Time, though ubiquitous in our daily experience, is a physical quantity not very well understood. It lies at the crux of efforts to unify the physical paradigms, being regarded as a constant background in some paradigms such as Newtonian mechanics or quantum mechanics, while completely internal to the objects in other paradigms such as general relativity. In quantum mechanics, specifically, the inability to find an operator for time as for spatial positions indicates the impossibility to find an observable which represents the external time \textit{coordinate}. Nevertheless, an operator can often be found to represent the internal time \textit{duration} of some certain process. The Eisenbud-Wigner-Smith (EWS) time scale is a famous example of such a time duration operator, which describes the single-particle scattering or ionization time scale.
The experimental determination of the EWS time scale for atomic photoionization has long been established and is a well-developed technique. With the assistance of ultrashort laser pulses, the relative time delay between photoionization from different states is measured, giving results in the attosecond (10−18s) range. This technique essentially measures the difference in time \textit{coordinate} between two photoionization events, while the absolute time coordinate of a single event cannot be determined due to the difficulty of defining the time-zero for the event.
In this thesis, a complementary approach is used to access the absolute and internal time \textit{duration} of photoelectron emission without explicit time resolution. Being better suited for photoemission from dispersive bands in solid-state materials, this method relies on the interference between multiple photoemission channels, which gives rise to spin polarization of the photoelectrons. The kinetic energy derivative of spin polarization contains information on the phase shift accumulated in the photoemission process, which can then be used to estimate the EWS photoemission time scale.
Building upon previous results estimated by the analytical model, which are τEWS≈26as for Cu(111) and τEWS≥120as for BSCCO, three materials have been selected to extend the parameter space in correlation strength and dimensionality, namely the quasi-2-dimensional transition metal dichalcogenides (TMDCs) 1T-TiSe2 and 1T-TiTe2, and the quasi 1-dimensional CuTe. A thorough study with the angle-resolved photoemission spectroscopy (ARPES) has been carried out to investigate their electronic structures and charge ordered phases. Their spin polarizations were then measured with spin- and angle-resolved photoemission spectroscopy (SARPES) to get an estimate of their EWS photoemission time scales. 1T-TiSe2 and 1T-TiTe2 show EWS time scales around 150,as, whereas in CuTe the photoemission takes more than 200,as. Analysis of results obtained thus far demonstrates a pattern in the dimensionality, as well as the symmetr
