London penetration depth in disordered unconventional superconductors with competing interactions*

A topic of an interplay between disorder and competing electronic phases in multiband superconductors have recently got renewed interest in the context of iron-based superconductors. In my talk I will present a theory of disordered unconventional superconductor with competing magnetic order. Our discussion will be based on the results obtained for on a two-band model with quasi-two-dimensional Fermi surfaces, which allows for the coexistence region in the phase diagram between magnetic and superconducting states in the presence of intraband and interband scattering induced by doping. We will demonstrate that disorder has a crucial effect on the magnetic field penetration depth as a function of disorder scattering rates.