Low-energy collective electronic excitations in a gold monolayer
The low-energy plasmonic properties of a free-standing Au(111) monolayer, frequently referred to as goldene, are investigated by time-dependent density functional theory in the random phase approximation. In the evaluation of dielectric and loss functions the first-principle band structure characterized by a single $s-p$ energy band at the Fermi level is taken into account. In this system with apparently simple band structure around the Fermi surface the calculations show the presence, besides the standard two-dimensional (2D) plasmon mode, at even lower energies of three anomalous branches in the momentum-energy region usually assigned to incoherent electron-hole pairs. This is an unexpected result since the electronic system of the gold monolayer is characterized by a single energy band crossing the Fermi level. The dispersion of these anomalous plasmonic branches is strongly anisotropic in-plane and gapless. A general feature is that at small in-plane momentum transfers the modes have a sound-like dispersion in certain momentum directions. We rely the appearance of these anomalous modes to a notable deviation of the Fermi surface of a gold monolayer from a circular shape. As a result of its almost perfect hexagon shape, there is possibility to realize in a {\it single} electronic energy band a scenario of a multi-component electron system with the carrier groups moving with different Fermi velocities in certain momentum directions. The found modes correspond to the out-of-phase charge oscillations of the carriers at different sides of the hexagonal Fermi surface. Hence our work presents evidence how in a metal system with apparently simple band structure around the Fermi level its shape can result in conversion of single-particle charge excitations into collective charge excitations.