Change in the order parameter symmetry in the vicinity of the surface of a superconductor with $s_\pm$ pairing

The behavior of the order parameter and the local density of states near the impenetrable surface have been theoretically studied in a two-band superconductor in which the gapless state with $s_\pm$ symmetry of the superconducting order parameter is realized. It has been shown that, over a wide range of the parameters, the spatial behavior of the order parameter on the surface is not reduced to a standard suppression. If the probability of the interband reflection on the surface is of the order of or higher than the probability of the intraband reflection, it can be energetically more favorable to change the symmetry of the superconducting state near the surface from $s_\pm$ symmetry to common $s$ symmetry. The region of existence of the surface $s$-superconductivity is very sensitive to relative values of the interband and intraband pairing potentials. It has also been shown that the self-consistent calculation (i.e., with allowance made for the dissimilarity of the near-surface order parameter from the bulk value) can lead to a qualitatively different behavior of the near-surface local density of states as compared to the results of the non-self-consistent calculation.