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The Electron–Phonon Coupling at the Mo(112) Surface

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The Electron–Phonon Coupling at the Mo(112) Surface University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Peter Dowben Publications Research Papers in Physics and Astronomy 2010 The electron–phonon coupling at the Mo(112) surface Ning Wu University of Nebraska-Lincoln Keisuke Fukutani University of Nebraska-Lincoln Peter A. Dowben University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/physicsdowben Part of the Physics Commons Wu, Ning; Fukutani, Keisuke; and Dowben, Peter A., "The electron–phonon coupling at the Mo(112) surface" (2010). Peter Dowben Publications. 245. https://digitalcommons.unl.edu/physicsdowben/245 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Peter Dowben Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 22 (2010) 245501 (7pp) doi:10.1088/0953-8984/22/24/245501 The electron–phonon coupling at the Mo(112) surface Ning Wu1, Ya B Losovyj1,2, Keisuke Fukutani1 and P A Dowben1,3 1 Department of Physics and Astronomy and the Nebraska Center for Materials and Nanoscience, University of Nebraska-Lincoln, Lincoln, NE 68588-0111, USA 2 The J Bennett Johnston Sr Center for Advanced Microstructures and Devices, Louisiana State University, 6980 Jefferson Highway, Baton Rouge, LA 70806, USA E-mail: [email protected] Received 1 April 2010, in final form 26 April 2010 Published 26 May 2010 Online at stacks.iop.org/JPhysCM/22/245501 Abstract We investigated the electron–phonon coupling (EPC), in the vicinity of the Fermi level, for the surface-weighted states of Mo(112) from high resolution angle-resolved photoemission data taken parallel to the surface corrugation (i.e. 1¯11¯ ). The surface-weighted bandwidth may be discussed in terms of electron–electron interactions, electron impurity scattering and electron–phonon coupling and exhibits a mass enhancement factor λ = 0.42, within the Debye model, determined from the experimentally derived self-energy. Gold overlayers suppress the −1 mass enhancement of the Mo(112) surface-weighted band crossing the Fermi level at 0.54 A˚ . 1. Introduction Angle-resolved photoemission spectroscopy (ARPES) [1, 3–5, 13–24], along with high resolution electron There is now a large body of evidence that electron– energy loss [25] and scanning tunneling spectroscopy [26], phonon coupling can affect the band structure, particularly are attractive techniques for investigating electron–phonon in the region of the Fermi level [1–3]. The resulting mass coupling providing useful information about the real and enhancement factors have not only now been characterized imaginary parts of the self-energy as well as the mass for a whole host of metal surfaces [1], but also for the enhancement factor. The mass enhancement factor λ can surfaces of a semimetal like graphite [4] and the surface of be estimated from the temperature-dependent band structure a superconductor like 2H-NbS2 [5]. As noted in a recent near the Fermi energy [14–20], as would typically be done review of Mo(112) [6], there is a strong interplay between the with high resolution electron energy loss [25] and scanning surface band structure and the surface structure, where both are tunneling spectroscopy [26]. Another approach, favored here, affected by the electron–phonon coupling and the wavevector- is to extract the mass enhancement factor λ from the shape of dependent surface phonon density. the real part of self-energy at the Fermi level or fitting the self- While electron–phonon coupling has been seen to lead to energy with the Debye model [3, 13, 21–23]. Another more significant mass enhancement for bands in the region of the sophisticated way is to directly extract the Eliashberg function Fermi level for the Mo(110) surface [3], the Mo(112) has a very from high resolution ARPES and λ can be derived from the significant surface layer spacing relaxation, with a significant integral of the Eliashberg function [1, 24]. The advantage of oscillatory layer spacer extending at least five layers from the this method is that the Eliashberg function is not temperature- surface into the bulk [6]. The relation of surface layers, for dependent and the dominant phonon modes may be obtained Mo(112) [6], is, in fact, very similar to the strong surface layer as well. relaxation that includes several layers in the surface region of Be(0001) [7–12], where the effective mass enhancement factor 2. Experimental details of the surface state in the vicinity of the Fermi level is seen to be anisotropic and dependent upon crystal direction [13]. The Mo(112) surfaces, schematically shown in figure 1,were prepared by using standard methods of flashing and annealing 3 Address for correspondence: Department of Physics and Astronomy, Nebraska Center for Materials and Nanoscience, Theodore Jorgensen Hall - in oxygen [6, 27–37], and the surface order characterized by Physical Science Building, 855 North 16th Street, University of Nebraska- LEED [6]. The high resolution angle-resolved photoemission Lincoln, NE 68588-0299, USA. studies were carried out on the 3 m normal incidence 0953-8984/10/245501+07$30.00 1 © 2010 IOP Publishing Ltd Printed in the UK & the USA J. Phys.: Condens. Matter 22 (2010) 245501 NWuet al Figure 2. The Mo(112) surface-weighted state band dispersion, at −1 roughly 0.54 A˚ along the ¯ –X,¯ in the vicinity of the Fermi energy, from high resolution angle-resolved photoemission. Quasi-particle band dispersion extracted from MDCs is shown in the inset, where the dashed line shows the free-electron-like expected parabolic band dispersion. the Mo(112) surface where a strongly surface-weighted band −1 crosses the Fermi level in the region of 0.54 A˚ . To better Figure 1. A schematic of the rectangular surface structure of illustrate the increase in the effective mass due to the electron– unreconstructed Mo(112). phonon coupling in this region of the Fermi level, only a small −1 region of the surface Brillouin zone from 0.26 to 0.61 A˚ monochromator (NIM) beamline with a 70 mrad acceptance has been plotted out. The inset to figure 2 shows the quasi- angle of horizontal radiation from a dipole magnet at the particle band dispersion extracted from momentum distribution Centre for Advanced Microstructures and Devices (CAMD) curves within a 150 meV region below the Fermi level, and the synchrotron, as described elsewhere [38]. The normal dashed line represents the bare parabolic quasi-‘free’ electron- incidence monochromator is combined with an angle-resolved like fitting of the band dispersion without consideration of the ultraviolet photoemission spectroscopy (ARUPS) endstation self-energy. With the high energy and wavevector resolution, (Scienta SES2002 electron energy analyzer) with a combined the phonon–electron-induced mass enhancement kink in the resolution of less than 15 meV at about 30 K [38]. The band structure, in the vicinity of the Fermi energy, is clearly photoemission spectra taken here are for a photon energy of significant and obviously identified in this surface band without 18 eV, resulting in an improved wavevector resolution because any fitting procedures [6]. of the lower photon energy. All binding energies are referenced The angle-resolved photoemission spectroscopy (ARPES) to the Fermi level. The acceptance angle of our electron spectral shape may be characterized by the single-particle analyzer is about 8◦, with an error in angle of about 0.3◦, spectral function A(ω, k) [3, 21–23]: as is typical of such measurements [3, 5], thus translating −1 −1 π | (ω, k)| to an uncertainty of no more than ±0.01 A˚ in wavevector A(ω, k) = I (1) [¯ω − ε0 − (ω, )]2 + (ω, )2 resolution along the surface. Though there may be other h k R k I k systematic errors adding to the uncertainty in the wavevector, ε0 these errors do not significantly affect estimates of the real and where k represents the non-interacting binding energy, and (ω, ) (ω, ) imaginary parts of the self-energy. R k and I k are the real part and imaginary part of the self-energy, respectively. Both the real and imaginary parts The band dispersion along the high symmetry line ¯ –X¯ of the self-energy should ideally be described as functions of (1¯11¯ direction of the surface, schematically shown in electron energy h¯ω, wavevector k and temperature, which is figure 1), in the whole surface Brillouin zone can be achieved not included in the ground state formulation of equation (1). by rotating the sample along its polar axis. The quantitative analysis of the dependence of the spectral (ω, ) 3. Electron–phonon coupling at the Mo(112) surface function A k on both wavevector and electron energy has been made using both the energy distribution curve (EDC) Figure 2 shows the k-dependent quasi-particle band structure mode and momentum distribution curve (MDC) mode. In along the ¯ –X¯ direction (along the surface 1¯11¯ direction) of other words, the energy–momentum plot (figure 2) has been 2 J. Phys.: Condens. Matter 22 (2010) 245501 NWuet al cut either vertically to get energy distribution curves at various wavevectors or horizontally to get momentum distribution curves at various energies. Since the photoemission signal is also dependent on the Fermi distribution function f (ω), the MDC (cuts at certain energy so that ω is fixed) tends to be preferable. Furthermore, strong electron–phonon coupling may not only create the mass enhancement kink in the band structure, but also can alter the peak shape of the spectra in EDC mode within 100 meV of the Fermi level [21, 39]. The theory suggests that the effect of multiple scattering of electrons with phonons could complicate the spectral shape near the Fermi level, creating a double-peaked Lorentzian function in EDC mode.
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