calation density can be obtained by plotting the corre-lation length, as shown in Fig.5. Atomically resolvedimages were taken, and the number of Ti intercalationsites were counted. The correlation length of CDWs was calculated from the autocorrelation of IFT images, asmentioned above. Ti intercalation concentration in Sam-ple B is lesser than Sample A and shows a large correla-tion length. The overall trend indicates that the corre-lation length of CDWs decreases as the Ti intercalationincreases. The dependence of correlation length on elec-tron doping nature of Ti intercalant strongly supportsour hypothesis discussed in the earlier part of the exci-tonic origin of CDWs. However, there are certain fea-tures in the graph that require close examination. Thecorrelation length tends to increase gradually at defectconcentration of 0 . .
5% thendecrease again. This feature could be connected to thein-equivalent
T i defect sites for each defect that are aconsequence of CDW modulation [48]. We believe our ex-perimental result will motivate further detailed DensityFunctional theory (DFT) based calculations to explainthis pattern in our correlation length.
IV. CONCLUSIONS
We have explored defects at the atomic scale in twocrystals of 1 T -TiSe grown using different methods. Tiatoms get intercalated in the van der Waals gap. We findthat the density of Ti intercalation affects the long-rangeorder of CDWs. An increased concentration of Ti inter-calation forces CDWs to form domains. There is no phaseshift across the domain walls. The correlation length ofCDWs is inversely proportional to the density of inter-calated Ti atoms. Intercalation of Ti in 1 T -TiSe sup-presses CDWs and forms domain boundaries that can beexplained by electron doping nature of Ti. IntercalatedTi atoms reduce the number of holes in the system. Inthe excitonic condensation model of CDW formation, thereduction of hole concentration depletes excitonic boundstates. CDW suppression is a direct consequence of exci-tonic bound state depletion. Thus we demonstrate thatour study of the dependence of correlation length on Tiintercalation supports the excitonic condensation modelof formation of CDWs in 1 T -TiSe . ACKNOWLEDGMENTS
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