Composition Dependence of the Charge Driven Phase Transition in Group-VI Transition Metal Dichalcogenides

TL;DR

This study uses first-principles calculations to analyze how composition influences charge-driven phase transitions in group-VI transition metal dichalcogenides, revealing barriers that affect phase stability and explaining experimental observations.

Contribution

It provides a detailed computational analysis of the energetics and barriers of phase transitions in TMDs, highlighting composition-dependent effects and their implications.

Findings

High transition barriers explain metallic phase proportions in WS₂ monolayers.

Calculated barriers do not fully account for low metallic phase in MoS₂, indicating other effects.

Charge-induced phase transition barriers vary with composition and influence phase stability.

Abstract

Materials exhibiting multiple stable phases can be used as functional components in electronic and optical applications if the phase transition is controllable. Group-VI transition metal dichalcogenides (TMDs, MX$_2$, where M=Mo, W and X = S, Se) are known to undergo charge induced transitions from semi-conducting H phases to metallic T phases. This occurs, for example, when bulk TMDs are exfoliated with the aid of alkali ion intercalants. However, it is difficult to experimentally decouple the effect of composition-dependent phase transition barriers from indirect effects related to the exfoliation process. Here, using first-principles calculations, we study the energetics of transition between the different structural polytypes of four group-VI TMDs upon lithium adsorption. We find that both the activation barrier from the H phase to the metallic phase in charged monolayers and the reverse barrier in neutral monolayers are required to explain experimental results. We show that the high proportion of metallic phase found in WS$_2$ monolayers after alkali treatment can be explained by high transition barriers to revert back to the H phase once in a neutral state. The calculated barriers however cannot explain the low proportion of metallic phase found in MoS$_2$ monolayers in some experiments and so non-electronic effects must also play a role.

Figures

Tables

Table 1. Table 1:  The lattice parameters a, b (in Å) of the H, the T ′ , and the T ′′  mixed phase of \ch MoS2, \ch MoSe2, \ch WS2 and \ch WSe2.

	H		T′		T′′
	a	b	a	b	a	b
\chMoS2	5.48	3.16	5.57	3.22	11.23	3.16
\chMoSe2	5.71	3.30	5.79	3.34	11.69	3.27
\chWS2	5.48	3.17	5.59	3.23	11.24	3.18
\chWSe2	5.71	3.30	5.81	3.35	11.69	3.28

Table 2. Table 2:  The lattice parameters a, b (in Å) of the H, the T ′ , and the T ′′  mixed phase of Li 0.5 MX 2 and LiMX 2 in the orthorhombic unit cell.

	Li0.5MX2							LiMX2
	H		T′		T′′			H		T′		T′′
Å	a	b	a	b	a	b		a	b	a	b	a	b
\chMoS2	5.53	3.19	5.75	3.25	11.49	3.20		5.68	3.23	5.9	3.29	11.79	3.22
\chMoSe2	5.8	3.32	6.	3.37	11.95	3.34		5.98	3.36	6.12	3.46	12.2	3.38
\chWS2	5.51	3.18	5.74	3.26	11.47	3.19		5.98	3.36	5.88	3.27	11.72	3.19
\chWSe2	5.81	3.29	5.97	3.4	11.90	3.33		5.94	3.33	6.06	3.47	12.30	3.33

Table 3. Table 3:   Adsorption energy, E ads subscript 𝐸 ads E_{\mathrm{ads}} , of lithium on the H and T ′  TMD phases (eV per unit MX 2 ).

	Li0.5MX2		LiMX2
	E${}_{}{}^H{}_{ads}{}^{}$	E${}_{}{}^{T^{\prime }}{}_{ads}{}^{}$	E${}_{}{}^H{}_{ads}{}^{}$	E${}_{}{}^{T^{\prime }}{}_{ads}{}^{}$
\chMoS2	-0.97	-1.64	-2.51	-3.24
\chMoSe2	-0.99	-1.41	-2.36	-2.89
\chWS2	-0.85	-1.58	-2.26	-2.98
\chWSe2	-1.03	-1.38	-2.16	-2.70

Full text

I Introduction

Transition metal dichalcogenides (TMDs), comprised of layered sheets of transition metal atoms sandwiched between two layers of chalcogen atoms (MX2), are chemically versatile, exhibiting a broad range of electronic properties from insulating (ZrS2) to superconducting (NbSe2) Manzeli et al. (2017). As well as by changing the composition, the conductivity of a TMD can be modified by inducing a structural transition between different polymorphs. Several such polymorphs exist, distinguished by the metal coordination of the chalcogen atoms. In the semi-conducting H phase, the chalogen atoms are AA-stacked so that the metal atoms occupy alternate trigonal-prismatic voids. The metallic T phase, on the other hand, has a tetragonal symmetry, with the metal atoms occupying octahedral voids between AB-stacked chalcogen atoms. This particular phase can transform to a semi-metallic distorted octahedral phase, designated here T′. Recently, a further mixed phase, designated T*′′*, which can be viewed as a series of alternating H and T′ phases, was theoretically predicted to be lower in energy than the T′ phase for \chMoS2  Ma et al. (2016).

The ability to induce a transition in \chMoS2 from its ground state H phase to an octahedral phase via alkali metal intercalation has been known since the 1980s Py and Haering (1983). This phase transition was attributed to a transfer of charge from the intercalated atom to the TMD, and more specifically to the d states of the transition metal atom Kertesz and Hoffmann (1984); Chia and Pumera (2018). Indeed, the entire family of group-VI TMDs, where M = Mo, W and X = S, Se and Te, can be manipulated to undergo phase transitions close to ambient conditions Voiry et al. (2015). This has been achieved using a variety of methods, including alkali metal adsorption Gamble (1974); Py and Haering (1983); Wang et al. (2014); Lei et al. (2018), the introduction of impurities or vacancies Raffone et al. (2016); Kretschmer et al. (2017); Pizzochero and Yazyev (2017), electron or laser irradiation Kretschmer et al. (2017); Lin et al. (2014); Cho et al. (2015); Kang et al. (2014); Fan et al. (2015); Guo et al. (2015) and electrostatic gating Radisavljevic and Kis (2013); Wang et al. (2017).

The electronic properties of a TMD are evidently strongly dependent on its structural phase. In \chMoS2 the conductivity of the T phase was found to be up to $10^{7}$ times higher than that of the semiconducting H phase Acerce et al. (2015). The ability to reversibly and reliably switch between these two phases would result in applications as monolayer-thick field effect transistors Nourbakhsh et al. (2016), gas sensors Friedman et al. (2016) and catalysts Luxa et al. (2018). Such applications require precise control over the phase transition process so that a complete phase change to T′ phase can be achieved and maintained.

Liquid phase exfoliation, with the aid of alkali metal intercalation, is a common and effective way of isolating TMD monolayers from the bulk on an industrial scale. In such experiments, the alkali metal atoms are first intercalated into the bulk TMD using an organolithium compound. The intercalated TMD is then solvated in a polar solvent. This results in the discharging of the monolayers, the deintercalation of the metal ion and the exfoliation of individual monolayers from the bulk materials. These layers are subsequently measured to have both H and T phases present.

Of the group-VI TMDs, the phase transition in \chMoS2 has been investigated in detail. Yet, compared to other group-VI TMDs, the phase transition efficiency in \chMoS2 can be relatively low: a comprehensive side-by-side comparison of the experimental transition efficiency in four group-VI TMDs – \chMoS2, \chMoSe2, \chWS2 and \chWSe2 – found that \chWS2 exhibited the largest increase in the proportion of the 1T phase compared to the starting 2H phase (i.e., the 1T/2H ratio), followed by \chMoSe2 and \chWSe2, and eventually \chMoS2. Ambrosi et al. (2015) While the exact ratios were subsequently found to depend on the nature of the organolithium intercalant group used in the experiment, the general trend remained: \chWX2 compounds display a higher proportion of T phase compared to \chMoX2, for both X = S and Se Rohaizad et al. (2017); Tan et al. (2016).

In these alkali metal induced exfoliation experiments, the measured phase transition efficiency will depend not only on the intrinsic composition-dependent free-energy barrier between the different phases, but also on the composition-dependent exfoliation efficiency of the chosen organolithium intercalant. Experimentally, it is difficult to decouple these two contributions. As ion-assisted liquid phase exfoliation is the most suitable method of producing sufficient T phase TMDs on an industrial scale, a complete understanding the mechanism is essential to maximize the amount of metallic phase produced and to prevent a transition back to the H phase.

Previous computational investigations of the phase transition barrier have concentrated on \chMoS2, looking primarily at the threshold charge density required to induce the phase transition. However, a disconcertingly wide range of values have been reported, including 0.35 e per formula unit (f.u.) Li et al. (2016), 0.55 e per f.u. Ma et al. (2016), 0.78 e per f.u. Sun et al. (2016) and almost 2 e per f.u. Gao et al. (2015). The origin of this discrepancy is discussed in detail in the Appendix.

Here, using first-principle calculations, we determine the transition barriers between all possible polytypes of both the pristine and Li-adsorbed group-IV TMDs, with the aim of determining whether the composition dependence of experimental transition efficiency in four group-VI TMDs can be explained using the intrinsic barriers to the phase transitions alone.

II Computational Methods

Density functional theory (DFT) calculations are performed using the vasp-5.4 code Kresse and Furthmüller (1996a, b); Kresse and Joubert (1999). The optB86b-vdW exchange-correlation functional was used to account for long range dispersion interactions.Klimeš et al. (2011); Dion et al. (2004) This functional was previously shown to give accurate lattice parameters and energies for layered materials Björkman (2014); Patil and Caffrey (2018) All calculations are performed with a cutoff energy of 500 eV for the plane wave basis set. A $\Gamma$ centered K-point grid of 11$\times$7$\times$1 is used to calculate the total energy of the H and T′ phases, while a 11$\times$5$\times$1 grid is used for the T*′′* mixed phase.

The structures are relaxed until the force on each atom is less than 0.01 eV/Å. The unit cell length in the direction normal to the plane is fixed at 25 Å for H and T′ phase calculations, and 26 Å for T*′′* mixed phase calculations and all transition state calculations. This corresponds to a minimum vacuum of 18 Å between repeating monolayers and the dipole corrections are applied.

Transition states are determined using the climbing image nudged elastic band (CI-NEB) method Henkelman et al. (2000); Henkelman and Jónsson (2000) with a spring constant of 5. All atoms in the transition state calculations are optimized so that the force on each atom is less than 0.05 eV/Å.

III Results

III.1 Neutral Monolayers

The crystal structures of the H, T′ and T*′′* mixed phases are shown in Fig. 1. The structural parameters determined for all neutral monolayers (without adsorbed Li) are given in Table 1. The lattice constants are dictated by the chalcogen atom, with \chMoS2 and \chWS2 having very similar values in all three phases. Likewise, \chMoSe2 and \chWSe2 have almost identical lattice constants. These values are in good agreement with the available experimental data Gordon et al. (2002); Heising and Kanatzidis (1999); Wildervanck and Jellinek (1964); Schönfeld et al. (1983); Bronsema et al. (1986); Schutte et al. (1987); Dickinson and Pauling (1923); Bell and Herfert (1957); Podberezskaya et al. (2001); Samadi et al. (2018) and with previous calculationsKumar and Ahluwalia (2012); Gusakova et al. (2017); Liu et al. (2013); García et al. (2017) in the literature. For the T′ phase, the calculated $a$ lattice constant of 5.57 Å for \chMoS2 is consistent with the experimentally observed length of 5.6 Å.

In agreement with previous DFT studies, we find the H phase to be the ground state structure for all four materialsKretschmer et al. (2017); Sun et al. (2016); Wang et al. (2017); Kwon et al. (2018); Gao et al. (2015); Nasr Esfahani et al. (2015); Kan et al. (2014). The total energy differences between this phase and both the T′ phase and the T*′′* mixed phase are given in Fig. 2. We find that the energy difference between the H phase and the T′ phase is larger for the sulphides compared to the selenides. It reduces from 0.57 eV for \chMoS2 to 0.35 eV for \chMoSe2 and from 0.56 eV for \chWS2 to 0.29 eV for \chWSe2. Similarly, the energy difference between the H phase and the T*′′* mixed phase reduces from 0.49 eV for \chMoS2  to 0.35 eV for \chMoSe2 and from 0.52 eV for \chWS2 to 0.35 eV for \chWSe2. While the H phase is the ground state in all four cases, the T′ phase is energetically more favourable than the T*′′* mixed phase for \chWSe2 but the ordering is opposite for the \chMoS2 and \chWSe2 (the difference is negligible for \chMoSe2).

The activation barriers to induce a phase transition from the H phase to the T′ and T*′′* mixed phases, as calculated with the CI-NEB method, for all four materials are also shown in Fig. 2. In all cases, the energy barrier to transition directly from the H phase to the T′ phase is large, ranging between 1.22 eV and 1.54 eV. In general, the barrier is smaller for \chMSe2 than for \chMS2. The energy barrier to transition from the H phase to the T*′′* mixed phase is smaller, ranging between 0.64 eV and 1.01 eV. Again, the smallest values occur for the \chMSe2 compounds. In all cases the energy barrier to transition from the ground state H phase to the lowest-lying T phase (namely, T*′′* for \chMoS2, \chMoSe2 and \chWS2, and T′ for \chWSe2) lies between 0.64 eV and 1.22 eV. Evidently, the H phase is very stable and will not convert to the T phase spontaneously, in agreement with experiment. Note that the transition from the T′ phase to the T*′′* mixed phase requires the conversion of only half of the lattice from the T′ phase to the H phase while keeping the other half fixed. Consequently, the barrier to transition from the T′ phase to the T*′′* mixed phase is lower (by between 50 and 65%) than the barrier to undergo the complete transition from T′ phase to the H phase.

The calculated barriers reported here are in units of eV per formula unit (MX2) to facilitate comparison between four materials and the total activation energy required for transition will scale with the number of formula units which transition simultaneously Guo et al. (2015). Note that the phase transition between the H phase and the T phase was shown to be diffusive, rather than a simultaneous phase transition of the entire monolayer. As a result, the activation barrier per f.u. will be modified by the exact details of the nucleation process.

III.2 Charged Monolayers

Introducing extra charge to the TMD via an interaction with explicitly-modelled strong donor atoms bypasses issues related to static charging (discussed in Appendix). We consider two different concentrations of Li atoms adsorbed on the surface of the monolayers, namely Li0.5MX2 and Li1MX2. The stability of the alkali metal-adsorbed monolayer decreases at higher concentrations, and eventually becomes unstable for Li1.5MX2, in agreement with experiment.Leng et al. (2016); Li et al. (2017); Papageorgopoulos and Jaegermann (1995)

The adsorption sites were determined by calculating the total energy of lithium adsorbed on all of the unique candidate sites, shown as blue circles in Fig. 1. These sites include those directly on top of the metal atom, on top of the chalcogen atoms and on the hollow site. In agreement with previous calculations in the literature Hong et al. (2017), we find that irrespective of the material or phase the lowest energy adsorption site is on top of the metal atom (The preferred adsorption position on the T′ phase is shown with a dashed circle in Fig. 1). When increasing the Li concentration to LiMX2, the second Li atom per unit cell adsorbs on the opposite surface, minimizing the electrostatic interaction between the two Li atoms. This configuration is 0.1 eV per formula unit lower in energy than that with both Li atoms adsorbed on the same side of the monolayer. For the case of the T*′′* mixed phase, the lithium atoms are also positioned on top of the metal atoms. For Li0.5MX2, one lithium atom is placed in the H phase region and another in the T′  phase region. For Li1MX2, the remaining lithium atoms were placed on top the metal atoms on the opposite side of the slab.

The extra charge introduced by the Li atoms causes an expansion of the TMD lattice constants. These values are given in Table 2. A Li concentration of Li0.5MX2 increases the lattice constants of the H phase by between 0.3 and 1.75% compared to the neutral lattice. Similarly, Li adsorption increases the lattice constants of the T′ phase by between 9% and 3.23%. Increasing the lithium concentration causes the lattice to expand further, and the expansion is higher in the selenides compared to the sulfides. Bader charge analysis Tang et al. (2009) finds that, for both concentrations considered here, each Li atom donates approximately 0.82 electrons per formula unit. This value is independent of the material type and phase, indicating that the nature of the interaction is similar.

The energy differences between the different polytypes, for all four compounds and for both Li concentrations, are summarized in Fig. 3. The T′ phase becomes the ground state structure of all four Li-adsorbed TMDs. This is followed by the H phase and finally the T*′′* mixed phase. This is in agreement with previous studies on \chMoS2 which have shown a phase transition to occur at a Li concentration of Li0.4\chMoS2Enyashin and Seifert (2012), a K concentration of K0.225\chWSe2Lei et al. (2018) and a Na concentration of Na0.375\chMoS2Li et al. (2017).

The energy difference between both the T′ and T*′′* mixed phases compared to the H phase increases going down the group from S to Se and also going from Mo to W for both considered Li concentrations. On increasing the lithium concentration from Li0.5MX2 to Li1MX2, the energy difference between the T*′′* mixed phase and the H phase decreases slightly for the sulfides but increases for the selenides. In contrast to our observation that the energy of the T*′′* mixed phase increases with respect to the H phase, Ma et al. reported a threshold of 0.4 e per \chMoS2 to induce the transition from the H phase to the T*′′* mixed phase Ma et al. (2016). This discrepancy could be a consequence of the static charging method used in obtaining those results.

These trends in stability can be explained by simple electron filling in the rigid band approximation Lei et al. (2018). For the H and T*′′* mixed phases, excess electrons cause an increase in total energy equal to the band gap. As the T′ phase is semi-metallic, the next available energy level is at the Fermi level, and so this phase becomes lower in energy.

The barriers for the H to T′ phase transition in the charged monolayers are also shown in Fig. 3. In all cases, the barrier for the phase transition decreases due to lithium adsorption. The maximum barrier for the transition from the H phase to the T′ phase is found for \chMoS2 at a value of 0.96 eV for Li0.5\chMoS2 and 0.57 eV for Li0.5\chMoS2. The minimum transition barrier from the H phase to the T′ phase is found for \chWSe2 with a barrier of 0.62 eV for Li0.5\chWSe2 and 0.24 eV for Li1\chWSe2. \chWS2 has the second highest barrier, at a value of 0.55 eV for the Li1\chWS2 structure, while \chMoSe2 has a barrier of 0.42 eV at the same Li concentration. In all cases, the barrier to transition does not decease to zero. As such, the transition cannot be spontaneous and an energy equal to the barrier height needs to be provided to induce the transition.

IV Discussion

Li adsorption is an exothermic process. The adsorption energies, defined as $E_{\mathrm{ads}}=E_{\mathrm{Li}_{x}\mathrm{MX}_{2}}-E_{\mathrm{MX}_{2}}-xE_{\mathrm{Li}}$ where $E_{\mathrm{Li}_{x}\mathrm{MX}_{2}}$ is the total energy of the Li adsorbed structure, $E_{\mathrm{Li}_{x}\mathrm{MX}_{2}}$ is the total energy of the pristine monolayer, $E_{\mathrm{Li}}$ is the energy of an isolated Li atom and $x$ refers to the Li concentration, for all four materials are given in Table 3. The Li adsorption energy is higher for T′ phase as compared to the H phase. For Li0.5MX2, the adsorption energy is largest for \chWSe2 at $-1.03$ eV followed by \chMoSe2 and \chMoS2 at $-0.99$ and $-0.97$ eV per formula unit respectively, and smallest for \chWS2 at $-0.85$ eV per formula unit. This energy is comparable to the energy barrier to the phase transition at this Li concentration. For Li1MX2, the adsorption energy per MX2 approximately doubles, to at least 2.5 times the energy barrier. If some of this energy is used to overcome the barrier to the transition, Li adsorption may be sufficient to make the process spontaneous. Furthermore, given that the rate of transition decreases exponentially with activation energy (as per the Arrhenius equation), we can conclude that, for a given X, \chWX2 will transition at a slightly higher rate than \chMoX2. Likewise, for a given M, \chMSe2  will transition at a higher rate than \chMS2.

This is contradictory to the observation of a higher percentage of T′ phase found for \chWS2 compared to \chMoSe2 and \chWSe2. To explain this, we must also consider the fact that in order to measure the T/H ratio experimentally, the exfoliated monolayers are washed with deionized water and dried in vacuum. In this process the Li ions desorb and the monolayers revert to their neutral state. They are prevented from transitioning immediately back to the ground-state H phase by an energy barrier. This is supported by the observation of the M4+ oxidation state in X-ray photoelectron spectra (XPS) Li et al. (2017); Ambrosi et al. (2015); Rohaizad et al. (2017).

The barriers for the reverse transition from the neutral T′ phase to the neutral H phase, shown in Fig. 2, are now relevant. For all materials, the barrier to return directly to the H phase is prohibitively high, ranging between 0.90 eV and 0.99 eV. Instead, the barrier to transition to a mixed T*′′* type phase is significantly lower, ranging between 0.39 eV and 0.48 eV. Experimental evidence for such an indirect transition from the T′ phase back to the H phase for \chMoS2 via a mixed T*′′* mixed phase can be found: By fitting the rate equation to in-situ Raman measurements, the barrier to transform from the meta-stable metallic phase to the ground state was found to be 400 meV Guo et al. (2015). This barrier value is consistent with the calculated barrier to transition from the T*′′* mixed phase to the H phase of 450 meV calculated here (cf. Fig. 2) whereas the barrier to transition from the T′ phase back to the H phase directly is 970 meV. This suggests that the transition from the T′ phase to the H phase occurs in two steps for this material, via the T*′′* mixed phase.

The barrier to transition from the T*′′* mixed phase to the H phase is smallest for the two selenium compounds at 0.23 eV and 0.27 eV for \chMoSe2 and \chWSe2, respectively. The barrier for \chWS2 is twice as high, at 0.49 eV. The significance of this difference in barrier for \chWS2 and \chWSe2 can be determined by calculating the exponential factor of the Arrhenius equation at room temperature ($k_{B}T=25.7\mathrm{~{}meV}$). This is of the order of  $5\times 10^{-9}$ for \chWS2, whereas it is of the order of  $1\times 10^{-4}$ for \chWSe2. This rate difference is significant and its effects should be experimentally observable. This can explain the significant difference between the percentage of T′ phase observed in \chWS2 compared to both \chMoSe2 and \chWSe2, Ambrosi et al. (2015). However, the calculated activation barriers cannot explain the low 1T/2H ratio found in exfoliated \chMoS2. This discrepancy could be due to non-electronic effects, such as a poor exfoliation efficiency in certain organometallic compounds, edge effects related to the change in lateral size of the exfoliated monolayers, the presence of defects or the oxidation of the exfoliated layers. Another possibility is that the simplified phase transition mechanism considered here does not consider the full nucleation process.

Finally, we note that the T*′′* mixed phase comprises of alternating H and T′ phases, each a unit cell thick, as illustrated in Fig. 1. However, this phase can be viewed as just one example of a family of mixed T′ and H phase structures. By changing the T′:H ratio in \chMoS2 from 1:1 for the T*′′* structure to 2:1, the total energy difference between it and the H phase increases from 0.49 eV to 0.51 eV. By increasing the ratio further to 3:1, the energy difference increases further to 0.52 eV. Clearly, the total energy of \chMoS2 is strongly dependent upon the fraction of H phase. The energy of all such families of confined structures will be higher than that of the H phase but lower than that of the T′ phase. The exact composition of such confined structures will be dependent on the available energy and the TMD flake size and shape and are not confined to the idealised one dimensional structures discussed here. Experimentally, the boundary between the H phase and T′ phase areas are observed to be atomically sharp, as in the T*′′* mixed phase. This boundary evolves over time via a transversal displacement of one of the S planes Lin et al. (2014); Jin et al. (2018) leading to the complete phase transition of the flake. The observed partial phases, with mixed metallic (T′) and insulating (H) regions, can be understood as intermediate stable structures which have lower barriers of transition.

V Conclusion

Group-VI TMDs are known to undergo structural phase transitions from a semi-conducting H phase to a metallic T phase when subjected to alkali-metal assisted exfoliation. The efficiency of this process is strongly dependent on the chemical composition of the material. We show that the ratio of T′ to H phase is maximized if the charge-induced transition from the H phase to the T′ phase is favourable and the reverse transition upon removal of charge is unfavorable. For example, the high proportion of T phase found in WS2 monolayers after alkali treatment can be explained by a high barrier to revert back to the H phase after the initial phase transition has been induced. While charged \chMSe2 materials have the lowest energy barriers to the phase transition, the barriers to revert back to the H phase are also low. This can explain the relatively low content of metallic phase found in \chMoSe2 and \chWSe2 after exfoliation. Finally, the low proportion of metallic phase found in \chMoS2 monolayers in some experiments cannot be explained using the activation barriers alone and so non-electronic effects, such as a differing exfoliation efficiency or differing levels of monolayer oxidation, must also contribute to the outcome.

Acknowledgements.

This work was supported by a Science Foundation Ireland Starting Investigator Research Grant (15/SIRG/3314). Computational resources were provided by the supercomputer facilities at the Trinity Center for High Performance Computing (TCHPC) and at the Irish Center for High-End Computing (project tcphy091b).

Appendix A Implicit Charging

We highlight here some issues related to statically charging monolayers or slabs in DFT with periodic boundary conditions, as it is to these issues that we attribute the wide range of values reported in the literature for the critical charge required to induce a structural phase transition in TMDs.

For the case of isolated charged slabs, such as the TMD monolayers considered here, the electric field due to the extra uniform charge density is constant and should result in potential that varies linearly with distance from the surface of the slab. When periodic boundary conditions are implemented, this linear potential is replaced by the combined effective potential due to the consecutive periodic images. The quantities relating to the isolated slabs can be recovered from these periodic calculations by applying a correction term to the effective potential and total energy. The exact functional form of this potential is discussed in detail by Andreussi at al. Andreussi and Marzari (2014) As discussed in manual for vasp (in the section Monopole, Dipole and Quadrupole corrections) the leading term of this correction, which cancels the interaction of the linear potential with the background compensating charge, is absent. As a result, the total energy is essentially incorrect and cannot be relied upon.

Furthermore, we find that above a certain critical charge, positive eigenvalues are occupied. This was previously shown to occur for atomic anions and can be attributed to the self-interaction error Kim et al. (2011).

Finally, Topsakal et al. showed that, when the basis set is present in the vacuum region, excess negative charge does not stay on the slab but spills over in the vacuum, beyond a critical value which depends on the vacuum thickness Topsakal and Ciraci (2012). This phenomenon is demonstrated in Fig. 4(a) for the H phase of \chMoS2 with a vacuum length of 25 Å perpendicular to the surface of the slab and was previously shown for graphene Topsakal and Ciraci (2011). The excess charge density added is placed in the vacuum and on the outer faces of the monolayer rather than on the d orbital of the metal atom.

To illustrate how these issues affect the determination of the critical charge required to induce a structural phase transition, we show in Fig. 4(b) the total energy difference between the H and the T′ phase of \chMoS2 as a function of excess charge, and for two different vacuum lengths. All three sources of error are now present, namely charge has spilled into the vacuum (above a certain critical excess charge value), the appropriate monopole correction is absent and positive eigenvalues are occupied. We find that the vacuum length of 15 Å (blue squares) shows a phase transition for excess charge of around 0.5 e per f.u. On increasing the vacuum length to 25 Å (orange circles) no such transition is observed.

Clearly, it is not possible to get physically meaningful results using statically charged slabs combined with periodic boundary conditions in density functional theory. A similar erroneous dependence on the vacuum length was also reported by Bal et al. for adsorbed molecules on charged surfaces, further highlighting the irreproducibility of such resultsBal and Neyts (2018).