Large differential attosecond delays in solid state photoemission

Time-resolved photoelectron spectroscopy provides access to the electronic structure and non-equilibrium electron dynamics in matter. At solid surfaces photoemission dynamics can be investigated on its natural time scale by measuring attosecond time delays of emitted electrons. Photoelectrons with final state energies of several tens of eV need tens to hundreds of attoseconds to be released into the vacuum. Competing effects determine the emission dynamics and, hence, the full picture of the process is still under debate. The rather large energy differences between the final states probed in commonly reported relative photoemission delays obscure their complex fine structure and hinders the interpretation of the measurements. Here we report differential attosecond delays $\tau_{\mathrm{DAD}}$, i.e., relative photoemission delays for energetically close-lying spin-orbit split states. Differential attosecond delays on the order of 30 to 100 as for Bi 5d, Te 4d, and Se 3d core level photoemission from Bi$_2$Te$_3$ and Bi$_2$Se$_3$ can neither be attributed to intra-atomic delays, nor to ballistic transport and subsequent emission. Instead, calculations based on the one-step photoemission theory reveal that photoemission delays vary strongly on the energy scale of the spin-orbit splitting and quantitatively match experimental observations. This strong variation arises from multiple scattering at the surface leading to final states that involve both evanescent and propagating Bloch waves. Their relative amplitudes vary strongly affecting thereby the timing of the photoemission event since evanescent and propagating components exhibit inherently different dynamics.