A fundamental topological consequence of the unconventional (i.e., non-s-wave) pairing symmetry of high-T c superconductors (HTSC's) is the existence of midgap (quasi-particle) states (MS's) bound to surfaces, interfaces and other locations. This prediction by the author has most-likely solved a decade-old puzzle, viz., the ubiquitous observation of a zero-bias conductance peak (ZBCP) in tunneling experiments performed on HTSC's. There are also numerous other novel consequences of these MS's, predicted by various researchers, including a new Josephson critical current term; an (already observed) low-temperature splitting of the ZBCP due possibly to a spontaneous breaking of the time-reversal symmetry at a sample surface; a new explanation of the paramagnetic Meissner effect; and a giant magnetic moment, etc. Here the author will review the physical origin of the MS's, the several extensions of the original idea and the many novel consequences of these MS's, some of which have been investigated quantitatively and some others only deduced in qualitative terms so far.
Enhanced zero-bias conductance peak and splitting at mesoscopic interfaces between an s-wave superconductor and a 3D Dirac semimetal
