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Green's function approach to the lifetimes of image potential resonances at metal surfaces

AuthorsTsirkin, S. S.; Borisov, Andrei G.; Chulkov, Eugene V.
Issue Date2013
PublisherAmerican Physical Society
CitationPhysical Review B 88: 035449 (2013)
AbstractWe present a theoretical study of the image potential resonances (IPRs) at metal surfaces. We develop the Green's functions approach allowing us to calculate binding energies En and lifetimes τn of IPRs with high quantum numbers n (up to 10 in this work). A systematic study is performed at the Γ̄ point for the close-packed metal surfaces: Cu(111), Ag(111), Au(111), Al(001), Al(111), Be(0001), Mg(0001), Na(110), Li(110), and also at the Ȳ point on Cu(110). The calculated lifetimes of IPRs on close-packed surfaces demonstrate the scaling law τ nâ̂n3. Our results are in agreement with available experimental data. We show that at the Ȳ point on Cu(110) each quantum number n corresponds to a pair of IPRs n+ and n-, where the energy difference En+-En- is proportional to n -3. The lifetimes τn+ and τn- differ significantly, however, they both obey the scaling law τ n±â̂n3. Since the electrons trapped in the long-lived IPRs are strongly localized on the vacuum side, we argue that the inelastic electron-electron and electron-phonon scattering have a small contribution to the decay rate of these IPRs. The latter is dominated by the resonant electron transfer into the bulk.
Publisher version (URL)http://dx.doi.org/10.1103/PhysRevB.88.035449
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