Tuning the electronic properties of monolayer and bilayer transition metal dichalcogenide compounds under direct out-of-plane compression

Tuning the electronic properties of monolayer and bilayer transition metal dichalcogenide compounds under direct out-of-plane compression Ángel Morales García a,b*, Elena del Corro c,d*, Martin Kalbac c, Otakar Frank c a Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University in Prague, Hlavova 2030, 128 43 Prague 2, Czech Republic b Departament de Ciència de Materials i Química Física & Institut de Química Teòrica i Computacional (IQTUB), Universitat de Barcelona, c/ Martí i Franqués 1, 08028 Barcelona, Spain. c J. Heyrovsky Institute of Physical Chemistry of the CAS, v.v.i, Dolejskova 2155/3, 182 23 Prague 8, Czech Republic. d Catalan Institute of Nanoscience and Nanotechnology (ICN2), Campus UAB, Bellaterra, 08193 Barcelona, Spain. *e-mail: angel.morales@ub.edu , elena.delcorro@icn2.net


Modulation of out-of-plane compression
As it is described in the main text certain constraints are required to achieve successfully the out-ofplane compression regime to mimic the experimental conditions when anvil cell devices are used.
These constraints are related to the atomic internal coordinates and the lattice parameters. Hence to shed light on the effect of varying the lattice parameters on the semiconductor-semimetal (SC-SM) pressure, several calculations have been carried out (Tables S1, S2 and Figure S1).
As concluded in the main text, the X-M-X angle in monolayer and the layer distances in bilayer TMDs are the most significant structural parameters to promote the electronic transition from semiconducting the semimetal state. Therefore, the modulation of P SC-SM as a function of a lattice parameter is studied keeping fixed the X-M-X angle and the layer distances (Table S1). Although the metallization pressure changes by varying the lattice a parameter, there are no qualitative differences Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is © the Owner Societies 2017 2 in the transition sequence for the same ∂a/a. These sequences follow the same order as the ones reported in the main text, i.e. MoS 2 > MoS 2 > WSe 2 > WS 2 and MoS 2 > WS 2 > MoSe 2 > WSe 2 for mono-and bilayer TMDs compounds, respectively, moving from low to high pressure. It must be noted that the variation of P SC-SM as a function of a parameter is higher for monolayer than bilayer compounds and it is reflected in the fitting analysis (Table S2). The values of slope (A) show that monolayer compounds present higher sensitivity to a parameter compared to bilayer family ( Figure   S1). Table S1. Evolution of SM-SC transition pressure as a function of a parameter. Bold numbers correspond to the lattice parameter at the equilibrium position. The chalcogenides distances in bilayer structures correspond to distance between the highest and lowest chalcogenides.  Table S2. Linear fitting parameters of P SC-SM (GPa) = A a(Å) +B, where A and B are the slope and the intercept, respectively (see Figure S1).   Table S2.

Spin orbit coupling (SOC)
The spin-orbit coupling, which induces the splitting of the bands in K point of the Brillouin zone for both mono-and bilayer TMDs compounds, is also investigated. The most significant splitting is observed in the VB (see Figs. S2 and S3). Notice that the SOC splitting of the valence band is larger for WX 2 than for MoX 2 compounds (see Table S3)

Effect of the exchange-correlation functional on the band gap energy
The single layered MoS 2 is selected to investigate the effect of the exchange-correlation functional on the band gap energy (Table S4). PBE functional with and without SOC+D3 effects is selected along with top of hybrid (PBE0 and a modified version with 12.5% of Fock exchange) functionals.
The hybrid functionals clearly overestimate the band gap whereas the PBE functional with and without SOC+D3 underestimates it. In conclusion, a standard PBE calculation reports the most accurate band gap.  Figure S4 is analogous to Figure 3 including its interpretation. The data shown in Figure S4 correspond to PBE level. 1L-MoX 2 compounds undergo to metal state at lower stress than 1L-WX 2 compounds. On the other hand, 2L-MS 2 compounds metallize before 2L-MSe 2 compounds.