Local Real-Space View of the Achiral 1 T -TiSe 2 2 × 2 × 2 Charge Density Wave
B. Hildebrand, T. Jaouen, M.-L. Mottas, G. Monney, C. Barreteau, E. Giannini, D. R. Bowler, P. Aebi
aa r X i v : . [ c ond - m a t . m t r l - s c i ] A p r Local Real-Space View of the Achiral 1 T -TiSe × × B. Hildebrand, ∗ T. Jaouen, † M.-L. Mottas, G. Monney, C. Barreteau, E. Giannini, D. R. Bowler, and P. Aebi D´epartement de Physique and Fribourg Center for Nanomaterials,Universit´e de Fribourg, CH-1700 Fribourg, Switzerland Department of Quantum Matter Physics, University of Geneva,24 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland London Centre for Nanotechnology and Department of Physics and Astronomy,University College London, London WC1E 6BT, UK (Dated: April 11, 2018)The transition metal dichalcogenide 1 T -TiSe is a quasi-two-dimensional layered material under-going a commensurate 2 × × ≈
200 K. Scanning tunneling microscopy (STM) combined with intentionallyintroduced interstitial Ti atoms allows to go beyond the usual spatial resolution of STM and to in-timately probe the three-dimensional character of the PLD. Furthermore, the inversion-symmetric,achiral nature of the CDW in the z -direction is revealed, contradicting the claimed existence ofhelical CDW stacking and associated chiral order. This study paves the way to a simultaneousreal-space probing of both charge and structural reconstructions in CDW compounds. Transition metal dichalcogenides (TMDCs) have beenextensively studied for decades, but recently, the devel-opment of methods to obtain nanosheets or even mono-layers has brought renewed interest for these materialsbecause of their attractive electronic and optoelectronicproperties for applications [1, 2]. Many TMDCs alsoundergo charge density waves (CDW) or/and supercon-ducting phase transitions at low temperature [3–7] andrecently, 1 T -TiSe has been even proposed as the firstTMDC exhibiting a CDW with a scalar chiral order [8, 9].Scanning tunneling microscopy (STM) probes the real-space surface electron density. Therefore, the electronicreconstruction associated with the commensurate 2 × × T -TiSe can be easily tracked in the top-most Se layer up to atomic resolution [10, 11]. This localapproach has indeed allowed to propose the chirality ofthe CDW [8, 12] and to observe the formation of phase-shifted CDW domains induced by intercalation of Ti orCu atoms[13–16]. However, the three-dimensional (3D)character of the CDW as well as the periodic lattice dis-tortion (PLD) accompanying the phase transition can, inprinciple, not be directly probed, the displacement am-plitude induced by the PLD [17, 18] being well below theusual spatial resolution of STM [19].Yet, being able to obtain information about the 3Dcharacter of the CDW as well as getting insight about thePLD in real-space is of fundamental interest in the con-text of domain formation or CDW dimensional crossover[20], but also with respect to the question of chiralitywhich strictly signifies a loss of inversion symmetry be-tween two adjacent Se-Ti-Se sandwiches.Here, the electronic signature of defects induced bythe presence of interstitial Ti atoms in-between Se-Ti-Se sandwiches is exploited for probing the symmetry ofthe PLD. This combined STM-defect technique thereforegoes beyond the resolution limitation of STM providingaccess to the structural and intimate 3D nature of the 1 T -TiSe CDW. Interstitial Ti defects are first recognizedand characterized. A systematic asymmetry induced bythe surrounding surface PLD is observed and the asso-ciated deformation is uniquely determined with the helpof density functional theory (DFT) calculations. Further-more, the potential of this new technique is highlightedthrough a simultaneous measurement of two adjacent Se-Ti-Se sandwiches at a step edge where the CDW/PLD isfound to display the expected commensurate 2 × × et al. [17]. Therefore, there is no evidence of a lossof inversion symmetry, contradicting recent claims of achiral phase [8, 12].The strength of this combined STM-defect techniquealso relies on its relative simplicity. Indeed, a defect den-sity of less than 1% allows precise identification of thesurface PLD. Hence, this work not only paves the waytowards a better local understanding of structural recon-structions in CDW compounds but is also highly promis-ing for phase transition studies in general, where a localand real-space vision of entangled electronic and struc-tural instabilities is essential.The 1 T -TiSe single crystals were grown by iodine va-por transport at 700 ℃ with 5% additional Ti in thegrowth tube with respect to perfect stoichiometric con-ditions. Resistivity measurements were performed by astandard four-probe method using a lock-in as currentsource and voltage meter. The samples were cleaved in-situ below 10 − mbar at room temperature. Constantcurrent STM images were recorded at 4.6 K using anOmicron LT-STM, with bias voltage V bias applied to thesample. Base pressure was better than 5 × − mbar.DFT calculations have been performed using the plane-wave pseudopotential code VASP [21, 22], version 5.3.3.Projector augmented waves [23] were used with thePerdew-Burke-Ernzerhof (PBE) [24] exchange correla-tion functional. The cell size of our model was 28.035 FIG. 1. (a) Simulation of the CDW as observed in STM at V bias = 100 mV with indication of three min. and one max. ofthe charge modulation composing the 2 × × × T -TiSe layersseparated by a van der Waals (vdW) gap. The out-of-plane c lattice constant of the 1 × × × × up layer with respectto the PLD. The two possible orientations of displacement aredenominated right-handed and left-handed, respectively. ˚A × T -TiSe surface was modeled withtwo layers and the bottom Se layer fixed. A Monkhorst-Pack mesh with 2 × × k points was used to samplethe Brillouin zone of the cell. The parameters gave an en-ergy difference convergence of better than 0.01 eV. Dur-ing structural relaxations, a tolerance of 0.03 eV/˚A wasapplied. STM images were generated using the Tersoff-Hamann approach [25] in which the current I ( V ) mea-sured in STM is proportional to the integrated LDOS ofthe surface using the bSKAN code [26].Figure 1 (a) shows a DFT simulation, relaxed fromdisplacements following Di Salvo et al. [17], of a high-resolution low-temperature empty-state STM image of1 T -TiSe close to E F (small positive V bias ) [11]. In ad-dition to the 1 × × × up and Se down in Fig.1 (b)] corresponds to 0.028 ˚A at 77 K [17] which is al-most two orders of magnitude below the highest lateralresolution reached by standard STM and can thus notbe directly tracked with this technique. Interestingly,according to the PLD, the new unit cell also contains ex-actly one Se up atom which has not moved with respectto its normal state position and three Se up which haveundergone a small distortion. This observation demon-strates the close relationship between CDW modulationand PLD and allows to directly associate the CDW max.to the non-displaced Se atoms [see Se up max. atoms inFig. 1 (c)] and the CDW min. to the displaced ones [seearrows on Se up min. atoms in Fig. 1 (c)].Nevertheless, we would like to stress that, measuringthe 2 × handedness of the PLD oc-curing within the first Se-Ti-Se sandwich. Indeed, dueto the characteristic antiphase locking of the 2 × × right-handed or left-handed , see Fig. 1 (c)] for one CDWmodulation at the surface. STM alone is therefore com-pletely blind to this essential parameter exhibiting the3D character of the CDW.Figure 2 (a) displays a measured large empty-stateSTM image close to E F (150 mV). Many types of atomicdefects can be recognized, the overall impurity densityapproximately corresponding to ≈ down substitutionsby iodine and oxygen atoms, respectively, and defect D isassociated to intercalated Ti in the vdW gap. Based onsurveys from STM images obtained at different regionsof the sample (not shown), the density of intercalated Tidefects which is mostly determined by the growth tem-perature (700 ℃ ) [17], is 0.57 ± ± up atoms in filled-states [27], below -0.2 V. One FIG. 2. (a) 40 ×
17 nm constant current STM image of the 700 ℃ -grown 1 T -TiSe sample with 5% additional Ti in the growthtube. V bias = 150 mV, I = 0.2 nA. Native defects are labeled A-D according to the reference [27]. The new defect is labeledE. An inset showing the DFT-simulated STM image from Fig. 1 (a) is added as an eye guide; note that the image has beenrotated by 30 ° with respect to Fig. 1 (a). (b), (c) zooms-in on one defect of type D, and E, respectively. Dotted triangles areadded for highlighting the orientation of three Se atoms concerned with the electronic signatures of the defects. has to keep in mind that at this bias voltage (0.15 V),i.e. in empty-states, the electronic perturbation inducedby intercalated Ti is spatially much more extended, insuch a way that the difference between defect D and Eis manifest [see zooms-in on both defects in Fig. 2 (b)and (c) for comparison]. Figure 2 (c) also allows us tohighlight the particular asymmetric nature of the elec-tronic signature of defect E with respect to the lattice.Indeed, two of the three topmost Se atoms concernedwith its electronic perturbation are clearly brighter thanthe third one building a ”bright edge”.Given the special growth conditions, defect E can bereasonably attributed to additional Ti atoms. Also, theorientation of the triangular shape of defect E is identi-cal to the central triangle of the intercalated-Ti electronicsignature [see small dotted triangles Fig. 2 (b) and (c)].This indicates that, as intercalated Ti, defect E is in ver-tical alignment with a structural Ti atom. Therefore, weperformed DFT simulations of STM images in the 2 × × octahedron forming a Ti Se structure [Fig. 3(a))]. As seen in Fig. 3 (b), the DFT-simulated imagefor the relaxed structure at 150 mV of V bias is in ex-cellent agreement with our measurement and especiallyaccounts for the characteristic bright edge. The arrowsgive the direction of displacements of the top Se atomsaccording to the PLD introduced in the simulation.In particular, one of the atoms building the bright edgeis a CDW max. (non-displaced atom) and the secondbright atom corresponds to an atom which moves awayfrom the first one according to the PLD. Comparing thesimulation to the three observed conformations of thebright edge induced by interstitial Ti atoms in Fig. 2[see zoom-ins in Fig. 3 (c)-(e)] first confirms that it is al- FIG. 3. (a) Side view of the DFT-calculated relaxed structurewith an interstitial Ti atom. (b) DFT simulated STM imageat V bias = 150 mV. White circles mark the CDW max. andarrows show the direction of simulated PLD displacementsaccording to Di Salvo et al. [17] of the Se up atoms concernedwith the electronic perturbation of the defect. (c)-(e) Zoom-ins on three defects of type E from Fig. 2 with three differentorientations. White circles again mark the CDW max. ex-tended from the defect-free region and arrows show the direc-tion of PLD displacements deduced from (b). ways constituted of one CDW max. [28]. Then, plottingthe corresponding directions of distortion on the observedconformations [arrows Fig. 3 (c)-(e)] uniquely demon-strates that, here, the underlying PLD is the left-handedone [Fig. 1 (c)].One has to realize that one single interstitial-Ti atomdefect on a STM image is already sufficient for prob-ing the orientation of the underlying PLD ensuring, in FIG. 4. (a) 20 ×
10 nm constant current STM image at V bias = 150 mV and I = 0.1 nA of two adjacent 1 T -TiSe lay-ers. Inset: height difference of approximately 6 ˚A corre-sponding to the separation between two Se-Ti-Se sandwichesobtained along the profile represented by the blue dotted line.Two white rectangles indicate the presence of two defects in-duced by interstitial Ti, one on each layer. (b)-(c) zooms-inon the defects of the bottom and top layer respectively withwhite circles indicating the position of the maxima of theCDW charge modulation and black arrows indicating the cor-responding PLD-induced atomic displacements. (d)-(e) 2.8 × zooms-in showing the CDW modulation in the bot-tom and top layer respectively with arrows indicating the ori-entations of the CDW q -vectors. (f)-(g) FFT-amplitude plotsobtained from (d) and (e) with blue circles highlighting theextra spots originating from the CDW charge modulation. turn, that the 3D character of the CDW can be probedthrough this novel method with minimal defect-induceddisturbance. Figure 4 (a) shows an STM image at astep edge between two adjacent layers separated by ≈ c lattice constant [see inset ofFig. 4 (a)]. The CDW charge modulation is recogniz-able on both terraces and can be easily tracked. Also,two interstitial-Ti defects are clearly observable on eachside of the step edge [see white rectangles in Fig. 4 (a)]therefore providing atomic probes of the PLD orienta-tion for the top and bottom TiSe layers. Comparingthe positions of the CDW maxima with the electronicsignatures of the interstitial-Ti atoms for both layers [seewhite circles on zooms-in Fig. 4 (b) and (c)] allows fordetermining the direction of motion that the Se atoms have undergone through the phase transition [see blackarrows in Fig. 4 (b) and (c)]. The PLD is therefore foundto be left-handed for the top layer and right-handed forthe bottom [Fig. 1 (c)], demonstrating that we are facinga local real-space view of the 2 × × T -TiSe CDW.Furthermore, our experiment allows to readily con-clude on the inversion-symmetric achiral nature of theCDW as initially proposed by Di Salvo et al. [17]. In-deed, the recently claimed chirality of the 1 T -TiSe CDWis based on a helical stacking of the three CDW q -vectorsalong the z -direction with a 2 c /3 interval, leading to theexistence of so-called virtual layers with shifted CDWdensity peaks [8]. This implies different amplitudes ofCDW charge modulations along the three q -vectors notonly in a single layer but also between two c -separatedTiSe layers. Two identically sized defect-free regions ofboth layers are selected in Fig. 4 (a) and shown in Fig.4 (d) and (e). Their close similarity in real-space alreadysuggest that no relative phase shifts exist between thethree CDW q -vectors. In addition, the integrated intensi-ties of the CDW extra-spots on fast-Fourier transformed(FFT) images obtained from Fig. 4 (d) and (e) [Fig. 4(f) and (g)] show a negligible variation of less than 5%.This definitely confirms the conventional layer stackingin 1 T -TiSe and rules out the proposed 2 c /3 helical CDWstacking of chiral CDW phases [8].In summary, the combination of STM with a low-density of specific buried defects has been used to un-cover the periodic lattice distortion at the 1 T -TiSe sur-face. The potential of this new PLD-sensitive probe hasbeen then exemplified through the measurement of theinversion of its handedness at a step edge therefore pro-viding a real-space view of the 2 × × z -direction has been finally confirmed, contradict-ing the existence of CDW helical stacking and associ-ated chiral order. In principle, this new method couldbe easily extended to the analysis of the mixed CDW-superconducting state in Cu-intercalated 1 T -TiSe [14],as well as to other materials exhibiting phase transitionsfor which a better understanding of the interplay betweenelectronic and structural degrees of freedom is required.This project was supported by the Fonds National Su-isse pour la Recherche Scientifique through Div. II. Wewould like to thank C. Monney, C. Renner and M. Sperafor motivating discussions. Skillful technical assistancewas provided by F. Bourqui, B. Hediger and O. 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