Stacking change in MoS2 bilayers induced by interstitial Mo impurities

We use a theoretical approach to reveal the electronic and structural properties of molybdenum impurities between MoS2 bilayers. We find that interstitial Mo impurities are able to reverse the well-known stability order of the pristine bilayer, because the most stable form of stacking changes from AA’ (undoped) into AB’ (doped). The occurrence of Mo impurities in different positions shows their split electronic levels in the energy gap, following octahedral and tetrahedral crystal fields. The energy stability is related to the accommodation of Mo impurities compacted in hollow sites between layers. Other less stable configurations for Mo dopants have larger interlayer distances and band gaps than those for the most stable stacking. Our findings suggest possible applications such as exciton trapping in layers around impurities, and the control of bilayer stacking by Mo impurities in the growth process.


SI Pristine band-structures
Fig. S1 shows the band structures for the most stable MoS 2 pristine bilayers in 1 × 1 unit cell. In the MoS 2 bilayers with impurities, we use in-plane lattice vectors three times larger than the basic MoS 2 unit cell. Thus, the Γ − K indirect gap of the 1 × 1 unit cell shown in Fig. S1 becomes a direct band gap at the Γ-point because of k-space folding.

SII Mo-impurities in AB stacking
Because the most stable configuration belongs to the 2H-phase, we discuss the properties of impurity within bilayers focusing on the AA' and AB' stackings in the main text. Another type of stacking labeled as AB is possible, in which a layer just glides on the other layer. Although our results show that pristine AB bilayer is slightly more stable than the pristine AA' bilayer, the presence of Mo imp changes the stability order in the order of eVs. The AB stacking configurations are shown in Fig. S2.

S1
Similar to the 2H-phase, the Mo imp in the 3R-phase prefers an octahedral environment, the T-AB configuration has the lowest energy in the 3R-phase. We next use as energy reference the T-AB' configuration, as in the main text. The T-AB configuration has a total energy of 0.75 eV in between the T-AB' and H-AA' configurations. The T'-AB configuration with its tetrahedral symmetry lies 1.82 eV above the most stable T-AB', between the T'-AB' and T'-AA' configurations. The total magnetic moment follows a similar trend according to the specific site, 0 for the T-AB configuration and 2 µ B for the T'-AB configuration.
The band structures presented in Fig. S3 have the same characteristics as in the main text. The T-AB band structure is similar to the one of the ground state (in Fig. 3(a)) and the T'-AB is similar to the T'-AA' (in Fig. 3(c))

SIII Geometrical parameters
Table S1 collects the geometrical parameters after relaxations. We tabulated the parameters measured near the impurities, labeled with an "*", and those measured far from them. The distance between Mo impurities is about 9.66Å, corresponding to the magnitude of the lattice vector. The ∆ z and Mo-S distances for pristine stackings are in agreement with previous reported values. [1][2][3][4] . The experimental ∆ z is 6.14Å for the 2H-phase and 6.12Å for the 3R-phase 5 .  Table S1. Relaxed geometry parameters for MoS 2 pristine bilayers and Mo imp bilayers, given in the order of stability. The length of Mo-S bond is d(Mo-S), and the interlayer Mo-Mo distance is given by ∆ z . The label "*" corresponds to distances measured near the Mo imp . Layer-gap is defined in the main text. All the distances are inÅ, angles are in degrees, and energies in eV.

SIV Technical details
Herein we provide extra technical details to assure the reproducibility of the results. The valence electronic configurations for the atoms in the pseudopotentials calculations were 5s 1 4d 5 and 3s 2 3p 4 for Mo and sulfur atoms, respectively. The pseudopotentials core radii and pseudocore radii are included in Table S2.  Table S2. Pseudopotentials core radii for s, p, d and f channels, and the pseudocore radii r pc for the Mo and S atoms. All the radii are in bhor.