Midgap edge states and pairing symmetry of quasi-one-dimensional organic superconductors

The singlets $s-$ and $d-,$ and triplet p-wave pairing symmetries in quasi-one-dimensional organic superconductors can be experimentally discriminated by probing the Andreev bound states at the sample edges. These states have the energy in the middle of the superconducting gap and manifest themselves as a zero-bias peak in tunneling conductance into the corresponding edge. Their existence is related to the sign change of the pairing potential around the Fermi surface. We present an exact self-consistent solution of the edge problem showing the presence of the midgap states for $p_x$-wave superconductivity. The spins of the edge state respond paramagnetically to a magnetic field parallel to the vector $\mathbf{d}$ that characterizes triplet pairing.