Title: Field-induced coexistence of $s_{++}$ and $s_{\pm}$ superconducting states in dirty multiband superconductors,
Abstract: In multiband systems, such as iron-based superconductors, the superconducting
states with locking and anti-locking of the interband phase differences, are
usually considered as mutually exclusive. For example, a dirty two-band system
with interband impurity scattering undergoes a sharp crossover between the
$s_{\pm}$ state (which favors phase anti locking) and the $s_{++}$ state (which
favors phase locking). We discuss here that the situation can be much more
complex in the presence of an external field or superconducting currents. In an
external applied magnetic field, dirty two-band superconductors do not feature
a sharp $s_{\pm}\to s_{++}$ crossover but rather a washed-out crossover to a
finite region in the parameter space where both $s_{\pm}$ and $s_{++}$ states
can coexist for example as a lattice or a microemulsion of inclusions of
different states. The current-carrying regions such as the regions near vortex
cores can exhibit an $s_\pm$ state while it is the $s_{++}$ state that is
favored in the bulk. This coexistence of both states can even be realized in
the Meissner state at the domain's boundaries featuring Meissner currents. We
demonstrate that there is a magnetic-field-driven crossover between the pure
$s_{\pm}$ and the $s_{++}$ states.