Structural evolution and phase transition mechanism of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {MoSe}_2$$\end{document}MoSe2 under high pressure

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {MoSe}_2$$\end{document}MoSe2 is a layered transition-metal dichalcogenide (TMD) with outstanding electronic and optical properties, which is widely used in field-effect transistor (FET). Here the structural evolution and phase transition of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {MoSe}_2$$\end{document}MoSe2 under high pressure are systematically studied by CALYPSO structural search method and first-principles calculations. The structural evolutions of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {MoSe}_2$$\end{document}MoSe2 show that the ground state structure under ambient pressure is the experimentally observed P6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_3$$\end{document}3/mmc phase, which transfers to R3m phase at 1.9 GPa. The trigonal R3m phase of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {MoSe}_2$$\end{document}MoSe2 is stable up to 72.1 GPa, then, it transforms into a new P6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_3$$\end{document}3/mmc phase with different atomic coordinates of Se atoms. This phase is extremely robust under ultrahigh pressure and finally changes to another trigonal R-3m phase under 491.1 GPa. The elastic constants and phonon dispersion curves indicate that the ambient pressure phase and three new high-pressure phases are all stable. The electronic band structure and projected density of states analyses reveal a pressure induced semiconducting to metallic transition under 72.1 GPa. These results offer a detailed structural evolution and phase diagram of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {MoSe}_2$$\end{document}MoSe2 under high pressure, which may also provide insights for exploration other TMDs under ultrahigh pressure.


Theoretical methods
We have conducted a systematical structure search for MoSe 2 under high pressure based on Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) approach and first-principles calculations [13][14][15][16][17][18][19][20] . The advantages of these techniques are to predict the stable and metastable structures at the given chemical compositions within certain condition 21,22 . The total energies and electronic properties are calculated within the density functional theory (DFT) framework, as it has implemented by Vienna ab initio simulation package (VASP) code 23 .
The projector augmented wave (PAW) method has employed in the DFT calculations to describe electron-ion interactions in MoSe 2 . The 4d 5 , 5s 1 and 4s 2 , 4p 4 are treated as the valence electrons for Mo and Se atoms, respectively 24 . We set the cutoff energy of 600 eV for the wave-function to expand plane waves and select dense Monkhorst-Pack k 25 meshes to ensure all enthalpy calculations are converged in 1 meV/atom. The phonopy code has used to calculate the phonon dispersion curves using 2 × 2 × 1 supercells for P6 3 /mmc, R3m, and R-3m phases of MoSe 2 26 . Based on the ground state structures of MoSe 2 under different pressure, the energy band structure, density of states, and elastic properties are also calculated 27 and discussed in detail.

Results and discussion
We have predicated about 1000 potential structures for MoSe 2 at each selected pressure. The top 100 candidate structures of MoSe 2 under 0 GPa, 50 GPa, 100 GPa, 200 GPa, and 500 GPa are reoptimized by high accuracy calculations. We have successfully identified the experiment observed P6 3 /mmc (2H) phase under ambient pressure, which verifies that the CALYPSO method is perfectly suitable for MoSe 2 and the searched results are reliable. It can be seen from Fig. 1a that the enthalpies of R3m and P6 3 /mmc phases are almost the same when the pressure increase from 0 to 100 GPa. Interestingly, some potential low energy phases at low-pressure range are all layered structures. Thus, we have considered the van der Waals (VDW) interactions in the DFT calculations under low-pressure between 0 to 10 GPa. From Fig. 1b, we can clearly find that the energy of P6 3 /mmc phase is lower than that of R3m phase at 0 GPa to 1.9 GPa 28 , and the energy of R3m phase is lower than that of P6 3 /mmc phase with pressure ranged of 1.9 GPa to 72.1 GPa. In fact, the transform pressure of MoSe 2 from R3m phase to P6 3 /mmc phase is almost unchanged with/without considering the VDW effects. The transform pressure of MoSe 2 from R3m phase to P6 3 /mmc phase is about 2.5 GPa by without considering the VDW interactions, which maybe due to that the Mo and Se atoms are relatively heavy and the influences of VDW interactions on the energy calculations of MoSe 2 are negligible. When the pressure is higher than 72.1 GPa, a new P6 3 /mmc phase is uncovered, which is different from the initial P6 3 /mmc phase. The main differences are the crystal lattice parameters and atomic coordinates of Se atoms. It is extremely robust under ultrahigh pressure and final changes to the trigonal R-3m phase under 491.1 GPa. The structural phase transition of MoSe 2 under ultrahigh pressure is shown in Fig. 1c. The corresponding crystal structures of MoSe 2 under high pressure up to 500 GPa are shown in Fig. 2. To further prove the structural stability of MoSe 2 , we have calculated the formation energies of possible phases and considered the potential energy decomposition to bulk Se and Mo crystals and relevant Mo-Se compounds. The calculations once again indicate that MoSe 2 is stable. The detailed results are shown in Fig. S1 in the Supplementary Information. From Fig. 2, we can find that the unit cell of P6 3 /mmc is stacked repeatedly with a period of two MoSe 6 layers, while cells of R3m and R-3m are stacked repeatedly with a period of three MoSe 6 layers. The optimized lattice parameters and atomic coordinates of the four phases are listed in Table 1.
We now test the chemical, dynamical, and mechanical stabilities of MoSe 2 . The cohesive energy of MoSe 2 can be calculated by the formula as following [29][30][31][32][33] ,   Fig. 3. There is no presence of imaginary frequency in the Brillouin zone, which indicates that these four phases of MoSe 2 are dynamically stable. Meanwhile, we have calculated the elastic constants of the four phases of MoSe 2 under different pressures, which are P6 3 /mmc phase at 0 GPa, R3m phase at 20 GPa, P6 3 /mmc phase at 80 GPa, and R-3m phase at 500 GPa. The elastic constants are listed in Table 2. The stability criteria of hexagonal and trigonal crystal structure are C 11 > |C 12 | , (C 11 + C 12 ) > 2C 2 13 , (C 11 − C 12 )C 44 > 2C 2 14 for trigonal crystal and C 11 > 0 , C 44 > 0 , C 11 > |C 12 | , (C 11 + C 12 ) > 2C 2 13 for hexagonal crystal 35 . According to the above criteria, we note that the calculated elastic constants match well with the stability criteria in corresponding space group symmetries [36][37][38][39] . Thus, we can conclude that these four phases of MoSe 2 are mechanical stability.
To deeply understand of the effect of pressure on the electronic properties, the evolution of electronic band structure and density of states of the four phases of MoSe 2 are shown in Fig. 4. At 0 GPa, the ground state structure is P6 3 /mmc phase. It can be seen from Fig. 4a, the P6 3 /mmc phase is a direct bandgap semiconductor with bandgap of 1.22 eV. With pressure increasing, the bandgap is slowly decreasing. At 1.9 GPa, the structure P6 3 / mmc transforms to R3m phase 28 , which is an indirect bandgap semiconductor. The bandgap is 0.154 eV under 20 GPa (see Fig. 4b). From 20 to 500 GPa, MoSe 2 becomes to a metal as shown in Fig. 4c,d. The detailed total and partial density of states are calculated (see Supplementary Information, Fig. S3). The states above − 5.5 eV in P6 3 /mmc phase at 0 GPa, − 7.5 eV in R3m phase at 20 GPa, and − 10 eV in P6 3 /mmc at 80 GPa are mostly originated from Mo-d and Se-p orbitals. The Mo-d and Se-p orbitals show strong p-d hybridization and indicate obviously covalent bonding characteristics of Mo-Se chemical bond. In P6 3 /mmc phase, the orbitals have more overlapping at 80 GPa than 20 GPa, which proves that covalent properties of Mo-Se bond is strengthened by increasing the pressure. In Fig. S3d, we can see a noticeable peak at − 12 eV in the density of states of R-3m phase at 500 GPa, which are mainly contributed by the p orbitals of Mo atoms. Furthermore,  www.nature.com/scientificreports/   www.nature.com/scientificreports/ except for Mo-d and Se-p orbitals, the contributions from Mo-p orbitals are visibly increased compared with low pressure conditions. This may due to the firmer MoSe 6 octahedra in R3m phase of MoSe 2 . We return again to search the potential structural phase transition mechanisms of MoSe 2 under high pressure. To clearly compare the four phases of MoSe 2 under different pressure, we have displayed the crystal structure with the same atomic number of Mo and Se stoms by using the supercell of 1 × 1 × 3 for P6 3 /mmc phase at 0 GPa, 1 × 1 × 2 for R3m phase at 20 GPa, 1 × 1 × 3 for P6 3 /mmc phase at 80 GPa, and 1 × 1 × 2 for R-3m phase at 500 GPa, respectively. The schematic diagrams are shown in Fig. 5.
From Fig. 5, we find that the structural phase transitions of MoSe 2 under high pressure are attributed to the chiral structure transitions of the top two MoSe 6 layers marked in red rectangles and the middle two MoSe 6 layers displayed in blue rectangles. The evolution of phase transitions is constituted by three steps. In the first step, three-unit cells of P6 3 /mmc phase translate into two R3m unit cell at 1.9 GPa. The main changes occur at the top two MoSe 6 layers in P6 3 /mmc and R3m phases, which is a chiral transform of the two MoSe 6 layers with mirror symmetry. In the second step, the two-unit cells of R3m phase return to three P6 3 /mmc unit cells, and the central symmetric transformation occurs again on the top two MoSe 6 layers. However, the interlayer spacing of the top two MoSe 6 layers decreases from 4.28 to 2.67 Å as pressure increasing from 0 to 80 GPa, as shown in the red square of Fig. 5. In the third step, the structure evolution of MoSe 2 under ultrahigh pressure is different from the previous two steps. The structural transformation happens at the middle layers of the MoSe 6 , as shown in the blue rectangles of Fig. 5. The three-unit cells of P6 3 /mmc phase return to two R-3m unit cells, with a chiral structure transition of the middle two MoSe 6 layers. Furthermore, it is easy to find that the pressure induced semiconducting to metallic transition of MoSe 2 under high pressure, which is mainly attributed to the different stacking modes of the MoSe 6 layers in different phases of MoSe 2 . These results offer important insights for exploration the evolutions of structures and electronic properties of other TMDs at extreme conditions.

Conclusion
In summary, we have performed comprehensively structure predictions of MoSe 2 under high pressure up to 500 GPa by CALYPSO method and first-principles calculations. Three new high pressure phases of MoSe 2 are uncovered, and the phase transition sequence follows the order of P6 3 /mmc → R3m → P6 3 /mmc → R-3m. The energy band structure calculations indicate MoSe 2 are evolution from direct bandgap semiconductor to indirect bandgap semiconductor, eventually, to a metal with pressure increase. These attractively electronic properties are due to the chiral structure changes of the top two MoSe 6 layers in MoSe 2 . The present findings establish the structural phase diagram of MoSe 2 under high pressure and describe the evolutions of structures and electronic properties of MoSe 2 , which offer important insights for exploration other TMDs at extreme conditions.