Optical Signatures of Defect Centres in Transition Metal Dichalcogenide Monolayers
Pedro Miguel M. C. de Melo, Zeila Zanolli, Matthieu Jean Verstraete
OOptical Signatures of Defect Centres in Transition Metal Dichalco-genide Monolayers
Pedro Miguel M. C. de Melo* Zeila Zanolli* Matthieu J. Verstraete
Optical absorption, Transition metal dichalcogenides, defect centres, quantum dots
Even the best quality 2D materials have non-negligible concentrations of vacancies and impurities. It is critical to understand andquantify how defects change intrinsic properties, and use this knowledge to generate functionality. This challenge can be addressedby employing many-body perturbation theory to obtain the optical absorption spectra of defected transition metal dichalcogenides.Herein metal vacancies, which are largely unreported, show a larger set of polarized exitons than chalcogenide vacancies, introducinglocalized excitons in the sub-optical-gap region, whose wave functions and spectra make them good candidates as quantum emitters.Despite the strong interaction with substitutional defects, the spin texture and pristine exciton energies are preserved, enabling graft-ing and patterning in optical detectors, as the full optical-gap region remains available. A redistribution of excitonic weight betweenthe A and B excitons is visible in both cases and may allow the quantification of the defect concentration. This work establishesexcitonic signatures to characterize defects in 2D materials and highlights vacancies as qubit candidates for quantum computing.
Transition metal dichalcogenides (TMDs) have become strong contenders for the engineering of opticaldevices, especially thanks to their coupling of the spin and valley degrees of freedom, and the presenceof strongly bound excitons, opening avenues for next generation opto-electronics [1,2] . Manufactured sam-ples have strongly improved in quality, but will always contain a significant concentration of defects [3,4] .Graphene can be crystallized almost perfectly in very large flakes, but TMDs present many more naturaldefects, in particular chalcogen vacancies (see e.g. Ref. [5] ). On the bright side, defects and substitutionaldopants can be used to tune the electronic structure and optical properties of materials [6] . By doing so,devices sensitive to specific wavelengths and polarizations can be engineered (reviewed in Ref. [7] ), andcan even behave as single photon emitters [8] . There is an ongoing search for long lived spin states atroom temperatures in TMDs. Here defects are expected to play a crucial role in both scattering andstoring spin information - we showed recently that intrinsic scattering mechanisms (the electron-phononinteraction) can quickly destroy the pumped spin-polarisation [9] . Chalcogen vacancies can also be usedas grafting sites for functional groups, to create bio and chemical sensors [10,11] . Alkane and other func-tional groups can be incorporated directly into the matrix (as opposed to thiol links, for instance, whichnecessitate Au). Carbon atoms have also been used as acceptor dopants for bulk semiconductors [12] .In TMDs, mixed phases with transition metal carbides have been shown to have applications in catal-ysis [13,14] , while in MoS it was shown that carbon substitutions had a strong effect on the TMD elec-tronic and optical properties [15,16] .Many experiments give access to the presence and properties of localized defects. In TMDs the mostcommonly used are: Scanning Tunnelling Microscopy which shows contrast changes due to chemical sub-stitution and electron cloud reconstruction around defects [17] ; Scanning Tunnelling Spectroscopy, which a r X i v : . [ c ond - m a t . o t h e r] O c t robes the detailed electronic structure at the defect site [17] ; optical spectroscopy showing absorptionand photoluminescence by the defect-induced states [18–20] ; tunnelling transport from insulated contactsthrough a core material, which is resonant through defect states in the core band gap [19] ; transmissionelectron microscopy, which gives both structural and chemical information [3,21] .Understanding how defects affect optical properties is a first essential step towards controlled function-alization of materials, both for fingerprinting (optical characterization is simple, remote, and non de-structive) and to understand derived optical functionalities. First-principles computational techniquesprovide a high degree of physical insight and predictive power in the spectral features of defects, to findnew peaks and yield quantitative positions and weight transfers.In this work, we present a fully First-principles investigation of defected monolayers of WS , based onthe Bethe Salpeter Equation (BSE) for electron-hole interactions within many body perturbation theory.We analyze the resulting changes in electronic band structure and optical absorption spectra, aimingto answer the question: can we identify a defect, and ideally quantify its concentration [22] , just by look-ing at the absorption spectrum? While chalcogenide vacancies have been subject to some studies [22] ,metal vacancies and isovalent substitutions like Mo W and (CH ) S are still largely unreported, limitingour knowledge of their behaviour as quantum emitters or chemical detectors. We find that defects fallinto two functional categories, based on the presence of bound states within the band-gap of WS . Wediscuss their spectra, spin textures and the criteria which could be used to identify each defect.In Figure 1 we show the four defects that are the focus of our work: two vacancies (S and W ions);and two substitutions, Mo W and (CH ) S . The S vacancy is the most commonly found defect in mono-layers of WS and often assigned to specific features below the optical gap [18] . In the substitution caseMo W is quite commonly found in nature, and carbon is a common dopant in semiconductors [23] . Studieshave been made on the potential transport applications of TMDs and transition metal carbides [13,24] . Inthe case of MoS experiments point to changes to the electronic structure due to carbon doping, whichshould translate into new optical features [15,25] .In ideal defect engineering, induced changes in the system should yield new controllable features thatare distinct from the pristine properties. In the case of TMDs, a key property that relates to optics isthe polarisation of states at the K wave vector in the Brillouin zone. The polarization will control theallowed optical transitions that form bright excitons. We label in order of increasing energy the lasttwo occupied states and the first two unoccupied states at K as ( v , v , c , c ). For pristine WS (seethe Supplementary Material for more information), the first bright exciton would be made of an opticaltransition from v to c , while the second brightest exciton would be made by a transition from v to c . This is due to the fact that optical selection rules enforce spin conservation in TMDs: the valenceand conduction manifold differ in orbital character, guaranteeing the needed angular momentum changewhen absorbing a helical photon [26] .We start by analyzing two systems which feature states in the pristine band gap: the sulfur and tung-sten vacancies. Their DFT band structures are shown in Figure 1 a) and 1 c), respectively. Note thatusing a 5 × [16,27] . At K the first band is almost completely spin-unpolarized, while the second is completely polarized. This opens a path for new emission channels, aselectronic transitions from the pristine valence states to these new defect states are allowed, with differ-ent oscillator strengths and different excitation energies.The W vacancy is more challenging numerically: the defect bands are split off from the bulk conductionand valence bands, but in the 5 × [16] , and we extract a semi-quantitative picture of the optical properties.Together with the six new mid-gap states, there are also four new occupied states bound to the defect n the valence region (unlike the S vacancy). All these states are spin polarized at K, so if we consideroptical selection rules, we can expect new peaks to show up in the absorption spectrum. These peakswill be a combination of transitions between pristine and defect states, and others between defect states(occupied to empty) in the mid-gap region.The effects of changes in the band structure on the BSE optical spectrum are shown in Figure 3 . Forcomparison the absorption spectrum of the pristine system is shown in grey. The energies of all identi-fied excitons are listed in Table 1 in the SI, along with the reference energies for the pristine case. Notein passing that the higher energy peaks beyond A and B are not reproduced in full in our calculations,due to limitations in the number of states included in the BSE for such large systems.With an S vacancy in Figure 1 a) two new peaks arise at 1.35 and 1.14 eV due to the mid-gap states.They are marked D and D in Figure 1 b). As shown in the inset, D and D correspond to opticaltransitions from the top valence band to the defect state at 1.28 eV and 1.08 eV, respectively. However,since the lowest defect state is not fully polarized, the resulting dipole matrix element is much smallerthan that of the D peak, where the defect state is fully polarized.The exciton wave function for the peak corresponding to D is shown in Figure 3 a). Here the hole isplaced at the position of the vacant sulfur ion (marked by the green sphere) and the magnitude on thecolour-map shows the probability density of the electron (see the Figure 5 in the SI where all the exci-tonic wave functions are depicted). The color map shows that exciton states are highly localized on theneighboring tungsten atoms, indicating that the S vacancy does indeed form a quantum dot.For the W vacancy, whose spectrum is shown in Figure 1 d), more peaks are present due to the increasednumber of defect states. In total we identify five excitons: three composed from holes in the valenceband and electrons in defect states, D to D ; and two others with both the electron and the hole boundto two different manifolds of defect states, D and D . The states involved in the formation in the exci-tons are shown in the inset of Fig 1 d). The most striking feature is the relative intensity of the D andD excitons relative to the A and B excitons. As defect states have very weak dispersion, the associatedelectrons and holes will have large effective masses. It is possible to show [28] that oscillator strengths areproportional to the reduced mass of electron and hole, which explains why the effect is further magnifiedfor transitions between defect states in the case of the W vacancy.A more detailed analysis to the excitonic wave functions shows that two of the low intensity peaks (D and D ) are artefacts due to the interaction of defect states in neighboring periodic replicas. They resultfrom electron-hole pairs localized on different vacancy sites (see Figure 7 in the SI for zoomed out plotsof excitonic wave function). The majority of the electronic charge in the exciton is not localized nearthe same ion vacancy as the hole, and is bound thanks to a finite overlap of the DFT defect state wave-functions. These two peaks will disappear if larger supercells are used: the dipole matrix element andoscillator strength will go do 0. We note that while the BSE is solved only for q = 0, the introduction ofnon-dispersive defect states allows for many transitions to occur throughout the BZ, so an exciton func-tion can actually be composed of several vertical transitions at different momenta (NB: this is distinctfrom a finite wave vector for the whole exciton).In the case of D , shown in Figure 7 in the SI, there is a residual interaction with adjacent vacancy sites,but now the hole is correctly bound to an electron located at the same site. For D , shown in Figure 3 b)both the electron and hole are entirely located at the same site.We studied two cases of substitutions in the WS monolayer; one with a molybdenum atom replacing atungsten atom; and another where a sulfur atom was replaced by a methyl, the simplest (divalent) grouprepresenting grafted organic substituents.In both cases no mid gap states where found (see Figure 4 in the SI for their bandstructures), whichcan be rationalized as follows. In the case of Mo W substitution, molybdenum and tungsten have thesame valence, close atomic and covalent radii [29–31] , resulting in similar chemical properties. A smallconcentration of defects does not lead to strong changes in the charge density, thus leaving the systempractically unchanged when compared to the pristine case. For the (CH ) S substitution, the methylenegroup provides the same number of valence electrons as the sulfur atom. The breaking of local symmetryis not strong enough to perturb the band edges. he lack of mid-gap states is reflected in the absorption spectra shown in Figure 4 . In both cases theexcitonic peaks lie almost on top of those of the pristine system, with the largest deviation being 60meV for the Mo W A peak. The energies for the defected A and B peaks are shown in Table 1 in the SI.There is, however, both weight transfer and changes in spin texture for the A and B peaks at higher en-ergies in the absorption spectrum of both substitutions, which suggests methods to identify these defectsexperimentally. The strongest signature of the substitution lies within the exciton wave functions shownin
Figure 5 . While the exciton cloud is still dispersed throughout the crystal, there is a higher chargeconcentration near the substitution. In the (CH ) S case this is valid for the A exciton (Figure 5 c)), andin Mo W both A and B excitonic states localize near the defect. The (CH ) S case also shows breaking of C symmetry by the methyl molecule. The localization is due both to the defect-related electronic statesand to the choice of the initial position of the hole. For reference, in boron nitride similar extensions of3-5 nearest neighbors are found in Ref. [32] .The two peaks which correspond to the bulk excitons A and B known from literature, and are within 50meV of those of the pristine system in all cases (this is below the absolute precision of the first principlesmethods, and shows the basic convergence of our supercell sizes).We can now establish a more complete picture of how different defects change optical properties ofTMDs. The main changes to the optical spectrum come from new mid-gap states. Isovalent substitu-tions like Mo W and (CH ) S will not be trivially seen in the absorption spectra, but can still be detectedby the ratio of the A and B peak intensities, and by localisation in the exciton’s spatial distribution.In terms of potential applications, the two vacancies are clear front runners for designing quantum dotsand quantum emitters. In particular the S vacancy has already shown some promising results as a singlephoton emitter [33] . The two mid-gap defect states are actively considered for quantum computing ap-plications: they are separated in energy by 0.21 eV, making them addressable using mid-infrared lasers,and insulating them from the highest phonon energy in pristine WS , which is 53 meV [34,35] .The W vacancy offers a larger set of localized excitons, but is more energetic and harder to produce(see Table 1 in the SI). Here the brightest excitons are made of transitions between single particle defectstates, due to their large effective masses. These exciton states show potential in devices as they wouldbehave as bright emitters with multiple internal states, behaving like an embedded molecule for multi-valued quantum computing [36] . The residual band width will disappear only in a 7 × [16] , butthe spin texture and qualitative features are already well represented here (see Figure 3 in the SI). Inactual samples, this vacancy type is more likely to be charged, with electrons filling the dangling S ion’sorbitals.We have shown that the isovalent substitutions Mo W and (CH ) S will not produce in-gap states. Thoughthis is intuitive, it is not trivial, and the local electronic structure is strongly modified as shown by theexcitonic wave functions. For purposes of grafting organic molecules, this means the full band gap win-dow of intrinsic WS will be available for optical sensing.In conclusion, we employ powerful and accurate first principles techniques to shed some light into thechanges in optical properties introduced by point defects in TMDs. Two promising systems, S and Wion vacancies, have potential for quantum emitters and even quantum computing. Isovalent vacancies donot introduce mid-gap states in the band structure, but do change the relative intensity of the canonicalA and B peaks, and the spatial distribution of the first and second excitonic states, in the (CH ) S caseeven leading to a breaking of symmetry. In both cases the full sub optical gap region is available for usein detection of molecules that might graft themselves onto the TMD’s surface. Supporting Information
Supporting Information is available from the Wiley Online Library. Additional details on the conver-gence with cell size, the wave functions for all defect-bound exciton states, and DFT and Many-bodyPerturbation theory methods and numerical parameters used in our calculations.
Acknowledgements
We wish to acknowledge important input, discussions, and stimulus from M. Terrones, B. Biel, and M.Palummo, as well as extensive support from the
Yambo developer team. EFERENCES REFERENCES
PMMCM and MJV acknowledge funding by the Belgian FNRS (PDR G.A. T.1077.15, T.0103.19, andan “out” sabbatical grant to ICN2 Barcelona), and the Communaut´e Fran¸caise de Belgique (ARC AIMEDG.A. 15/19-09). This publication is based upon work of the MELODICA project, funded by the EUFLAG-ERA JTC2017 call.The work benefited from HPC-EUROPA3 (INFRAIA-2016-1-730897) H2020 Research Innovation Ac-tion hosted by the Theory and Simulation group at ICN2 supported by the Barcelona SupercomputingCenter, and from the access provided by ICN2 (Barcelona, Spain) within the framework of the NFFA-Europe Transnational Access Activity (grant agreement No 654360, proposal ID 717, submitted byPMMCM).Z.Z. acknowledges support by the Ram´on y Cajal program RYC-2016-19344 (MINECO/AEI/FSE, UE),Spanish MINECO (FIS2015-64886-C5-3-P), the Severo Ochoa Program (MINECO, SEV-2017-0706), theCERCA programme of the Generalitat de Catalunya (Grant 2017SGR1506), the EC H2020-INFRAEDI-2018-2020 MaX Materials Design at the Exascale CoE(grant No. 824143), and the Netherlands sectorplan program 2019-2023.Computational resources have been provided by the Consortium des Equipements de Calcul Intensif(CECI), funded by FRS-FNRS G.A. 2.5020.11; the Zenobe Tier-1 supercomputer funded by WalloonG.A. 1117545; and by PRACE DECI grants 2DSpin and Pylight on Beskow (G.A. 653838 of H2020,and FP7 RI-312763). The authors thankfully acknowledge the computer resources at Mare Nostrumtechnical support provided by the Barcelona Supercomputing Center (Spanish Supercomputing Net-work, RES). This publication is based upon work from COST Action TUMIEE (CA17126), supportedby COST (European Cooperation in Science and Technology).
Conflicts of Interest
The authors have no commercial or financial conflicts of interest.
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Figure 2: (color online) a) and c): DFT band structures and spin-texture of defected WS for the S and W vacancies,respectively. Color scale indicates value of (cid:104) S z (cid:105) (red for 1 and blue for -1). The reference Fermi level at 0 is set to the lastoccupied state. In both cases new states arise in the mid-gap region, with new occupied defect states also showing in theW vacancy’s band structure. b) and d): Optical absorption spectra of the S and W vacancies, respectively. Absorptionof the pristine system is shown in grey. The positions of the first excitonic peaks are shown by vertical lines. Labels andvertical lines have matching colours. Two new peaks arise for the S vacancy due to the two new manifolds of mid-gapstates. The W vacancy exhibits several new peaks, as four new manifolds of defect states arise. The insets in b and d showthe level scheme and main excitonic transitions. 8 EFERENCES REFERENCES
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Figure 4: (color online) Optical absorption spectra for the 5 × W substitution; b) (CH ) S sub-stitution. Absorption of the pristine system is shown in grey. The positions of the first excitonic peaks are shown byvertical lines. Labels and vertical lines have matching colours. Both cases show no new peaks, with the A and B excitonsat energies that almost match those of the pristine case. 10 EFERENCES REFERENCES