Pressure induced metallization with absence of structural transition in layered molybdenum diselenide

Layered transition-metal dichalcogenides have emerged as exciting material systems with atomically thin geometries and unique electronic properties. Pressure is a powerful tool for continuously tuning their crystal and electronic structures away from the pristine states. Here, we systematically investigated the pressurized behavior of MoSe2 up to ∼60 GPa using multiple experimental techniques and ab-initio calculations. MoSe2 evolves from an anisotropic two-dimensional layered network to a three-dimensional structure without a structural transition, which is a complete contrast to MoS2. The role of the chalcogenide anions in stabilizing different layered patterns is underscored by our layer sliding calculations. MoSe2 possesses highly tunable transport properties under pressure, determined by the gradual narrowing of its band-gap followed by metallization. The continuous tuning of its electronic structure and band-gap in the range of visible light to infrared suggest possible energy-variable optoelectronics applications in pressurized transition-metal dichalcogenides.


Supplementary Note 1: X-ray diffraction measurements and analysis
Synchrotron X-ray diffraction (XRD) data was measured in beamline 16-BMD, Advanced Photon Source (APS), Argonne National Laboratory (ANL). The sample-detector distance was set at 304.32 mm with X-ray wavelength at 0.4246 Å. Neon served as the pressure transmitting medium. MAR345 image plate was used to collect the diffraction data. The 2D diffraction data with diffraction rings was then integrated into 1D diffraction patterns through Fit2D program. During compression, all diffraction peaks continuously shift to higher 2θ (smaller d-spacing) as seen from Supplementary Fig. 1.
No new diffraction peak from MoSe 2 is seen throughout our measurements. Notice that diffraction peaks from neon (marked by asterisks) start to appear at 9.8 GPa.
Decompression run shows that the shifts of all peaks are reversible.
We performed Rietveld refinement, a commonly used least-squares approach in solving powder XRD data, using the GSAS-EXPGUI package 1 . Representative Rietveld refinement results are shown in Supplementary Table. In Supplementary Fig. 2 The 2H c -type structure can well fit all XRD patterns which supports the absence of structural transition.
The refined atomic positions then determine the ratio of Se-Mo layer distance to Se-Se layer distance. Supplementary Fig. 3 shows the ratio of Se-Mo layer distance to Se-Se layer distance, which drops fast at low pressure and but decreases much slower at high pressure. It indicates the gradual closure of the van der Waals (vdW) gap in between Se-Se layers.

Supplementary Note 2: Raman measurements
To probe the change of phonon modes of MoSe 2 under pressure, we measured its Raman spectra at high pressure. The spectra were collected using a Renishaw inVia micro

Supplementary Note 4: Infrared measurements and analysis
High-pressure IR measurements were conducted in beamline U2A of the National Synchrotron Light Source (NSLS), Brookhaven National Laboratory (BNL). A MoSe 2 single crystal (thickness ~ 4 μm) was sandwiched between the pressure transmitting medium (KBr) and one side of the culet. Infrared microspectroscopy was performed on a Bruker Vertex 80v FT-IR spectrometer coupled to a Hyperion-2000 microscope with a MCT mid-band detector. Fringes in raw IR data were removed by filtering high frequency harmonic after Fourier transformation. Supplementary Fig. 6 shows Representative optical density (OD) vs photon energy curves under pressure. OD is defined as -log(T), T is transmittance. There is no sharp cut-offs in these curves, which supports the "indirect" feature in the electronic structure. The band gap closure is seen from gradual lifting of these curves.
For an indirect-band-gap semiconductor, the absorption coefficient is proportional to the square of the photon energy and band gap. Using this empirical model for semiconductors, we obtained the indirect-band-gap E g via linear extrapolations of (ℎ ) 1/2 . A representative fitting at 29.5 GPa is shown as result Supplementary Fig. 7.

Supplementary Note 5: Electrical resistivity measurements
For temperature-dependent four-probe resistivity measurement, cubic BN was used as the insulating layer and pressure transmitting medium. A single crystal of MoSe 2 with suitable size was chosen for measurement. Ruby was used as the pressure calibrant. The four electrodes with sharp heads were cut from Pt foils, see Supplementary Fig. 8. The Van der Pauw geometry of these four electrodes is outlined by green lines. The position of ruby is marked by red circle. The temperature-dependent sheet resistance of the sample was measured by cooling down to 10 K in a liquid helium cryostat after changing each pressure at room temperature. The difference in pressures before and after the cooling and warming cycle is typically ~ 5 %.

Supplementary Note 6: Orbital details in band structure
HSE06 hybrid function 6 was employed for calculations. The k-points mesh is taken as 12 × 12 × 10 for all bulk self-consistent calculations. The conduction bands and valence bands near the E F show large movements. At ambient pressure, the dxz and dyz dominated conduction bands are further away from the Fermi level than the dxy and dx 2y 2 dominated bands. Interestingly, two band minima are observed at high pressure. For example, at 41 GPa as seen in Supplementary Fig. 9, one dxz and dyz dominated conduction band quickly goes down at K point to form two conduction band minimum.
This is because that dxz and dyz orbitals gain more overlap with Se p orbitals to widen the band dispersion than dxy and dx 2 -y 2 within the 2H c structure under pressure. The conduction band minimums may play a role in determining the transport properties.