Phonon-dressed two-dimensional carriers on the ZnO surface

Two-dimensional (2D) metallic states formed on the $\mathrm{ZnO}(10\overline{1}0)$ surface by hydrogen adsorption have been investigated using angle-resolved photoelectron spectroscopy (ARPES). The observed metallic state is characterized by a peak-dip-hump structure at just below the Fermi level and a long tail structure extending up to 600 meV in binding energy. The peak and hump positions are separated by about 70 meV, a value close to the excitation energy of longitudinal optical (LO) phonons. Spectral functions formulated on the basis of the 2D electron-phonon coupling well reproduce the ARPES intensity distribution of the metallic states. This spectral analysis suggests that the 2D electrons accumulated on the ZnO surface couple to the LO phonons and that this coupling is the origin of the anomalous long tail. Our results indicate that the 2D electrons at the ZnO surface are described as the electron liquid model.

Figure 1

Results of the ARPES measurements for the H-dosed $\mathrm{ZnO}\left(10\overline{1}0\right)$ surface with $h\nu =65\mathrm{eV}$ at 13 K. (a) An intensity map near the ${\overline{\mathrm{\Gamma }}}_{00}$ point along the $\overline{\mathrm{\Gamma }}\text{−}\overline{X^{\prime }}$ axis. The arrows indicate the intensity dips at $E_{\mathrm{F}}-70\mathrm{meV}$. (b) The curvature intensity plot [23] of the Fermi surface. The surface Brillouin zone is also shown. (c) An MDC of the 2D metallic state at $E_{\mathrm{F}}$. The experimental line shape was fitted by three Voigt functions: Two represent the 2DQP states, and one represents the background contribution. The positions of the 2DQP states at $E_{\mathrm{F}}$ are indicated by triangles. (d) The energy distribution curves (EDCs) at $k_x=0{\mathrm{nm}}^{-1}$ and $k_{\mathrm{F}}$. The peak and hump structures of the EDC at $k_{\mathrm{F}}$ are indicated by triangles.

Figure 2

(a) Expanded images of Fig. 1. The positions of the 2DQP states are indicated by circles. The fitted result of the parabolic curve is drawn by solid lines. (b) Depth profiles of the CBM position. The corresponding eigenfunctions of the first and second sub-bands are displayed. The depth profile of the carrier electron density is shown in the inset.

Figure 3

(a) The ARPES intensity map near the $\overline{\mathrm{\Gamma }}$ point in the second surface Brillouin-zone $\left({\overline{\mathrm{\Gamma }}}_{10}\right)$ of the H-dosed ${\mathrm{SrTiO}}_3\left(001\right)$ surface $\left(h\nu =81\mathrm{eV},20\mathrm{K}\right)$. (b) The EDCs (circles) and calculated spectral functions (solid curves) at $k_x=0{\mathrm{nm}}^{-1}$ and $k_{\mathrm{F}}$. (c) The ARPES intensity map (a lower panel), which is symmetrized with respect to the center line $\left(k_x=0{\mathrm{nm}}^{-1}\right)$ and smoothed, is compared with the calculated spectral functions of $A^{\left(0\right)}+A^{\left(1\right)}$ (upper). (d) Schematic of the 2D $e\text{−}\mathrm{ph}$ coupling. The brownish curve indicates the band bending structure near the surface. A blue curve indicates the 2DQP band, whereas green to pale-green curves represent the 2D $e\text{−}\mathrm{ph}$ satellites. The scattering process of an electron is illustrated by yellow circles.

Figure 4

(a) and (b) The EDCs (circles) and calculated spectral functions at (a) $k_x=0{\mathrm{nm}}^{-1}$ and (b) $k_{\mathrm{F}}$ at the H-dosed $\mathrm{ZnO}\left(10\overline{1}0\right)$ surface taken at $h\nu =65\mathrm{eV}$ at 13 K. (c)–(e) The calculated spectral functions of (c) $A^{\left(0\right)}$, (d) $A^{\left(1\right)}$, and (e) $A^{\left(0\right)}+A^{\left(1\right)}$. (f) The ARPES intensity map, which is symmetrized with respect to the center line $\left(k_x=0{\mathrm{nm}}^{-1}\right)$ and smoothed.