Protected hole valley states in single-layer $\mathrm{Mo}{\mathrm{S}}_2$

We present an angle-resolved photoemission spectroscopy study of single-layer $\mathrm{Mo}{\mathrm{S}}_2$ where interaction with a supporting highly ordered pyrolytic graphite substrate was controlled by temperature change, consistent with related modifications in the layer-substrate distance. The impact of interface potential landscape changes on the electronic properties and charge dynamics on the $\mathrm{Mo}{\mathrm{S}}_2$ layer was evaluated by valence-band dispersion and photoemission line-shape analysis. Our results indicate that the hole states at the $K$-valley point are essentially unaffected by interface potential, reflecting the strong-in plane localization of the electronic wave function.

Figure 1

(a),(b) ARPES intensity plot (normalized to maximum) showing the VB dispersion of $\mathrm{Mo}{\mathrm{S}}_2$ ML along ΓΚ  at (a) 295 K and (b) 11 K. Dashed black curves in (a) denote the calculated band dispersion for freestanding $\mathrm{Mo}{\mathrm{S}}_2$ ML. The energy separation between the band extrema at the Γ and Κ points $\left(\mathrm{\Delta }{E}_{\mathrm{\Gamma }K}\right)$ is also indicated at both temperatures. (c) EDCs around Γ and Κ at 295 K (red filled circles) and 11 K (cyan filled circles). ARPES data were integrated over $\pm 0.02{\AA }^{-1}$ around Γ and Κ. Intensities were normalized to the highest point of the EDCs. (d) Calculated $\mathrm{\Delta }{E}_{\mathrm{\Gamma }K}$ with varying lattice constant $a$ in a freestanding ML (see inset). (e) Calculated $\mathrm{\Delta }{E}_{\mathrm{\Gamma }K}$ change with reduction of $\mathrm{Mo}{\mathrm{S}}_2$ layer distance $d$ from supporting substrate (single-layer graphite used, for computational efficiency) (see inset).

Figure 2

(a)–(d) EDCs (closed circles) at Γ for (a) 295 K and (b) 11 K and at the $K$ point for (c) 295 K and (d) 11 K. EDCs near VB local maximum were fitted by Voigt functions (dashed curve with green shading) (see text for details). The extracted Lorentzian $\left(w_{\mathrm{L}}\right)$ and Gaussian $\left(w_{\mathrm{G}}\right)$ are reported in (a)–(d). (e) $w_{\mathrm{L}}$ and (f) $w_{\mathrm{G}}$ temperature dependence at Γ (closed yellow squares) and the $K$ point (closed green triangles). (g) Schematic impact of substrate interaction and impurities/defects Coulomb potential on the $\mathrm{Mo}{\mathrm{S}}_2$ ML electronic states near the local VB maximum at Γ and $K$. Calculated charge density plot reflects the wave-function symmetry at different points of the BZ.

Figure 3

Schematic of the ARPES experimental geometry.

Figure 4

(a) Schematic structure of a $\mathrm{Mo}{\mathrm{S}}_2$ ML (side and top view) with in-plane unit cell (lattice constant $a$) defined by the shaded area. (b) BZ of the $\mathrm{Mo}{\mathrm{S}}_2$ ML. (c) Constant ARPES energy intensity map in the 2D momentum space $(k_x,k_y)$ of $\mathrm{Mo}{\mathrm{S}}_2$ ML on HOPG, at 295 K near the energy of the $\mathrm{Mo}{\mathrm{S}}_2$ valence-band maximum (VBM) ($\pm 10\mathrm{meV}$ of integration range) and within the following momentum ranges: $-0.15<k_x<1.45{\AA }^{-1}$ and $-0.15<k_y<1.00{\AA }^{-1}$. The data obtained were then symmetrized according to the hexagonal lattice of the system to obtain the presented fully hexagonal pattern.

Figure 5

Energy distribution curves (EDCs) as a function of momentum $k_x$ for $\mathrm{Mo}{\mathrm{S}}_2$ (ML)/HOPG. ARPES data were acquired at (a) 295 K and (b) 11 K. EDCs near the high-symmetry points (Γ, Κ, Μ) of the single-crystal BZ are highlighted by black curves. For clarity purposes, EDCs were plotted with an interval of $0.02{\AA }^{-1}$.

Figure 6

ARPES intensity map around the $K$ point of the $\mathrm{Mo}{\mathrm{S}}_2$ BZ. Data were acquired at (a) 295 K and (b) 11 K. The spin-orbit valence-band splitting was clearly observed. Inset in (a): Honeycomblike structure of the full hexagonal reciprocal space. The high-symmetry points of the first BZ (Γ,Κ) (black hexagon) and second BZ ($M$) (gray hexagon) are shown. Pink shaded area indicates the $k_x$ scanning direction.

Figure 7

(a) Schematic in-plane lattice contraction (blue arrows) of $\mathrm{Mo}{\mathrm{S}}_2$ freestanding layer (side view). (b),(c) Representative VB calculation along the ΓΚ for freestanding $\mathrm{Mo}{\mathrm{S}}_2$ ML with different lattice constants: (b) $a=3.160\AA$ and (c) 3.144 Å. Energy scale is referring to the valence-band maximum at $K$. (d) Side view: schematic structure of $\mathrm{Mo}{\mathrm{S}}_2$ (ML)/graphene heterostructure (interlayer distance $d$). Top view: $\mathrm{Mo}{\mathrm{S}}_2$ (ML)/graphene supercell used in the theoretical calculation. (e)–(g) Calculated valence-band structure of $\mathrm{Mo}{\mathrm{S}}_2$ (ML)/graphene as projected along the ΓΚ direction of the $\mathrm{Mo}{\mathrm{S}}_2$ layer at (e) $d=\infty$ (i.e., freestanding $\mathrm{Mo}{\mathrm{S}}_2$ ML), (f) $d=3.50\AA$, and (g) $d=3.20\AA$.

Figure 8

(a) EDCs evolution at the Γ point as a function of the sample temperature, from 295 K (red) to 11 K (blue), and after warming up back to 295 K (green). The Shirley backgrounds were substrates for the raw EDCs and then data normalized with respect to the peak maximum (see main text for detailed discussion). The position of the peak maxima is indicated by vertical bars. (b) Same as (a) for EDCs at the $K$ point.

Figure 9

ARPES EDCs curve around the (a) Γ point and (b) $K$ point of the $\mathrm{Mo}{\mathrm{S}}_2$ BZ acquired at 295 K. The first derivative of the experimental data is shown by the dotted (orange) curve after intensity rescaling.

Figure 10

ARPES EDCs around the (a),(c) Γ and (b),(d) Κ points of the $\mathrm{Mo}{\mathrm{S}}_2$ BZ, acquired at (a),(b) 295 K and (c),(d) 11 K with calculated Shirley-type background (black curves).

Figure 11

ARPES EDCs at (a) Γ and (b) Κ points acquired at 295 K (red curve) and 11 K (blue curve). The Shirley backgrounds were subtracted from the raw EDCs and then data normalized with respect to the peak maximum. Data were aligned to the position of the peak maximum at 295 K to better compare the ARPES line shape. The impact of the sample temperature on the low binding energy tail of the photoemission peaks is highlighted in the insets of (a) and (b) (magnified intensity scale).

Figure 12

ARPES data at (a) 295 K and (b) 11 K with corresponding cumulative fitting curve (continuous black curves). The Lorentzian width $w_{\mathrm{L}}$ of the ${\mathrm{VB}}_1^k$ and ${\mathrm{VB}}_2^k$ peaks (shaded green and orange, respectively) is indicated.