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We develop a computational method for evaluating the damping of vibrationalmodes in mono-atomic metallic chains suspended between bulk crystals underexternal strain. The damping is due to the coupling between the chain andcontact modes and the phonons in the bulk substrates. The geometry of the atomsforming the contact is taken into account. The dynamical matrix is computedwith density functional theory in the atomic chain and the contacts usingfinite atomic displacements, while an empirical method is employed for the bulksubstrate. As a specific example, we present results for the experimentallyrealized case of gold chains in two different crystallographic directions. Therange of the computed damping rates confirm the estimates obtained by fits toexperimental data [Frederiksen et al., Phys. Rev. B, 75, 205413(R)(2007)]. Ourmethod indicates that an order-of-magnitude variation in the damping ispossible even for relatively small changes in the strain. Such detailed insightis necessary for a quantitative analysis of damping in metallic atomic chains,and in explaining the rich phenomenology seen in the experiments.

Atomistic theory for the damping of vibrational modes in mono-atomic gold chains