Study for Temperature dependence of upper critical magnetic field in Uranium based heavy- Fermion Superconductor UT e2 in the theoretical aspect

Abstract This research focuses on the theoretical study of mathematical manipulation of upper critical magnetic field of superconducting Uranium ditelluride (\({UTe}_{2}\)). The main objective of this work is to show the temperature dependence of the upper critical magnetic field, GL-coherence length and GL-penetration depth of superconducting \({UTe}_{2}\) by using the Ginzburg-Landau (GL) phenomenological equation. By having mathematical relationship between the upper critical field (\({Hc}_{2}\)) along the three symmetric axes, the GL coherence length (\({\xi }_{GL}\)) and penetration depth (\({\lambda }_{GL}\)) with temperature. We plotted the result as a function of temperature that shows the dependence of upper critical magnetic field (\({Hc}_{2}\)) as well as coherence length and penetration depth with temperature (T) and our finding agrees with experimental observations.