Charge density waves and Fermi level pinning in monolayer and bilayer ${\mathrm{SnSe}}_2$

Materials with reduced dimensionality often exhibit exceptional properties that are different from their bulk counterparts. Here, we report the emergence of a commensurate $2\times 2$ charge density wave (CDW) in monolayer and bilayer ${\mathrm{SnSe}}_2$ films by scanning tunneling microscopy. The visualized spatial modulation of the CDW phase becomes prominent near the Fermi level, which is pinned inside the semiconductor band gap of ${\mathrm{SnSe}}_2$. We show that both CDW and Fermi level pinning are intimately correlated with band bending and virtual induced gap states at the semiconductor heterointerface. Through interface engineering, the electron-density-dependent phase diagram is established in ${\mathrm{SnSe}}_2$. Fermi surface nesting between symmetry inequivalent electron pockets is revealed to drive the CDW formation and to provide an alternative CDW mechanism that might work in other compounds.

Figure 1

(a) Sketch of $1T\text{−}{\mathrm{SnSe}}_2$ (space group: $P\overline{3}m1$) films on Sn-terminated Si(111). (b) Differential conductance $dI/dV$ spectrum showing a Mott-Hubbard gap of $\sim 0.26$ eV around $E_{\text{F}}$ in $\sqrt{3}\text{−}\mathrm{Sn}/\mathrm{Si}$. The set point is stabilized at $V=1.6\mathrm{V}$ and $I=100\mathrm{pA}$. Inserted is a representative STM image of the $\sqrt{3}\text{−}\mathrm{Sn}/\mathrm{Si}$ surface ($8\mathrm{nm}\times 8\mathrm{nm}$, $V=-1.8\mathrm{V}$, $I=100\mathrm{pA}$). (c) 3D and 2D Brillouin zones of ${\mathrm{SnSe}}_2$. (d)–(f) STM topographies of ML, BL, and TL ${\mathrm{SnSe}}_2$ films epitaxially grown on $\sqrt{3}\text{−}\mathrm{Sn}/\mathrm{Si}$ ($8\mathrm{nm}\times 8\mathrm{nm}$), respectively. The white and green rhombuses mark the primitive and charge order unit cells, respectively. Imaging conditions are $V=0.5\mathrm{V}$ and $I=100\mathrm{pA}$, except for (e) $V=0.2\mathrm{V}$.

Figure 2

(a) Constant-current STM topography images of monolayer ${\mathrm{SnSe}}_2/\sqrt{3}\text{−}\mathrm{Sn}/\mathrm{Si}$ films in the same field of view ($12\text{nm}\times 12\text{nm}$, $I=100\mathrm{pA}$) and (b) the corresponding FFT amplitudes at the indicated sample biases. Every FFT image has been sixfold symmetrized to optimize the signal-to-noise ratio. The Bragg peaks and CDW spots of ${\mathrm{SnSe}}_2$ are white and green circled, respectively. The white hexagon in the left FFT image corresponds to the 2D Brillouin zone of ${\mathrm{SnSe}}_2$, while the three dashed circles denote the $2\times 2$ CDW spots just as the FFT images on the left. Note that the green arrows mark the CDW wave vectors that gradually decrease below $-0.1\mathrm{eV}$.

Figure 3

(a) Energy-dependent CDW intensity (top panel) and wide-energy-scale $dI/dV$ spectra ($V=1.5\mathrm{V}$, $I=100\mathrm{pA}$) at varied film thicknesses (bottom panel). The black (red) triangles mark the VBM (CBM) near (at) $\mathrm{\Gamma }$, with their spacing corresponding to the direct band gap $E_g^{\text{dir}}\left(\mathrm{\Gamma }\right)$ of ${\mathrm{SnSe}}_2$. The vertical dashed line denotes $E_{\text{F}}$ throughout, and the cyan rectangle indicates emergent in-gap states. (b) Energy band diagram for the ${\mathrm{SnSe}}_2/\sqrt{3}\text{−}\mathrm{Sn}/\mathrm{Si}$ semiconductor heterointerface, as well as the interfacial origin of the in-gap states. (c) Tunneling spectra showing CDW energy gaps near $E_{\text{F}}$ on both ML and BL ${\mathrm{SnSe}}_2$.

Figure 4

(a) Calculated CDW intensity of ML and BL ${\mathrm{SnSe}}_2$ films on the ${\mathrm{SrTiO}}_3$ substrate. Insets are STM images ($12\text{nm}\times 12\text{nm}$, $V=0.3\mathrm{V}$, $I=100\mathrm{pA}$) of ML and BL ${\mathrm{SnSe}}_2$ films on ${\mathrm{SrTiO}}_3$, with the dashed circles embracing the short-range CDW in the vicinity of defects. (b) Comparison among $dI/dV$ spectra ($V=0.5\mathrm{V}$, $I=100\mathrm{pA}$) of ML ${\mathrm{SnSe}}_2$ films on different substrates, measured in an energy range of $\pm 0.5\mathrm{eV}$. The magenta triangles represent the CBM at the $M$ point of the 2D Brillouin zone in ${\mathrm{SnSe}}_2$.

Figure 5

(a) Electronic phase diagram of ${\mathrm{SnSe}}_2$. The stars denote monolayer ${\mathrm{SnSe}}_2$ films on $\sqrt{3}\text{−}\mathrm{Sn}/\mathrm{Si}$, ${\mathrm{SrTiO}}_3$, and graphene/SiC substrates, respectively. (b) Fermi surface and (c) constant energy contour (i.e., the midgap energy level) of ${\mathrm{SnSe}}_2$ films. The black hexagons denote the 2D Brillouin zone of ${\mathrm{SnSe}}_2$, while green arrows the $q_{\text{CDW}}$ of CDW order.