Ultrafast electron dynamics in a metallic quantum well nanofilm with spin splitting

Using time- and angle-resolved two-photon photoemission spectroscopy, we investigate the energy- and momentum-dependent ultrafast electron dynamics in the Rashba spin-split quantum-well nanofilm Bi/Cu(111). We find an expected increase of electron lifetimes towards the band bottom due to a competition of intra- and interband scattering processes. In addition, we find an unexpected peculiar decrease of the lifetimes around the intersection of the split bands. We compare the experimental results with calculated lifetimes due to electron-electron scattering in a model system of a 2D electron gas including a Rashba interaction term and an effective statically screened Coulomb interaction. Although the Rashba model reproduces the increase of lifetimes towards the band bottom well, there is no indication of the experimentally observed decrease around the intersection point in this simple model system. To investigate spin-orbit coupling effects, beyond those contained in a pure Rashba model, we introduce a phenomenological $k$-dependent spin mixing that leads to a “spin hot spot.” It is shown that such a mixing would strongly increase the electron-electron scattering rate around the band intersection and thus improves the agreement with experiment.

Figure 1

(a) 2PPE map of the spin-split electron bands from angle-resolved 2PPE in a commensurate overlayer Bi/Cu(111). The gray scale represents photoemission intensity. (b) Corresponding inelastic lifetime map $\tau (E,k_{\parallel })$ of the spin-split electron bands from angle-resolved tr-2PPE. The lifetime $\tau$ is color coded as a function of energy $E$ and parallel momentum $k_{\parallel }$. Both spectra have been recorded for a series of emission angles and stitched here for qualitative illustration.[15] Note that the photoemission spectrum (a) has been collected with a narrow-bandwidth Ti:sapphire oscillator ($\Delta E=20$ meV, pulse length $>$100 fs), and the time-resolved data in (b) with a broad-bandwidth short-pulse Ti:sapphire oscillator [$\Delta E=100\left(5\right)$ meV, pulse length $\approx$27 fs]. (c) Exemplary autocorrelation traces (symbols) with fits (lines) extracted from the red and blue marked areas in Fig. 1b, however, from the nonstitched raw data, in comparison to the laser-autocorrelation trace. (d) Schematic of the time-resolved 2PPE process. $\Delta t$ is the temporal delay between the pulses.

Figure 2

(a) Energy dispersion of the Rashba bands and the filled parabolic band. (b) In-plane spin orientation in a Rashba system.

Figure 3

Calculated (lines) and measured lifetimes (red circles and blue circles for below and above the intersection point located at about $E-E_{\mathrm{F}}=2.65$ eV, respectively). The increased error bars around the intersection point account for the uncertainty due to limited experimental energy resolution. Note, however, that all extracted data points are well separated in $k_{\parallel }$ space [c.f. Fig. 1b]. The black line corresponds to a pure Rashba model with experimental parameters. The black dashed line illustrates the maximum deviation that might be introduced by the limited experimental energy resolution. In the results represented by the red (dash-dotted) and blue (dotted) lines, an additional spin-mixing is included (see text).