Image potential eigenstates and resonances on the (110) surfaces of noble metals: Energies and lifetimes

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MOLECULES, OPTICS

Image Potential Eigenstates and Resonances on the (110) Surfaces of Noble Metals: Energies and Lifetimes S. S. Tsirkina* and E. V. Chulkovb a

Tomsk State University, Tomsk, 634050 Russia *email: [email protected] b Departamento de Física de Materiales UPV/EHU, Centro de Física de Materiales CFM–MPC, and Centro Mixto CSIC–UPV/EHU, San Sebastian/Donostia, Basque Country, 20080 Spain Received June 12, 2013

Abstract—The energies and lifetimes of the image potential resonances at the Y point on the Cu(110), Ag(110), and Au(110) surfaces are studied, and the energies of the image potential states on the Pd(110) sur face are analyzed. It is shown that every quantum number n corresponds to a pair of image potential states (resonances) n+ and n– at the Y point. The average energy of a pair of eigenstates (resonances) at n ≥ 2 is well described by the formula E n = (En+ + En–) = E0 – (0.85 eV)/(n + δ)2, where δ is the quantum defect, E0 = (1/2me)(បπ/a)2, and a is the lattice parameter. The splitting energy of a pair of eigenstates (resonances) obeys the law ΔEn = En+ – En– ∝ n–3. The lifetimes τn± of image potential resonances are proportional to n3. DOI: 10.1134/S1063776114010191

1. INTRODUCTION Electron excitations in image potential states (IPSs) appear on metallic surfaces as a result of the interaction of an electron located in front of a surface with the charge induced in the metal [1–6]. Near the center of the surface Brillouin zone (the Γ point), IPSs form a Rydberg series [1, 2] 2 2

0.85 eV ប k E n ( k ) = –  + , 2 ( n + δ ) 2m *h

(1)

where n = 1, 2, … is the principal quantum number; δ is the quantum defect; k is the wavevector parallel to the surface; and effective masses m *n are close to the free electron mass. These states are widely used as a model system for theoretical and experimental inves tigations of the dynamics of electron excitations on metallic surfaces owing to a welldetermined IPS spectrum lying in a local energy gap [7, 8]. Image potential resonances (IPRs) are formed under degeneracy of IPS with bulk states. The authors of [2, 9–12] were able to experimentally detect only IPSs with small quantum numbers n ≤ 3, since the energies of IPRs with large quantum numbers are close to each other. Therefore, it is necessary to have a high energy resolution to distinguish these states as separate photoemission peaks. However, the recent progress in timeresolved twophoton photoemission makes it possible to measure the energies and lifetimes of IPRs with larger quantum numbers [13, 14].

The decay rate (line width) Γ = ប/τ (where τ is the lifetime) of an electron excitation is determined by the following four processes: inelastic electron–electron scattering [15, 16], electron–phonon scattering [17], scattering by defects [18, 19], and electron tunneling into the bulk [20]. The authors of [21–24] showed that electron–phonon scattering weakly contributes to the electron decay rate in IPS even for the first IPS, which substantially penetrates deep into a cr

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