Excitonic precursor states in ultrafast pump–probe spectroscopies of surface bands

Abstract

Phone: þ385 1 4698 805, Fax: þ385 1 4698 889We discuss the formation and evolution of transient coherent excitonic states induced by ultrashort laser irradiation of metal surfaces supporting the surface and image potential bands (typically the low index surfaces of Cu and Ag). These states, which evolve into the image potential states in the course of screening of primary optically excited electron-hole pair, may play the role of early intermediate states in pump-probe spectroscopies of surfaces (e.g. two-photon-photoemission or sum-frequency generation) if the formation of image charge density proceeds on the time scale of the order of or longer than the pump-probe pulse duration and delay. In this regime a pump-probe experiment may yield information on the characteristics of such states rather than the states in relaxed image potential bands. Time scales of the various stages of these processes are estimated using an exactly solvable model of surface screening.1 Early time interactions of quasiparticles excited at surfaces The interpretation of excitation and detection of quasiparticles at surfaces in pump-probe experiments utilizing ultrashort laser pulses requires the assessment of quasiparticle dynamics and system relaxation from a true early evolution standpoint. While the nonadiabatic dynamics has been discussed in connection with the studies of surfaces and surface reactions by pulsed laser beams (for review see Refs. [1, 2]), the non-Markovian relaxation effects [3,4] following optical excitation of surfaces have only recently become the subject of interest and theoretical modelling [5]. Here we shall discuss these effects on the example of two-photon-photoemission (2PPE) from paradigmatic systems whose initial ground state accommodates partly occupied quasi-two-dimensional surface state bands (Q2D SS-bands) on top of the bulk valence and conduction band structure [typically on (111) surfaces of Cu and Ag]. The discussion will be focused on electronic screening processes as the dominant relaxation mechanism and in this context on the dynamics of formation of the much discussed Q2D image potential band states (IS-states) that are observed in the surface projected band gaps between the vacuum level E V and the Fermi energy E F of the substrate [6]. These bands are not incorpotated in the initial equilibrium electronic structure because they arise as a result of the response of the system to introduction of electronic charge outside the surface.In the initial step of 2PPE from surface bands [7] an electron excited out of the SS-band state by absorption of a pump pulse photon of energy v pu E V À E F will first feel the initial state effective substrate potential and the interaction with unscreened SS-hole left behind. This leads to formation of a coherent primary exciton whose bound state discrete energy levels E l < E V may form a Rydberglike series characterized by the quantum numbers l that reflect the specificities of constrained electronic motion [8][9][10]. Subsequently, the two photocreated quasipart...

Ultrafast electronic response of Ag(111) and Cu(111) surfaces: From early excitonic transients to saturated image potential

“…4 in Ref. [47]). The induced e-h potentialṼ ind e−h (t) is obtained from the induced electronic charge density q ind (Q, z 2 , t) which in the linear response theory is obtained from…”

“…44 The primary and intermediate states of MPPE and SFG are polarization states comprising the hole evolving from the initial state and electrons excited and relaxing during the sequence of excitations induced by the pump photon field. Here it is important to observe that before the formation of screening charge the photoexcited electron and hole interact through the bare (unscreened) Coulomb potential which may bind the pair into a localized excitonic state [45][46][47] (see Fig. 1(a)).…”

“…[12,13,47] we have set foundations for a theoretical description of the temporal and spatial evolution of the induced screening charge and ensuing potentials, respectively, and applied it to the Cu(111) surface. The latter is considered as a prototype system for demonstrating the existence of well defined SS-and IP-band states on metals, both experimentally and theoretically.…”

“…5 of Ref. [47] and calculated using the semiempirical N Q (ω ). This is so because the semiempirical ones include also the contributions from higher energy interband transitions which cause additional dephasing and hence faster attenuation of coherent oscillations of T (t).…”

Optical dielectric function of silver

“…[4][5][6][7][8] This role continues for understanding the ultrafast electron dynamics of metals. [9][10][11][12][13][14][15] Silver in particular assume a special status due to its high optical conductivity and wide range of applications from mirrors to plasmonics and optical metamaterials.…”