Two-dimensional (2D) metallic states formed on the ZnO(10$bar{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.
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