Manipulating charge-density-wave in 1T -TaS 2 by charge carrier doping: A first-principles investigation
D. F. Shao, R. C. Xiao, W. J. Lu, H. Y. Lv, J. Y. Li, X. B. Zhu, Y. P. Sun
aa r X i v : . [ c ond - m a t . s t r- e l ] S e p Manipulating charge-density-wave in T -TaS by charge carrier doping: Afirst-principles investigation D. F. Shao, ∗ R. C. Xiao,
1, 2, ∗ W. J. Lu, † H. Y. Lv, J. Y. Li,
1, 2
X. B. Zhu, and Y. P. Sun
3, 1, 4, ‡ Key Laboratory of Materials Physics, Institute of Solid State Physics,Chinese Academy of Sciences, Hefei 230031, People’s Republic of China University of Science and Technology of China, Hefei, 230026, People’s Republic of China High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, People’s Republic of China Collaborative Innovation Center of Microstructures, Nanjing University, Nanjing 210093, China
The transition metal dichalcogenide (TMD) 1 T -TaS exhibits a rich set of charge density wave(CDW) orders. Recent investigations suggested that using light or electric field can manipulatethe commensurate (C) CDW ground state. Such manipulations are considered to be determinedby the charge carrier doping. Here we simulate by first-principles calculations the carrier dopingeffect on CCDW in 1 T -TaS . We investigate the charge doping effects on the electronic structuresand phonon instabilities of 1 T structure and analyze the doping induced energy and distortionratio variations in CCDW structure. We found that both in bulk and monolayer 1 T -TaS , CCDWis stable upon electron doping, while hole doping can significantly suppress the CCDW, implyingdifferent mechanisms of such reported manipulations. Light or positive perpendicular electric fieldinduced hole doping increases the energy of CCDW, so that the system transforms to NCCDW orsimilar metastable state. On the other hand, even the CCDW distortion is more stable upon in-plainelectric field induced electron injection, some accompanied effects can drive the system to cross overthe energy barrier from CCDW to nearly commensurate (NC) CDW or similar metastable state.We also estimate that hole doping can introduce potential superconductivity with T c of 6 ∼ T -TaS , which makes the novel material havevery promising applications in the future electronic devices. PACS numbers: 71.45.Lr, 71.20.-b, 63.20.dk
I. INTRODUCTION
Materials with correlated electrons exhibit some ofthe most intriguing quantum states in condensed matterphysics [1–3]. Since the number of electric charge car-riers essentially determines such states, external electricor light field can be applied for controllable manipula-tions. Stability of electric field or light induced states hasbeen demonstrated in some novel systems, where switch-ing occurs between neighboring equilibrium thermody-namic states [4–9]. This powerful characteristic can beapplied in electric devices such as transistors and mem-ories, which are of great importance to not only the fun-damental physics research but also the information pro-cessing technology [10]. Correlated materials with a richset of quantum states delicately balanced on a similarenergy scale will be promising platforms to realize suchdevices.The transition metal dichalcogenide (TMD) 1 T -TaS is one of the promising candidate due to the multi-ple competing ground states in it [11]. As shown inFig. 1 (a), 1 T -TaS shows a CdI -type layered crystalstructure with Ta atoms octahedrally coordinated by Satoms. A unit layer consists of one Ta layer sandwiched ∗ The authors contributed equally to this work. † Electronic address: [email protected] ‡ Electronic address: [email protected]
FIG. 1: (a) Crystal structure of 1 T -TaS . (b) Top view ofTa-Ta plane of 1 T -TaS . The unit cells of conventional 1 T structure and low temperature CCDW structure are denotedwith green solid and dashed lines, respectively. The blackhexagrams are the so-called “David Star” pattern in CCDWphase. (c) Schematic diagrams of “David Star” (left), CCDW(middle), and NCCDW (right) in 1 T -TaS . between two S layers. At low temperatures, strong q -dependent electron-phonon coupling induced periodiclattice distortion makes a √ × √
13 superlattice [12–14], in which Ta atoms displace to make “David Star”clusters (Fig. 1 (b)). The outer twelve atoms within eachstar move slightly towards the atom at the center, lead-ing to the commensurate charge-density-wave (CCDW)ground state. In particular, in CCDW state, the correla-tion effect of 5 d electrons of Ta atoms turns the systeminto Mott insulating state [11, 15–17]. Upon heating to225 K, it undergoes a sequence of first order phase transi-tion to a nearly commensurate (NC) CDW. The NCCDWphase is composed of metallic incommensurate (IC) net-work and Mott insulating CCDW domains. The CCDWdomains shrink upon heating and finally disappear at355 K, while the system transforms to ICCDW state.The standard metallic 1 T structure appears above 535K. Moreover, when CCDW state is suppressed, supercon-ductivity emerges in this system [18–20]. One can expectthat the controllable switching between those states willbe helpful for figuring out the mechanism of CDW andsuperconductivity, and realizing the high performancememory and transistor in future technology. To meetthis goal, many groups performed investigations on thisnovel material. Yu et al. reported a gate-controlled Li ionintercalation can suppress CCDW and introduce super-conducivity [21]. Tsen et al. [22], Hollander et al. [23],Yoshida et al. [24], and Mihailovic et al. [25, 26] reportedthe in-plane electric field induced transition from CCDWstate to NCCDW or some metastable hidden state. Choet al. applied perpendicular electric pulse on 1 T -TaS and found positive electric pulse can introduce IC net-work to suppress Mott state at low temperature [27].Moreover, Zhang et al. [28], Mihailovic et al. [26, 29],and Han et al. [30] suggested that light can introducea transition from CCDW state to NCCDW or hiddenstate as well. In all those manipulations, the transitionsare considered to be determined by the charge carrierdoping. However, the mechanisms of such transitions arenot fully clear yet.In this work, we simulated by first-principles calcula-tions the charge carrier doping effect on CDW in 1 T -TaS . We found that CCDW is stable upon electrondoping, while hole doping significantly suppresses CCDWinstability, implying different mechanisms of recently re-ported electric and photoelectric manipulations of CDWin 1 T -TaS . We figured out such mechanism by analysisof carrier doping effects. Furthermore, we show that su-perconductivity with T c about 6 ∼ II. METHODS
The density functional theory (DFT) calculationswere carried out using QUANTUM ESPRESSO pack-age [31] with ultrasoft pseudopotentials. The exchange-correlation interaction was treated with the generalizedgradient approximation (GGA) with PW91 parametriza-tion [32]. The energy cutoff for the plane-wave basisset was 35 Ry. The Marzari-Vanderbilt Fermi smear-ing method [33] with a smearing parameter of σ = 0 . × ×
8, whilea denser 32 × ×
16 grid was used in the electronphonon coupling calculations. Phonon dispersions werecalculated using density functional perturbation theory(DFPT) [35] with an 8 × × q -points. Forthe monolayer sample, k -points grids of 64 × × × × q -points grids of 8 × × and relaxing the atomic positions,as described later. III. RESULTS AND DISCUSSIONS
The low symmetry CDW structure is usually consid-ered as the high symmetry phase with distortion intro-duced by some instability. Therefore, we firstly investi-gated carrier doping effects in the bulk 1 T -TaS . Theelectronic structures and phonon properties for the sam-ples with different doping level were calculated. As ex-amples, Figure 2 shows the calculated band structuresand Fermi surfaces of the pristine bulk 1 T -TaS , thedoped bulk 1 T -TaS with the doping level of n = 0 . T -TaS with n = 0 . , our results areof good agreement with the previous calculations [11].There is a gap of ∼ . E F )(Fig. 2 (b)). In the Γ- A direction, the two bands aroundthe gap are nearly flat due to the quasi-2D nature of thelayered structure. The band above the gap crosses Fermienergy ( E F ), forming a 2D electron pocket around M point (Figs. 2 (b) and (e)). Such gap increases uponelectron doping and decreases upon hole doping (Figs. 2(a) and (c)). Electron doping increases E F . As shownin Figs. 2 (a) and (d), for the doped bulk 1 T -TaS with n = 0 . E F expands and opensup the original electron pockets around M , leaving holepockets centered at K point. Besides the original bandcrossing E F , a band with higher energy starts to cross E F , forming a 2D cylinder-like electron pocket aroundthe zone center. On the contrary, the hole doping en-hances the dispersion in the Γ- A direction and weakensthe quasi-2D nature by shrinking the lattice and decreas- FIG. 2: The doping effects in bulk TaS investigated using the high symmetry 1 T structure. For the doped TaS with n = 0 . , and the doped TaS with n = 0 . q z dependence of unstable acoustic branch in pristine TaS .(j) and (k) show the charge carrier doping induced variations of lattice parameters a and c , respectively. (l) shows the phononfrequency variations of mode near CCDW instability. The green star in (l) denotes the phonon frequency of mode near CCDWinstability of the doped bulk 1 T -TaS with n = 0 . .The negative charge means the electron doping, while the positive charge means the hole doping. ing the interlayer distance. As shown in Figs. 2 (c) and(f), for the doped bulk 1 T -TaS with n = 0 . E F are not flat anymore. Hole dop-ing reduces E F . The decrease of E F shrinks the originalelectron pockets around M point. Moreover, a lower en-ergy band starts to cross E F , forming a 3D hole pocketaround Γ point.The phonon instability of the high symmetry structureis considered to be directly related to the CDW distor-tion: At high temperatures, the phonon of the high sym-metry structure softens at CDW vector ( q CDW ). Abovethe transition temperature the phonon frequency near q CDW drops but does not go to zero. Just below thetransition temperature the phonon frequency near q CDW is imaginary, meaning there is a restructuring of lat-tice with a superlattice vector of q CDW [36]. Therefore,phonon dispersion without imaginary frequency impliesthat the structure is stable compared to CDW struc-ture. The phonon calculation is proved to be an ef-fective method to simulate the CDW instability: Thecalculated phonon dispersions show instability just lo-cating at q CDW of some TMDs [12–14, 37–39]. Morespecially, for the present 1 T -TaS , experimental reportshowed CDW can be suppressed by pressure [18], whichis correctly simulated by Liu’s phonon calculation [12].In this work we also performed the phonon calculationson each sample. For the pristine 1 T -TaS , our calculationis of good agreement with Liu’s calculation (Fig. 2 (h)). The phonon dispersion show instability very close to theCCDW vector q CCDW = a * + b * . This instabilitypersists at all values of q z , as shown in inset of Fig. 2 (h).For the electron doped sample, the acoustic branches be-come more unstable. As shown in Fig. 2 (g), the unsta-ble modes in the doped bulk 1 T -TaS with with n = 0 . K - M and K -Γ directions, indi-cating the area of instability are largely expanded. Onthe contrary, the hole doping significantly stabilizes lat-tice. As shown in Fig. 2 (i), no unstable mode can befound in the phonon dispersion of the doped bulk 1 T -TaS with n = 0 . locates near q = a * + b * + c * ,we used such mode as an indicator of doping effect onCCDW in TaS . The frequency variation of such modeunder doping is shown in Fig. 2 (l). One can note thatupon electron doping the mode is always unstable in bulk1 T -TaS , while hole doping significantly suppresses theinstability. According to our calculation, the lattice be-comes completely stable when the doping level is higherthan n = 0 . T -TaS with n=0.3holes/f.u., in which the lattice parameters are fixed tothose of the undoped pristine 1 T -TaS . As shown in Fig.2 (l), CCDW can be suppressed by just doping holesinto 1 T -TaS without changing its lattice volume. Thatdemonstrates the suppression of CCDW in the presentcase is predominately by the hole doping effect.Furthermore, we investigated the doping induced en-ergy and the distortion variations in the CCDW statefor the pristine TaS , the doped TaS with n = 0 . with n = 0 . E as∆ E = E CCDW − E T , (1)where E CCDW and E T are the total energies of the re-laxed CCDW structure and the 1 T structure. The dis-tortion rations dr can be expressed as dr in = a − r in a × , (2)and dr in = √ a − r out √ a × , (3)where a is the in-plane lattice parameter of the undis-torted 1 T structure, r in and r in are radius of the innerand outer circles of “David Star”, as shown in Fig. 3 (b).For 1 T -TaS with CCDW structure, the layers stackingorder is not clear yet. Therefore, we simply constructthe √ × √ × √ a and c , where a and c are from Figs. 2 (j) and (k), respectively. In the re-laxed CCDW structures, we found that for the pristineTaS and the doped TaS with n = 0 . with n = 0 . T unit cell is very small ( < T structure. Wealso relaxed the atomic positions with a and c fixed tothose in the pristine TaS to prevent the volume varia-tion. With the lattice parameters of the pristine TaS ,the doped TaS with n = 0 . with n = 0 . T unit cell.If we simply consider that the roles of elec-tron/hole doping on the electronic structures are to in-crease/decrease E F , we can estimate the population ofthe added/removed electrons when electron/hole dopingand understand the calculated results more clearly. Fig-ure 3 (d) shows the density of states (DOS) near E F FIG. 3: The doping effects in the bulk TaS investigated usingthe low symmetry CCDW structure. (a), (b), and (c) arethe charge density in Ta-Ta plane of the doped TaS with n = 0 . , and the doped TaS with n = 0 . directly calculated in CCDW structure. The coloredareas below and above E F denote the electron density whichcan be integrated to one electron. The related electron chargedensities are plotted in the insets of (d). of the pristine TaS in the CCDW structure calculateddirectly by DFT. Based on the integrations of the DOSupwards/downwards from E F , we can see that if one elec-tron is doped into a “David Star” (the doping level isequal to n = 1 /
13 electron/f.u.), it will be mainly addedinto the center of the “David Star”. Obviously, it willenhance the clustering of the charge density. Therefore,CCDW is stable upon electron doping. On the contrary,doping one hole into a “David Star” will notably decreasethe charge density at the center and inner atoms of the“David Star”, which will weaken the charge density clus-tering. Therefore, CCDW is suppressed upon hole dop-ing.We also investigate the doping effect in monolayer 1 T -TaS . As examples, Fig. 4 shows the calculated elec-tronic structures and phonon properties of the mono-layer pristine TaS , the doped TaS with n = 0 . with n = 0 . T structure. For the undoped pristine monolayer1 T -TaS , the band structure is similar to that of pris-tine bulk sample. One band crosses E F , forming a 2Delectron pocket around M point (Figs. 4 (b) and (e)).There is a gap of 0.8 eV below the band crossing E F .In the electrons and holes doped monolayer samples, thegap slightly changes, which is different from the case ofbulk samples. For the doped monolayer 1 T -TaS with n = 0 . T -TaS with n = 0 . E F changes withelectron doping, there is still only one band crossing E F .The 2D cylinder-like electron pocket in the doped bulk1 T -TaS with n = 0 . TABLE I: CCDW formation energy ∆ E and distortion ratios dr in and dr out in the pristine TaS , the doped TaS with n = 0 . with n = 0 . / ” are calculated by fixing thelattice parameters to those of the prinstine TaS and relaxing the atomic positions.∆ E (meV/f.u.) dr in (%) dr out (%)Prinstine − .
54 5 .
39 3 . n = 0 . − . / − .
31 6 . / .
77 3 . / . n = 0 . − . / .
41 0 . / .
00 0 . / . T -TaS . For thedoped TaS with n = 0 . , andthe doped TaS with n = 0 . T -TaS with tensile strainof 5%. monolayer sample (Fig. 4 (d)). For the doped mono-layer 1 T -TaS with n = 0 . E F (Fig. 4 (c)). Similar to the case of bulksamples, the phonon calculation shows that the CDW in-stability in the monolayer 1 T -TaS cannot be suppressedby electron doping (Fig. 4 (g)), while it can be sup-pressed under hole doping (Fig. 4 (i)). The result indi-cates the suppression of CCDW in 1 T -TaS is not dueto the hole doping enhanced band dispersion along Γ- A direction (Figs. 2 (c) and (f)). The suppression shouldbe attributed to the weakening of the electron-phononcoupling at q CDW upon hole doping.Besides, one may note in the monolayer sample, a smallinstability near Γ can be found in the phonon dispersion
FIG. 5: Schematic picture of suppression of CCDW by holedoping. (a) The situation of TaS in the CCDW state whenholes are doped locally. The solid orange “David Stars” arethe area under CCDW distortion. The hollow orange “DavidStars” are the area in which only one hole per a “David Star”is doped, which are still under CCDW distortion. The dashedlight orange “David Stars” are the area with more dopedholes, in which the CCDW distortion is fully suppressed. Theblack arrows denote the diffusion of the doped holes. (b) Theschematic band structure of TaS with CCDW distortion. (c)The schematic band structure of TaS with CCDW distortionwhen one hole per “David Star” is doped. (d) The schematicband structure of TaS in 1 T structure. (Fig. 4 (h)). In a very recent calculation of phonondispersion of monolayer 1 T -TaS by Zhang et al. [40],there is a similar instability near Γ. Such instability isconsistent with the instability against long-wavelengthtransversal waves [41, 42]. This instability is suggest tobe fixed by defects, such as ripples or grain boundaries,which do not allow these waves by limiting the size [41–43]. Furthermore, we found tensile strain can suppresssuch instability near Γ, which can be easily applied tomonolayer materials [44, 45]. As an example, in Fig. 4(h), the red dashed lines show the phonon dispersion of1 T -TaS under a tensile strain of 5%, in which the in-stability near Γ is suppressed. The observation indicatesthat the application of tensile strain is helpful for stabiliz-ing the experimentally exfoliated monolayer or fewlayer FIG. 6: Schematic diagram of (a) energy in the ground state of 1 T -TaS , mechanism of switching between CCDW andNCCDW/metastable state induced by (b) perpendicular positive electric field, (c) light and (d) in-plane electric field. T -TaS .Based on our calculations of phonon properties in 1 T structure, CCDW formation energies and distortion ra-tios in CCDW structure, we can conclude that when thedoping level is above n = 0 . T -TaS for bulk and monolayer, i.e. all the “DavidStars” should be melted. Experimentally, holes can di-rectly be introduced by a positive electric field perpen-dicular to the sample [27], or by light [26, 28–30]. Onecan expect that in reality the doped holes will firstly dis-tribute in a local area and gradually diffuse out, i.e. eventhe doping level might be much lower than 0.2 holes/f.u.,in the local area, the doping level could be high enough tomelt the “David Stars” in this area and destroy the long-range CCDW, as shown in Fig. 5 (a). We describe thepossible picture of such process here: In 1 T structure, theelectronic structure near E F are formed predominantlyfrom a single Ta d band, which splits into subbands bythe formation of CCDW state. Six of these subbandsare fulfilled with 12 electrons per new CCDW unit cell,forming a manifold of occupied states. The 13th leftoverelectron is localized on the central Ta atom of the “DavidStars”, forming a half-filled subband at E F . This half-filled subband further splits by the Coulomb interactioninto upper and lower Hubbard bands (UHB and LHB), asshown in Fig. 5 (b). Light or positive perpendicular elec-tric filed can firstly excite one electron from LHB to UHB,and create one hole in LHB (Fig. 5 (c)). In real space,the hole doped by light or positive perpendicular electricfiled locates at the center of the “David Stars”, leavinga polaron with an excess charge. The other 12 electronsin this polaron are still star-shaped around the central,thus screening the excess charge. When more holes aredoped into the “David Stars”, the CCDW distortion issuppressed locally, the structure transforms into 1 T inthe doping area. The splitting subbands merge to a sin-gle band again (Fig. 5 (d)). In this case, the “DavidStars” shaped clusters are annihilated and cannot screenthe holes any more. So the holes diffuse into neighboring“David Stars”. Therefore, upon hole doping in 1 T -TaS in CCDW phase, CCDW should firstly transform to a NCCDW or metastable phase composed of CCDW do-mains and ICCDW network. For example, Cho et al.[27] applied a very small positive perpendicular voltagepulse on 1 T -TaS single crystal sample within a typi-cal scanning tunneling microscope (STM) set-up. Sincelocal hole concentration under the STM tip is largely en-hanced, a pulse creates a textured CDW domain of afew tens of nanometers with an irregular domain wallnetwork inside. They considered that such network isconsistent with those in the thermally excited NCCDWphase [27]. Besides, dI/dV measured implies the weaken-ing and broadening of the Hubbard states together withthe reduction of the Mott gap inside the textured CDWdomain induced by positive perpendicular electric filed[27]. That is corresponding to our picture: Holes diffusefrom the domain wall into the neighboring area insidethe domain. Although the concentration of the diffusedholes is not high enough to suppress CCDW distortioninside the domain, it can create the hole-electron pairin LHB and UHB to reduce the Mott gap. Moreover,the photoexcitation of electrons can be considered as di-rectly doping holes into system. Mihailovic’s group founda laser pulse can introduce a transition from CCDW toa hidden state in 1 T -TaS thin flake [26, 29]. The Ra-man spectrum of such hidden state is completely differ-ent from that in CCDW and NCCDW phases [29]. Suchhidden state is demonstrated to be a metastable phase,which is different from NCCDW, but should be composedof CCDW domains and ICCDW network as well [26, 29].Han et al. observed the electron diffraction spots variesfrom CCDW case to ICCDW case when applying laserto TaS in CCDW phase [30]. Very recently, Zhang etal. showed laser can introduce a CCDW-NCCDW tran-sition in bulk 1 T -TaS single crystal [28]. On the otherhand, in experiments upon hole doping in 1 T -TaS inhigh temperature phase, the CCDW transition tempera-ture is significantly lowered [28, 30]. Both the two kindsof structural evidences can be well explained by our cal-culation. For the sake of illustration we draw, we drewa schematic diagram to describe the mechanism of thehole doping induced CCDW-NCCDW/metastable phasetransition, as shown in Figs. 6 (a), (b) and (c). In thepristine 1 T -TaS , CCDW phase has the lowest energy(Fig. 6 (a)). The hole doping by perpendicular field orby light can stabilize lattice and largely increase the en-ergy of CCDW phase. In this case, the system transformsto NCCDW or other metastable phase (Figs. 6 (b) and(c)).On the other hand, according to our calculation,CCDW lattice distortion is stable upon electron doping.According to the report by Cho et al., negative perpen-dicular voltage pulses could not make change in CCDWstate [27], which is consistent with our estimation. How-ever, some recent experimental works suggest the oppo-site results. Yu et al. doped electron into 1 T -TaS byintercalation of Li ions and found CCDW can be sup-pressed [21]. The intercalated ions cannot only carry elec-trons, but also strongly influence the lattice structuresand induce disorder, which can suppress CDW in TMDs[11, 46, 47]. Therefore, one cannot simply attribute thesuppression to the electron doping. To demonstrate thepure electron doping effect on CDW, more direct dop-ing experiments by negative perpendicular electric fieldor liquid-gated method should perform. Some works re-ported the suppression of CCDW by in-plane electric field[22–26]. By measuring the temperature dependence of re-sistivity ( R − T ), Yoshida et al. found the in-plane fieldcannot affect the NCCDW/ICCDW transition in R − T curve, but can introduce a metastable state with verylow resistivity at low temperatures [24]. If we considerthat the R − T in CCDW, NCCDW, and ICCDW re-flects the related structural characteristics, one can inferthat the in-plane field induced the metastable state withdifferent structural characteristics, i.e. the in-plane fieldcan suppress CCDW distortion as well. The suppressionsof CCDW by the in-plane field are usually explained aselectron injection effect [23, 26]. However, according toour calculation, CCDW could be stable upon electrondoping. Therefore, the effect of in-plane field should bemore complex. We consider some potential mechanismsof the suppressions by in-plane field: Besides the purecharge carrier injection, one can expect that the in-planeelectric field can also force the electrons in the “DavidStar” to be delocalized. Moreover, the in-plane electricfield might depinning the CDW, which is suggested in1 T -TaS bulk single crystals [48]. The suppression ofCCDW by in-plane electric field might also be due tothe thermal activation by local Joule heating as currentflows through the material. The real mechanism of thesuppression of CCDW by in-plane field needs to be fig-ured out by more experimental and theoretical works.Here we only offer a general description of such process:Although CCDW state might still have the lower energy,the in-plane electric field can drive the system to crossover the energy barrier from CCDW to NCCDW or othermetastable phase, as shown in the schematic diagram inFig. 6 (d).As described above, once long range CCDW is sup-pressed, the transition between Mott insulating state tometallic state can be observed: When CCDW is sup- F( ) ( ) (a) under 2.5% strain F( ) ( ) (b) F () (cm -1 ) () FIG. 7: Eliashberg function (left) and the integrated electron-phonon coupling strength (right) for (a) the doped bulk 1 T -TaS with n = 0 .
25 holes/f.u. and (b) the doped monolayer1 T -TaS with n = 0 .
35 holes/f.u. under a tensile strain of2.5%, respectively. pressed, domain walls show up, which can be seen asconducting channels to induce metallic state [18]. In theCCDW area near the domain walls, the Hubbard statesare weakening and broadening and the Mott gap is re-duced. [27]. Furthermore, superconductivity can emergein percolated metallic IC network [18]. While we arenot able to directly model the textured IC phase, we canstill estimate the superconductivity using 1 T structurequalitatively. Approximately using the high symmetrydoped bulk 1 T -TaS with n = 0 .
25 holes/f.u. and thedoped monolayer 1 T -TaS with n = 0 .
35 holes/f.u. un-der a tensile strain of 2.5%, for which all the phononinstabilities are just suppressed, we estimated the po-tential carrier doping induced superconductivity by theelectron-phonon coupling calculation. Figure 7 shows thecalculated Eliashberg spectral function α F ( ω ) = 1 N ( E F ) X k , q ,ν,n,m δ ( ǫ n k ) δ ( ǫ m k + q ) | g ν,n,m k , k + q | δ ( ω − ω ν q ) , (4)where N ( E F ) is the density of states at E F , ω ν q is phononfrequency, ǫ n k is electronic energy, and g ν,n,m k , k + q is electron-phonon coupling matrix element. The total electron-phonon coupling strength is then λ = 2 Z ∞ α F ( ω ) ω dω. (5)The calculated λ for the two samples are 0.81 and 0.96,respectively. We estimated T c based on the modifiedMcMillan formula [49]: T C = ω log . (cid:18) − . λ ) λ − µ ∗ − . λµ ∗ (cid:19) , (6)where the Coulomb pseudopotential µ ∗ is set to a typicalvalue of µ ∗ = 0 .
1. The logarithmically averaged charac-teristic phonon frequency ω log is defined as ω log = exp (cid:18) λ Z dωω α F ( ω ) log ω (cid:19) . (7)The calculated ω log for the two samples are 136.7 and98.4 K, respectively. Using those parameters, we canestimate that the superconductivity with T c of 6 ∼
7K can emerge in the hole doped 1 T -TaS . To observethe superconductivity we predicted, the doping inducedmetallic network between CCDW domain in NCCDWor other metastable phase must be percolated, which re-quires experimental devices with ability to dope moreholes. Recently, Suda et al. suggested a high level holedoping technique using photoactive electric double layer[50], which might be applied to verify our prediction. IV. CONCLUSION
In conclusion, based on the first-principles calculation,we simulated the carrier doping effect in the bulk andmonolayer 1 T -TaS . We found that CCDW is stableupon electron doping, while hole doping can notably sup-press the CCDW. According to our analysis, the dif-ferent mechanisms of the reported electric and photo-electric manipulations of CCDW in 1 T -TaS are figured out: Light or positive perpendicular electric field in-duced hole doping significantly increases the energy ofCCDW, so that the system transforms to NCCDW orsimilar metastable state. Although the CCDW distor-tion is more stable upon the in-plane electric field in-duced electron injection, some accompanied effects candrive the system to cross over the energy barrier fromCCDW to NCCDW or similar metastable state. We alsoestimated that a potential superconductivity with T c of6 ∼ T -TaS , which makes the novel materialhave a very promising application in the future electronicdevices. Acknowledgments
We thank Prof. Z. G. Sheng and Dr. Y. Z.Zhang for helpful discussion. This work was supportedby the National Key Research and Development Pro-gram under Contract No. 2016YFA0300404, the Na-tional Nature Science Foundation of China (Grant No.11674326, 11304320, 11274311, 11404340, 1408085MA11,and U1232139). [1] M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys.70, 1039 (1998).[2] E. Dagotto, Rev. Mod. Phys. 66, 763 (1994).[3] P. A. Lee, N. Nagaosa, and X. -G. Wen, Rev. Mod. Phys.78, 17 (2006).[4] H. Ohno, D. Chiba, F. Matsukura, T. Omiya, E. Abe, T.Dietl, Y. Ohno, and K. Ohtani, Nature 408, 944 (2000).[5] Y. Yamada, K. Ueno, T. Fukumura, H. T. Yuan, H. Shi-motani, Y. Iwasa,[6] L. Gu, S. Tsukimoto, Y. Ikuhara, and M. Kawasaki, Sci-ence 332, 1065 (2011).[7] R. E. Glover, III and M. D. Sherrill, Phys. Rev. Lett. 5,248 (1960).[8] N. Takubo, Y. Ogimoto, M. Nakamura, H. Tamaru,M. Izumi, and K. Miyano, Phys. Rev. Lett. 95, 017404(2005).[9] A. Zakery, S. R. 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Nagaosa, and X. -G. Wen, Rev. Mod. Phys.78, 17 (2006).[4] H. Ohno, D. Chiba, F. Matsukura, T. Omiya, E. Abe, T.Dietl, Y. Ohno, and K. Ohtani, Nature 408, 944 (2000).[5] Y. Yamada, K. Ueno, T. Fukumura, H. T. Yuan, H. Shi-motani, Y. Iwasa,[6] L. Gu, S. Tsukimoto, Y. Ikuhara, and M. Kawasaki, Sci-ence 332, 1065 (2011).[7] R. E. Glover, III and M. D. Sherrill, Phys. Rev. Lett. 5,248 (1960).[8] N. Takubo, Y. Ogimoto, M. Nakamura, H. Tamaru,M. Izumi, and K. Miyano, Phys. Rev. Lett. 95, 017404(2005).[9] A. Zakery, S. R. Elliott, Optical Nonlinearities in Chalco-genide Glasses and Their Applications (Springer, NewYork, 2007).[10] M. Nakano, K. Shibuya, D. Okuyama, T. Hatano, S. Ono,M. Kawasaki, Y. Iwasa, and Y. Tokura, Nature 487, 459(2012).[11] J. A. Wilson, F. J. Di Salvo, and S. Mahajan, Adv. Phys.24, 117 (1975).[12] A. Y. Liu, Phy. Rev. B 79, 220515(R) (2009).[13] Y. Ge and Amy Y. Liu, Phy. Rev. B 82. 155133 (2010).[14] Y. Liu, D. F. Shao, L. J. Li, W. J. Lu, X. D. Zhu, P.Tong, R. C. Xiao, L. S. Ling, C. Y. Xi, L. Pi, H. F. Tian, H. X. Yang, J. Q. Li, W. H. Song, X. B. Zhu, Y. P. Sun,Phys. Rev. B 94, 045131 (2016).[15] P. Darancet, A. J. Millis, and C.A. Marianetti, Phys.Rev. B 90, 045134 (2014).[16] R. Ang, Y. Tanaka, E. Ieki, K. Nakayama, T. Sato, L. J.Li, W. J. Lu, Y. P. Sun, and T. Takahashi, Phys. Rev.Lett. 109, 176403 (2012).[17] R. Ang, Y. Miyata, E. Ieki, K. Nakayama, T. Sato, Y.Liu, W. J. Lu, Y. P. Sun, and T. Takahashi, Phys. Rev.B 88, 115145 (2013).[18] B. Sipos, A. F. Kusmartseva, A. Akrap, H. Berger, L.Forr´o, and E. Tutiˇs, Nature Mater. 7, 960 (2008).[19] Y. Liu, R. Ang, W. J. Lu, W. H. Song, L. J. Li, and Y.P. Sun, Appl. Phys. Lett. 102, 192602 (2013).[20] L. J. Li, W. J. Lu, X. D. Zhu, L. S. Ling, Z. Qu, and Y.P. Sun, Europhys. Lett. 97, 67005 (2012).[21] Y. Yu, F. Yang, X. F. Lu, Y. J. Yan, Y. -H. Cho, L.Ma, X. Niu, S. Kim, Y. -W. Son, D. Feng, S. Li, S. -W.Cheong, X. H. Chen, and Y. Zhang, Nat. Nanotechnol.10, 270 (2015).[22] A. W. Tsen, R. Hovden, D. Wang, Y. D. Kim, J.Okamoto, K. A. Spoth, Y. Liu, W. J. Lu, Y. P. Sun,J. Hone, L. F. Kourkoutis, P. Kim, and A. N. Pasupathy,PNAS 8, 15054(2015).[23] M. J. Hollander, Y. Liu, W. J. Lu, L. J. Li, Y. P. Sun, J.A. Robinson, and S. Datta, Nano Lett. 15, 1861 (2015).[24] Masaro Yoshida, Ryuji Suzuki, Yijin Zhang, MasakiNakano, and Yoshihiro Iwasa, Sci. Adv. 1, e1500606