Electronic Structure of Epitaxial Single-Layer ${\mathrm{MoS}}_2$

The electronic structure of epitaxial single-layer ${\mathrm{MoS}}_2$ on Au(111) is investigated by angle-resolved photoemission spectroscopy. Pristine and potassium-doped layers are studied in order to gain access to the conduction band. The potassium-doped layer is found to have a $(1.39\pm 0.05)\mathrm{eV}$ direct band gap at $\overline{K}$ with the valence band top at $\overline{\mathrm{\Gamma }}$ having a significantly higher binding energy than at $\overline{K}$. The moiré superstructure of the epitaxial system does not lead to the presence of observable replica bands or minigaps. The degeneracy of the upper valence band at $\overline{K}$ is found to be lifted by the spin-orbit interaction, leading to a splitting of $(145\pm 4)\mathrm{meV}$. This splitting is anisotropic and in excellent agreement with recent calculations. Finally, it is shown that the potassium doping does not only give rise to a rigid shift of the band structure but also to a distortion, leading to the possibility of band structure engineering in single-layers of transition metal dichalcogenides.

Figure 1

Electronic structure of epitaxial single-layer ${\mathrm{MoS}}_2$: (a)–(d) Constant energy slices through the first Brillouin zone, showing (a) the Fermi contour dominated by Au bulk states and the surface state (Au S) and (b)–(d) evolution of ${\mathrm{MoS}}_2$ valence band features around $\overline{K}$, ${\overline{K}}^{\prime }$, and $\overline{\mathrm{\Gamma }}$ points. (e) Valence band dispersion in the $\overline{K}-\overline{\mathrm{\Gamma }}-{\overline{K}}^{\prime }$ direction. The band structure for freestanding single-layer ${\mathrm{MoS}}_2$ from Ref. [24] has been superimposed. The inset shows a STM image of the ${\mathrm{MoS}}_2$ islands and the moiré ($I_t=0.4\mathrm{nA}$, $V_t=-1.2\mathrm{V}$). (f) Close-up of the ${\mathrm{MoS}}_2$ upper valence band dispersion around $\overline{\mathrm{\Gamma }}$. The red line is the peak position extracted from energy distribution curves shown in (g). The curvature of the parabolic band provides the stated effective mass $m$ in units of the free electron mass $m_0$. The two-dimensional high-symmetry points in this figure refer to the SL ${\mathrm{MoS}}_2$ structure.

Figure 2

Detailed dispersion around valence band maximum at ${\overline{K}}^{\prime }$ ($\overline{K}$) and analysis of spin-orbit interaction. (a)–(b) Cuts along directions defined in the constant energy contours in (c). The points $\overline{A}$ and ${\overline{A}}^{\prime }$ are along the line perpendicular to the $\overline{\mathrm{\Gamma }}-\overline{K}$ direction passing through $\overline{K}$. (d)–(e) EDCs at the given momentum values. The peaks are fitted by a double Lorentzian function, and the difference between peak positions is taken as the splitting of the bands, which is stated in meV below the curves.

Figure 3

Tuning of the band structure by potassium adsorption. (a),(d) Clean sample, (b),(e) first dose, and (c),(f) second dose. The scan directions for the cuts in (a)–(c) and (d)–(f) are given in the insets of (a) and (d), respectively. The points $\overline{A}$ and ${\overline{A}}^{\prime }$ are defined in the caption of Fig. 2. The energies are given in eV.