Dense Network of One-Dimensional Midgap Metallic Modes in Monolayer ${\mathrm{MoSe}}_2$ and Their Spatial Undulations

We report the observation of a dense triangular network of one-dimensional (1D) metallic modes in a continuous and uniform monolayer of ${\mathrm{MoSe}}_2$ grown by molecular-beam epitaxy. High-resolution transmission electron microscopy and scanning tunneling microscopy and spectroscopy studies show that these 1D modes are midgap states at inversion domain boundaries. Scanning tunneling microscopy and spectroscopy measurements further reveal intensity undulations of the metallic modes, presumably arising from the superlattice potentials due to the moiré pattern and the quantum confinement effect. A dense network of the metallic modes with a high density of states is of great potential for heterocatalysis applications. The interconnection of such midgap 1D conducting channels may also imply new transport behaviors distinct from the 2D bulk.

Figure 1

STM micrographs of ${\mathrm{MoSe}}_2$ on HOPG. (a) Topographic image (size: $80\times 80{\mathrm{nm}}^2$, sample bias $V_{\text{sample}}=2.0\mathrm{V}$) of a 1.4 ML ${\mathrm{MoSe}}_2$ film. The white arrows point to the exposed substrate (1) and the second (2) and third (3) layer ${\mathrm{MoSe}}_2$ islands, respectively. The inset is the reflection high-energy electron diffraction pattern taken along [$11\overline{2}0$]. (b) Topographic image of the same area as (a) but at $V_{\text{sample}}=-1.0\mathrm{V}$. (c),(d) Close-up STM images [size: $35\times 35{\mathrm{nm}}^2$, $V_{\text{sample}}=-1.0\mathrm{V}$ for (c); $13\times 13{\mathrm{nm}}^2$ and $V_{\text{sample}}=-1.46\mathrm{V}$ for (d)], revealing the wagon-wheel patterns and the intensity undulations. (e) STM image (size: $9.2\times 9.2{\mathrm{nm}}^2$, $V_{\text{sample}}=-1.78\mathrm{V}$) showing the moiré pattern, e.g., in the upper-left corner of the micrograph. The inset is the intensity profile along the white line, showing the period of the moiré pattern to be of $\sim 1\mathrm{nm}$.

Figure 2

STS spectra and calculated DOS of the IDB defect. (a) STS spectra of ML ${\mathrm{MoSe}}_2$ at the points as marked by the crosses in (b), i.e., (i) away from or (ii) in the vicinity of a defect. (b) A STS map (size: $8.6\times 8.6{\mathrm{nm}}^2$) obtained at $V_{\text{sample}}=-0.42\mathrm{eV}$, showing the 1D defect modes and their intensity undulations along the lengths of the defects. (c),(d) Calculated DOS and the band structure. The red and green dots in (d) represent states from Mo and Se atoms at the core of the defect, respectively, and the dotted blue states are from Mo next to the core. In (c), the red-shaded regions are the valence and conduction bands of bulk ML ${\mathrm{MoSe}}_2$ and the black line is the DOS from the defect. (e),(f) STS maps obtained at $V_{\text{sample}}=-1.85$ and 0.72 eV, respectively, superimposed with the calculated DOS maps and the ball model of the structure [refer to Fig. 3 below] at the corresponding energies. The calculated maps represent the central region of a larger ribbon model (cf. the Supplemental Material, Sec. 3), showing the DOS of the defect.

Figure 3

HRTEM micrographs of the defect (a) HRTEM image of ML ${\mathrm{MoSe}}_2$ on HOPG (graphene). The red-to-yellow lines mark rows of the bright spots in two neighboring domains. The numbered boxes highlight the boundaries corresponding to one (1) or two (2) vacant Se rows, or a mixture (box 3) of the two structures. (b),(c) Simulated HRTEM images (the highlighted regions) based on the model of (d) but with one or two rows of Se atoms removed at the defect, as shown by the overlaid models (the purple and green balls represent Mo and Se atoms, respectively). (d) Stick-and-ball model of the IDB defect in both the plan view (top) and the cross-sectional view (bottom).

Figure 4

STS maps and extracted intensity undulations of the 1D modes. (a),(b) STS maps (size: $4.5\times 4.5{\mathrm{nm}}^2$) at energies as indicated. The intensities $I$ along the lengths of the defects (marked by the white lines) are extracted and fitted by the following equation: $I=A{\text{sin}}^2(kx+\phi )+D$, where $A$, $k$, $\phi$, and $D$ are fitting parameters, as exemplified in the inset of (c). (c) Wave vectors derived by fittings of seven defects of different lengths (labeled by different colors) and at different energies. The dotted and solid circles highlight the undulation wave vectors that correspond to the moiré period and the QWS, respectively. (d) Energy bands of Fig. 2 but folded into the reduced BZ of the moiré superlattice potential.