Direct observation of a surface resonance state and surface band inversion control in black phosphorus

We report a Cs-doping-induced band inversion and the direct observation of a surface resonance state with an elliptical Fermi surface in black phosphorus (BP) using angle-resolved photoemission spectroscopy. By selectively inducing a higher electron concentration ($1.7\times {10}^{14}{\mathrm{cm}}^{-2}$) in the topmost layer, the changes in the Coulomb potential are sufficiently large to cause surface band inversion between the parabolic valence band of BP and a parabolic surface state around the $\mathrm{\Gamma }$ point of the BP Brillouin zone. Tight-binding calculations reveal that band gap openings at the crossing points in the two high-symmetry directions of the Brillouin zone require out-of-plane hopping and breaking of the glide mirror symmetry. Ab initio calculations are in very good agreement with the experiment if a stacking fault on the BP surface is taken into account. The demonstrated level of control over the band structure suggests the potential application of few-layer phosphorene in topological field-effect transistors.

Figure 1

(a) Sketch of the bilayer phosphorene structure with Cs adsorbed. The dashed line denotes the mirror plane of the glide mirror symmetry. The glide axes are in the $x$ and $y$ directions. The four atoms in the bilayer unit cell are indicated by $a–d$ and 1–4. (b) The surface BZ of BP and the high-symmetry points. Two-dimensional, $k$-dependent ARPES spectra along the $\mathrm{\Gamma }Y$ direction measured with (c) $p$- and (d) $s$-polarized light. A fit of the effective electron mass yielding $m^{*}=1.38m_e$ is shown ($m_e$ is the free-electron mass). (e) The $s$- and $p$-polarized spectra added together.

Figure 2

Three-dimensional energy band dispersion of BP with a monolayer of Cs adsorbed on its surface. The points are the experimental ARPES maxima (measured at $h\nu =21$ eV with $s$- and $p$-polarized light), and the surfaces are an interpolation of the symmetrized data. Red (blue) denotes electronlike (holelike) bands. The right part shows equienergy contours of ARPES data for three binding energies. Additional equienergy contours (see the Appendix) were used to interpolate the three-dimensional dispersion. The left part originates from radial fits to the surfaces of the kind shown on the right.

Figure 3

(a) XPS spectra ($h\nu =300$ eV) of the P $2p$ core levels before doping (blue) and after Cs doping (black and red). The black spectrum is for normal emission, and the red spectrum is for grazing emission. (b) Cs $3d$ core-level spectrum ($h\nu =300$ eV) for normal emission (black) and for grazing emission (red). These two spectra are normalized to the corresponding P $2p$ core-level spectra shown in (a). (c) Near-edge x-ray absorption fine-structure spectrum of pristine (blue) and Cs-doped (red) BP measured in the total-electron-yield configuration. The inset shows that the onset of the absorption edge for doped BP is upshifted by $\sim 65$ meV when compared to pristine BP.

Figure 4

(a) ARPES scans along the $\mathrm{\Gamma }Y$ direction along with a tight-binding (TB) fit. (b) Energy distribution curve at $k=0$ indicating two peaks at $E=-0.4$ eV and $E=-0.6$ eV. (c) ARPES scan along $\mathrm{\Gamma }X$ with a TB fit. (d) Second derivative of the $\mathrm{\Gamma }X$ scan overlaid on TB results. (e) $k_z$ scan using a photon energy sweep between 15 and 40 eV and the inner potential given in Ref. [22]. (f) and (g) TB calculations assuming an out-of-plane coupling of bulk BP and a TB parametrization that breaks the glide mirror symmetry, respectively. (h) In-plane TB parameters up to the sixth nearest neighbor. (i) Nearest and next-nearest out-of-plane TB parameters. (j) Glide mirror symmetry operations for monolayer phosphorene. (k) Glide mirror symmetry operations for bilayer phosphorene. The arrows denote the nearest-neighbor out-of-plane hopping (parameter $s1$). The Supplemental Material [26] contains a video animation of the glide mirror symmetry operations.

Figure 5

Structure and electron energy bands of Cs-doped bilayer phosphorene. (a) One Cs atom per unit cell. (b) One Cs atom per unit cell with inverse stacking. (c) One Cs atom per two unit cells with inverse stacking. Colors in the band plots give the projection onto the top layer, Cs (blue), and the bottom layer (dark red). For some selected states at $\mathrm{\Gamma }$ (colored arrows) we show the ${\left|\varphi \right|}^2$ integrated in plane and as a function of the out-of-plane coordinate $z$.

Figure 6

Equienergy contours for (a) Fermi surface, (b) 100 meV, (c) 200 meV, (d) 300 meV, (e) 400 meV, (f) 700 meV, (g) 850 meV, and (h) 950 meV binding energy. The red and blue dots are the maxima of the electronlike and holelike bands, respectively.

Figure 7

Left: Band structure of a Cs-doped four-layer phosphorene in the original BP-like geometry. Colors indicate the center of mass of the states according to the color scale in the middle (where black triangles give the position of P atoms and a red triangle gives that of Cs). Middle: The $xy$ integral of $|{\varphi }_{n\mathbf{k}}{|}^2$ for selected states (shown by arrows in the band plot). Right: The crystal structure of this system.