Binary Two-Dimensional Honeycomb Lattice with Strong Spin-Orbit Coupling and Electron-Hole Asymmetry

Two-dimensional (2D) materials consisting of heavy atoms with particular arrangements may host exotic quantum properties. Here, we report a unique 2D semiconducting binary compound, a ${\mathrm{Sn}}_2\mathrm{Bi}$ atomic layer on Si(111), in which hexagons are formed by bonding Bi with a triangular network of Sn. Because of the unique honeycomb configuration, the heavy elements, and the energy-dependent hybridization between Sn and Bi, 2D ${\mathrm{Sn}}_2\mathrm{Bi}$ not only shows strong spin-orbit coupling effects but also exhibits high electron-hole asymmetry: Nearly free hole bands and dispersionless flat electron bands coexist in the same system. By tuning the Fermi level, it is possible to preserve both nearly free and strongly localized charge carriers in the same 2D material, which provides an ideal platform for the studies of strongly correlated phenomena and possible applications in nanodevices.

Figure 1

A highly ordered honeycomb structure of a Sn-Bi overlayer on Si(111). (a) Large-scale STM image ($V_{\mathrm{tip}}=-2.0\mathrm{V}$, $I=90\mathrm{pA}$) of about 0.9 ML Sn on a $\beta \text{−}\mathrm{Bi}/\mathrm{Si}(111)$ surface. An area of uncovered substrate is highlighted by the red dotted circle. (b) Atomic resolution STM image ($V_{\mathrm{tip}}=1.0\mathrm{V}$, $I=90\mathrm{pA}$) taken on the Sn-Bi overlayer structure showing a uniform honeycomb lattice. (c) Height profile along the red arrow in (a), which indicates the height difference between the Sn-Bi overlayer and $\beta \text{−}\mathrm{Bi}/\mathrm{Si}(111)$. (d) Line profile along the red arrow in (c). The periodicity of $0.77\pm 0.01\mathrm{nm}$ illustrates the formation of a $2\times 2$ superstructure on Si(111). (e) Amplified STM image ($V_{\mathrm{tip}}=1.0\mathrm{V}$, $I=99\mathrm{pA}$) of an area containing a boundary separating the Sn-Bi overlayer structure (bottom left) and $\beta \text{−}\mathrm{Bi}/\mathrm{Si}(111)$ (upper right). (f) FFT patterns of a high-resolution STM image containing both a honeycomb Sn-Bi overlayer and uncovered $\beta \text{−}\mathrm{Bi}/\mathrm{Si}(111)$. Red and blue dashed circles mark two sets of patterns that correspond to $\beta \text{−}\mathrm{Bi}/\mathrm{Si}(111)$ and the Sn-Bi overlayer, respectively.

Figure 2

Scanning tunneling spectroscopy measurements on the honeycomb structure of a Sn-Bi overlayer. (a) $dI/dV$ spectrum taken on the Sn-Bi overlayer (initiate set point: $V_{\mathrm{tip}}=-2\mathrm{V}$, $I=400\mathrm{pA}$). Blue arrows mark the position of the band gap. (b) $dI/dV$ map ($V_{\mathrm{tip}}=0.35\mathrm{V}$, $I=250\mathrm{pA}$) on the Sn-Bi overlayer. (c) FFT results of (b). The first Brillouin zone is indicated by a red dashed hexagon. (d) Energy dependence of QPI wave vector $q$ along the $\mathrm{\Gamma }\text{−}K$ direction. The data are well fitted by a red parabolic line, indicating the free-hole-like surface states.

Figure 3

Band structure of a Sn-Bi overlayer measured by ARPES. (a) Energy cut along the $M\text{−}\mathrm{\Gamma }\text{−}K\text{−}M$ direction represents two cones touching each other at the vertex below the Fermi level. (b) Constant energy contour taken at the valence band maximum ($-0.2\mathrm{eV}$). The first Brillouin zone with a red dashed hexagon is superimposed to guide the eye. (c) The bottom of the conduction band with nearly flat dispersion was observed by the pump-probe technique.

Figure 4

Calculated phase diagram, atomic structures, and band dispersions of the honeycomb ${\mathrm{Sn}}_2\mathrm{Bi}$. (a) Surface phase diagram of stable Bi/Sn structures on Si(111) for varying chemical potentials of Sn (${\mu }_{\text{Sn}}$) and Bi (${\mu }_{\text{Bi}}$). ${\mu }_{\text{Sn}}$ (${\mu }_{\text{Bi}}$) is referenced to the Sn (Bi) bulk. (b),(c) Top and side view of the ball-and-stick model of the honeycomb ${\mathrm{Sn}}_2\mathrm{Bi}$, respectively. The black dashed rhombus indicates a unit cell, and two black triangles highlight the inequivalent Sn-Bi trimers. Calculated bands of the honeycomb ${\mathrm{Sn}}_2\mathrm{Bi}$ excluding (d) and including (e) the SOC. The size of the red (blue) balls represents contributions of Sn (Bi) atoms.

Figure 5

Comparison of experimental results and theoretical calculations of honeycomb ${\mathrm{Sn}}_2\mathrm{Bi}$. (a) Electron dispersion along the $K\text{−}{\mathrm{\Gamma }}_1\text{−}K$ direction from QPI measurements (yellow dots), DFT calculations (red balls), and second derivatives of ARPES data (background). (b),(c) STM images of honeycomb ${\mathrm{Sn}}_2\mathrm{Bi}$ taken at ($V_{\mathrm{tip}}=1.0\mathrm{V}$, $I=90\mathrm{pA}$) and ($V_{\mathrm{tip}}=-1.0\mathrm{V}$, $I=91\mathrm{pA}$). (d),(e) Simulated STM images of honeycomb ${\mathrm{Sn}}_2\mathrm{Bi}$ taken at $-1.0\mathrm{eV}$ below and $+0.46\mathrm{eV}$ above the calculated VBM, respectively.