How to Determine Fermi Vectors by Angle-Resolved Photoemission

Angle-resolved photoemission spectroscopy (ARPES) has been commonly applied to evaluate the shape of Fermi surfaces by employing simple criteria, such as maximum photoemission intensity at the Fermi level or discontinuity in the momentum distribution function, for the determination of the Fermi vector $k_F$ parallel to the surface. Here we show that these criteria may lead to large uncertainties, in particular for narrow band systems. We develop a reliable method for the determination of Fermi vectors employing high resolution ARPES at different temperatures. The relevance and accuracy of the method is discussed on data of the quasi-two-dimensional system ${\mathrm{TiTe}}_2$.