Spin Polarization and Attosecond Time Delay in Photoemission from Spin Degenerate States of Solids

Abstract

After photon absorption, electrons from a dispersive band of a solid require a finite time in the photoemission process before being photoemitted as free particles, in line with recent attosecond-resolved photoemission experiments. According to the Eisenbud-Wigner-Smith model, the time delay is due to a phase shift of different transitions that occur in the process. Such a phase shift is also at the origin of the angular dependent spin polarization of the photoelectron beam, observable in spin degenerate systems without angular momentum transfer by the incident photon. We propose a semiquantitative model which permits us to relate spin and time scales in photoemission from condensed matter targets and to better understand spin-and angle-resolved photoemission spectroscopy (SARPES) experiments on spin degenerate systems. We also present the first experimental determination by SARPES of this time delay in a dispersive band, which is found to be greater than 26 as for electrons emitted from the sp-bulk band of the model system Cu(111).

Spin polarization in photoemission from the cuprate superconductor Bi2Sr2CaCu2O8+δ

“…On the other hand, all the bands at positive and negative momenta for the nodal and antinodal directions present a clear momentum-resolved spin polarization along the x M direction, with a value that reaches 10%. Notably, each photoemission intensity peak in the antinodal direction presents an up-down spin structure reminiscent of the double polarization feature (DPF) observed in Cu(111) [19]. In the nodal direction, the photoemission intensity peaks are more structured, and there appear to be two partially overlapped DPFs, as can be better seen in Fig.…”

“…3(b), with an obtained absolute slope of 0.13 eV −1 . Since we have no information about the third component P y M , under the assumption that P does not vary direction but only its modulus in the measured E b range [19], we can write dP /dE b > dP x M /E b and therefore find an inferior limit for the EWS time delay. If, for example, P y M ≈ 0, we find τ EWS > 85 as, whereas if…”

“…A similar behavior is also observed at positive momenta, where, however, the total intensity is lower. It bears mentioning that the nature of the DPF, which seems to be a general property of dispersive bands whereas it does not appear in core levels [19], is not yet understood.…”

“…The size of P is related to the phase shift of the complex matrix elements describing the transitions under consideration [17][18][19]. One can, therefore, access the phase information by measuring the spin polarization of the photoelectrons.…”

“…In particular, a novel application of SARPES is the estimate of the Eisenbud-Wigner-Smith (EWS) time delay [20] τ EWS of photoemission, defined as the derivative of the phase shift with respect to the photoelectron kinetic energy, obtained from the measured P, as shown in Ref. [19] for the model system Cu(111). By expressing the spin polarization as a function of the radial parts and phase shifts of the matrix elements, along the lines of the atomic half-scattering formalism [18], one can analytically obtain an estimate for a finite inferior limit to the EWS time delay in the attosecond * Corresponding author: mauro.fanciulli@epfl.ch domain.…”