Stages of hot electron dynamics in multiexcitation processes at surfaces: General properties and benchmark examples

Mukamel, 1995 For applications of ultrafast spectroscopies in the studies of surfaces see: H. Zacharias (Ed.), Dynamics of Electron Transfer Processes at Surfaces, Prog. Surf. Sci. 82 (2007) 161–388. 2010, vol. I Petek, 1997, Prog. Surf. Sci., 56, 239, 10.1016/S0079-6816(98)00002-1 Ueba, 1995, Surf. Sci., 334, L719, 10.1016/0039-6028(95)80023-9 Ueba, 2007, Prog. Surf. Sci., 82, 193, 10.1016/j.progsurf.2007.03.002 Timm, 2004, J. Phys. Condens. Matter, 16, 661, 10.1088/0953-8984/16/4/015 Winkelmann, 2009, Phys. Rev. B, 80, 155128, 10.1103/PhysRevB.80.155128 Schenk, 2010, Phys. Rev. Lett., 105, 257601, 10.1103/PhysRevLett.105.257601 Adawi, 1964, Phys. Rev., 134, A788, 10.1103/PhysRev.134.A788 N.W. Ashcroft, W.L. Schaich, National Bureau of Standards Special Publication 323 (1970) 129. Schaich, 1971, Phys. Rev. B, 3, 2452, 10.1103/PhysRevB.3.2452 Mahan, 1970, Phys. Rev. B, 2, 4334, 10.1103/PhysRevB.2.4334 Langreth, 1971, Phys. Rev. B, 3, 3120, 10.1103/PhysRevB.3.3120 Chang, 1972, Phys. Rev. B, 5, 3512, 10.1103/PhysRevB.5.3512 Chang, 1973, Phys. Rev. B, 8, 4638, 10.1103/PhysRevB.8.4638 Caroli, 1973, Phys. Rev. B, 8, 4552, 10.1103/PhysRevB.8.4552 Lazić, 2009, Surf. Sci., 603, 1571, 10.1016/j.susc.2008.09.061 Abramavicius, 2009, Chem. Rev., 109, 2350, 10.1021/cr800268n Gumhalter, 2005, Phys. Rev. B, 72, 165406, 10.1103/PhysRevB.72.165406 Lazić, 2006, Phys. Rev. Lett., 97, 086801, 10.1103/PhysRevLett.97.086801 Lazić, 2007, Phys. Rev. B, 76, 045420, 10.1103/PhysRevB.76.045420 Gumhalter, 2008, Phys. Rev. B, 78, 155410, 10.1103/PhysRevB.78.155410 S. Marion, B. Gumhalter, Phys. Status Solidi B, in press, http://dx.doi.org/10.1002/pssb.201100543. Mahan, 1981 Gerlach, 1991, Rev. Mod. Phys., 63, 63, 10.1103/RevModPhys.63.63 Weiss, 1999 Engelsberg, 1963, Phys. Rev., 131, 993, 10.1103/PhysRev.131.993 Hedin, 1965, Phys. Rev., 139, A796, 10.1103/PhysRev.139.A796 Mahan, 1994, Comments Condens Matter Phys., 16, 333 Lundqvist, 1967, Phys. Konden. Materie, 6, 193 Hedin, 1980, Phys. Scr., 21, 417, 10.1088/0031-8949/21/3-4/039 Holm, 1998, Phys. Rev. B, 57, 2108, 10.1103/PhysRevB.57.2108 Aryasetiawan, 1996, Phys. Rev. Lett., 77, 2268, 10.1103/PhysRevLett.77.2268 Almbladh, 2006, J. Phys. Conf. Ser., 35, 127, 10.1088/1742-6596/35/1/011 Gavoret, 1969, J. Phys. (Paris), 30, 987, 10.1051/jphys:019690030011-12098700 Doniach, 1970, Phys. Rev. B, 2, 3898, 10.1103/PhysRevB.2.3898 Ruckenstein, 1987, Phys. Rev. B, 35, 7551, 10.1103/PhysRevB.35.7551 Uenoyama, 1990, Phys. Rev. Lett., 65, 1048, 10.1103/PhysRevLett.65.1048 Bechstedt, 1982, Phys. Status Solidi B, 112, 9, 10.1002/pssb.2221120102 Bechstedt, 1994, Phys. Rev. B, 49, 7357, 10.1103/PhysRevB.49.7357 Del Sole, 1994, Phys. Rev. B, 49, 8024, 10.1103/PhysRevB.49.8024 Shirley, 1996, Phys. Rev. B, 54, 7758, 10.1103/PhysRevB.54.7758 Schindlmayr, 1998, Phys. Rev. Lett., 80, 1702, 10.1103/PhysRevLett.80.1702 Langreth, 1970, Phys. Rev. B, 1, 471, 10.1103/PhysRevB.1.471 Langreth, 1973, Nobel, 24, 210 Müller-Hartmann, 1971, Phys. Rev. B, 3, 1102, 10.1103/PhysRevB.3.1102 Blomberg, 1972, Can. J. Phys., 50, 2286, 10.1139/p72-303 Almbladh, 1983, vol. 1 Verdozzi, 1995, Phys. Rev. Lett., 74, 2327, 10.1103/PhysRevLett.74.2327 Wilkinson, 1997, Nature, 387, 576 Rothe, 2006, Phys. Rev. Lett., 96, 163601, 10.1103/PhysRevLett.96.163601 Sakaue, 2005, J. Phys. Condens. Matter, 17, S245, 10.1088/0953-8984/17/8/004 Šiber, 2003, Phys. Rev. Lett., 90, 126103, 10.1103/PhysRevLett.90.126103 Doniach, 1974 Kubo, 1962, J. Phys. Soc. Jpn., 17, 1100, 10.1143/JPSJ.17.1100 Nozières, 1969, Phys. Rev., 178, 1097, 10.1103/PhysRev.178.1097 Dunn, 1975, Can. J. Phys., 53, 321, 10.1139/p75-042 Gunnarsson, 1994, Phys. Rev. B, 50, 10462, 10.1103/PhysRevB.50.10462 Brenig, 2004, J. Phys. Chem. B, 108, 14549, 10.1021/jp040151e Sunko, 2004, Am. J. Phys., 72, 231, 10.1119/1.1587703 Khalfin, 1958, Sov. Phys. JETP, 6, 1053 Abrikosov, 1965 Barišić, 2004, Phys. Rev. B, 69, 064302, 10.1103/PhysRevB.69.064302 Barišić, 2007, Europhys. Lett., 77, 57004, 10.1209/0295-5075/77/57004 Facchi, 2008, J. Phys. A Math. Theor., 41, 493001, 10.1088/1751-8113/41/49/493001 Gumhalter, 1984, Progr. Surf. Sci, 15/1, 1, 10.1016/0079-6816(84)90003-0 Contrary to the popular belief these tails are generally not Lorentzian-like. The spectral wing shapes far away from the QE peak are determined by the short time behaviour of exp[C(k,t)] which due to (22) does not give rise to Lorentzian tails in the quasiparticle spectrum N(k,ω′). A similar procedure of remeding the threshold properties of multiple boson excitation probabilities was introduced in Section IV of Ref. [56]. The mapping N(ω′)→ρ(ω) in which N(ω′) exhibits a sharp upper band edge cutoff may give rise to negative values of the cumulant spectrum ρ(ω) in certain intervals of ω, likewise in Section 3.2.2. The root giving the position of GWA plasmaron maximum exceeds Ek by more than the surface plasmon excitation energy [28]. An analogous identification of the corresponding quantities was carried out in Ref. [30]. Chulkov, 1999, Surf. Sci., 437, 330, 10.1016/S0039-6028(99)00668-8 Echenique, 2004, Surf. Sci. Rep., 52, 219, 10.1016/j.surfrep.2004.02.002 Chulkov, 2006, Chem. Rev., 106, 4160, 10.1021/cr050166o Pitarke, 2008, J. Phys. Condens. Matter, 20, 304207, 10.1088/0953-8984/20/30/304207 Schöne, 2007, Prog. Surf. Sci., 82, 161, 10.1016/j.progsurf.2007.03.004 Rufeil Fiori, 2006, Chem. Phys. Lett., 420, 35, 10.1016/j.cplett.2005.12.025 Gumhalter, 2010, Phys. Status Solidi B, 247, 1907, 10.1002/pssb.200983944 Silkin, 2010, J. Phys. Condens. Matter, 22, 304013, 10.1088/0953-8984/22/30/304013 The need for a separate treatment of the case K=0 was also pointed out in Refs. [[25,43]]. The inclusion of the effects of nondispersive surface plasmons amounts to taking a convolution of the spectrum from Eq. (49) with the spectrum from Eq. (26). Liebsch, 1997 Marini, 2002, Phys. Rev. Lett., 88, 016403, 10.1103/PhysRevLett.88.016403 Hyeon-Deuk, 2011, Nano Lett., 11, 1845, 10.1021/nl200651p Himpsel, 1982, Phys. Rev. Lett., 49, 1583, 10.1103/PhysRevLett.49.1583 Rogozik, 1984, Surf. Sci., 145, L481, 10.1016/0039-6028(84)90760-X Reihl, 1985, Phys. Rev. B, 31, 8282, 10.1103/PhysRevB.31.8282 Straub, 1986, Phys. Rev. B, 33, 2256, 10.1103/PhysRevB.33.2256 Bartynski, 1986, Phys. Rev. B, 33, 6588, 10.1103/PhysRevB.33.6588 Yang, 1991, Phys. Rev. B, 43, 2025, 10.1103/PhysRevB.43.2025 Bertel, 1994, Surf. Sci., 307–309, 947, 10.1016/0039-6028(94)91521-0 Bertel, 1995, Surf. Sci., 331–333, 1136, 10.1016/0039-6028(95)00074-7 Gumhalter, 1985, Surf. Sci., 157, L355, 10.1016/0039-6028(85)90628-4 Gumhalter, 1988, Phys. Rev. B, 37, 8048, 10.1103/PhysRevB.37.8048 Rohlfing, 2000, Phys. Rev. B, 62, 4927, 10.1103/PhysRevB.62.4927 Wang, 2003, Phys. Rev. B, 67, 115111, 10.1103/PhysRevB.67.115111 Marini, 2003, Phys. Rev. Lett., 91, 176402, 10.1103/PhysRevLett.91.176402 Marini, 2009, Comp. Phys. Commun., 180, 1392, 10.1016/j.cpc.2009.02.003 Bechstedt, 1997, Phys. Rev. Lett., 78, 1528, 10.1103/PhysRevLett.78.1528 Schöne, 2000, Phys. Rev. B, 62, 13464, 10.1103/PhysRevB.62.13464 Shen, 2003 Chemla, 1996, Chem. Phys., 210, 135, 10.1016/0301-0104(96)00050-X For example of another type interactions and time scales of transients see Refs. [20,21]. For the time scales of formation of image potential and corresponding bands see Figs. 5 and 6 in Ref. [71]. Cohen-Tannoudji, 1992