Effective mass effect in attosecond electron transport

Abstract

The electronic band structure governs the electron dynamics in solids. It defines a group velocity and an effective mass of the electronic wave packet. Recent experimental and theoretical studies suggest that an electron acquires the effective mass of its excited state over distances much larger than the lattice period of the solid. Therefore, electron propagation on atomic length scales was typically considered to be free-electron-like. Here, we test this hypothesis by probing attosecond photoemission from a Cu(111) surface. We use attosecond pulse trains in the extreme-ultraviolet (21-33 eV) to excite electrons from two initial bands within the 3d-valence band of copper. We timed their arrival at the crystal surface with a probing femtosecond infrared pulse, and found an upper limit of 350±40 as (1 as=10−18 s) for the propagation time an electron requires to assume the effective mass of its excited state. This observation implies that a final-state Bloch wave packet forms within a travel distance of 5-7 Å, which is at most two atomic layers. Using well-established theory, our measurements demonstrate the importance of the band structure even for atomic-scale electron transport. The electronic band structure governs the electron dynamics in solids. It defines a group velocity and an effective mass of the electronic wave packet. Recent experimental and theoretical studies suggest that an electron acquires the effective mass of its excited state over distances much larger than the lattice period of the solid. Therefore, electron propagation on atomic length scales was typically considered to be free-electron-like. Here, we test this hypothesis by probing attosecond photoemission from a Cu(111) surface. We use attosecond pulse trains in the extremeultraviolet (21-33 eV) to excite electrons from two initial bands within the 3d-valence band of copper. We timed their arrival at the crystal surface with a probing femtosecond infrared pulse, and found an upper limit of 350 40 as (1 as 10 −18 s) for the propagation time an electron requires to assume the effective mass of its excited state. This observation implies that a final-state Bloch wave packet forms within a travel distance of 5-7 Å, which is at most two atomic layers. Using well-established theory, our measurements demonstrate the importance of the band structure even for atomic-scale electron transport.

Equivalence of RABBITT and Streaking Delays in Attosecond-Time-Resolved Photoemission Spectroscopy at Solid Surfaces

“…This corresponds to a streaking amplitude of 1.2 eV at E kin = 25 eV and to a streaking amplitude of 1.7 eV at E kin = 50 eV, which is comparable to typical results for streaking at solid surfaces [9][10][11]39]. IR intensity applied in the RABBITT experiments was in the same order of magnitude [23,32,40].…”

“…In a RABBITT experiment using longer IR pulses (>20 fs), side-band delays are usually determined by fitting a cosine function to side-band intensity I SB [2,6,23,32]. However, in the simulations presented here, background-free few-cycle RABBITT spectra were calculated using a 5 fs IR pulse, i.e., its finite spectral width comes into play.…”

“…To guarantee comparability, we applied identical 5fs IR pulses for RABBITT and streaking calculations. Note that RABBITT experiments are usually performed with longer IR pulses (>20 fs) [2,6,23,32]. Although the application of longer IR pulses reduces experimental difficulties, there is no fundamental obstacle to perform RABBITT experiments with carrier-envelope-phase-stabilized few-cycle IR pulses.…”

Attosecond timing of the dynamical Franz–Keldysh effect

“…The recent development of spectroscopic techniques based on attosecond extreme-ultraviolet (XUV) pulses has given us the ability to follow the ultrafast electron motion in solids that underlies fundamental processes of lightmatter interaction. Besides photoelectron spectroscopy [1][2][3][4], all-optical techniques like attosecond transient absorption spectroscopy (ATAS) [5] have shown their potential for the investigation of fundamental phenomena in semiconductors [6], dielectrics [7], metals [8] and magnetic systems [9], up to petahertz driving fields [10]. The first pioneering experiments brought unprecedented insights in strong-field physics in solid systems, addressing the role of inter-and intra-band excitation from a new perspective [11][12][13].…”

Semiclassical approach for solving the time-dependent Schrödinger equation in spatially inhomogeneous electromagnetic pulses

“…This was demonstrated in proof-of-principle experiments for gaseous atomic [10][11][12][13][14][15][16] and molecular [17][18][19] targets. Attosecond time-resolved photoemission spectroscopy is currently being extended to complex targets [6,20], such as nanostructures and nanoparticles [21][22][23][24][25][26][27][28], and solid surfaces [9,[29][30][31][32][33][34][35][36], making it possible to examine, for example, the dynamics of photoemission from a surface on an absolute time scale [37] and suggesting, for example, the time-resolved observation of the collective motion of electrons (plasmons) in condensed-matter systems [38][39][40].…”