Investigation of upper critical magnetic field in multi-band iron-based superconductor 〖Ba〗_(1-x) K_x 〖〖Fe〗_2 〖As〗_2〗_

This work focuses on the theoretical investigation of the upper critical magnetic field(H_c2 ), Ginzburg-Landau coherence length (ξ_GL (T))and Ginzburg-Landau(GL) penetration depth (λ_GL (T)) by using the Ginzburg-Landau(GL)phenomenological equation for the two-band iron-based superconductor Ba_(1-x) K_x 〖Fe_2 As_2〗_. At zero external magnetic field, Ba_(1-x) K_x 〖Fe_2 As_2〗_ was found to undergo a transition from the normal state to the superconducting state at T_c=38 K.By using the phenomenological Ginzburg-Landau(GL) equation for the two-band coupled superconducting Ba_(1-x) K_x 〖Fe_2 As_2〗_, we obtained expressions for the upper critical magnetic field(H_c2), Ginzburg-Landau(GL) coherence length,ξ_GL (T) and Ginzburg-Landau(GL) penetration depth,λ_GL (T) as a function of temperature and the angular dependency of upper critical magnetic field. By using the experimental values in the obtained expressions, the phase diagrams of the upper critical magnetic field parallel 〖(H〗_c2^(∥c)) and perpendicular (H_c2^(⊥c) )to the symmetry axis versus temperature are plotted. We also obtained the phase diagrams of the Ginzburg-Landau upper criticalmagnetic field (H_c2 (θ)) versus the angle θ. Similarly, the phase diagrams of the Ginzburg-Landau (GL) coherence length ξ_GL (T)and Ginzburg-Landau(GL) penetration depth λ_GL (T)parallel and perpendicular to the symmetry axis versus temperature are plotted for the superconductor Ba_(1-x) K_x 〖Fe_2 As_2〗_. Our findings are in agreement with experimental observations.