Extracting the temperature of hot carriers in time- and angle-resolved photoemission

The interaction of light with a material's electronic system creates an out-of-equilibrium (non-thermal) distribution of optically excited electrons. Non-equilibrium dynamics relaxes this distribution on an ultrafast timescale to a hot Fermi-Dirac distribution with a well-defined temperature. The advent of time- and angle-resolved photoemission spectroscopy (TR-ARPES) experiments has made it possible to track the decay of the temperature of the excited hot electrons in selected states in the Brillouin zone, and to reveal their cooling in unprecedented detail in a variety of emerging materials. It is, however, not a straightforward task to determine the temperature with high accuracy. This is mainly attributable to an a priori unknown position of the Fermi level and the fact that the shape of the Fermi edge can be severely perturbed when the state in question is crossing the Fermi energy. Here, we introduce a method that circumvents these difficulties and accurately extracts both the temperature and the position of the Fermi level for a hot carrier distribution by tracking the occupation statistics of the carriers measured in a TR-ARPES experiment.