Fig. 2: Nature of grain-boundary superconductor.
The band structure [a, c, e and g] and the accompanying local density of states (LDOS) at zero energy [b, d, f, and h] for increasing exchange field (h) directed along the grain boundary. Each column corresponds to a particular value of the exchange field, with h = 0.1t (where t) in (a) and (b), h = 0.2t in (c) and (d), h = 0.25t in (e) and (f), and h = 0.28t in (g) and (h). Here, t is the hopping parameter. The two zero-energy modes localized at the top and the bottom edge in (b) and (d) pertain to the parent topological superconductor (SC), see also Fig. 3a. We note that in figs. (e) and (f), the grain boundary is gapless, and connects two edge zero modes of the parent gapped SC. In (h), there are four zero modes, as the grain boundary SC becomes topological, see also Figs. 3b and 4a. The red and blue coloring in the band-structure plots act only as a visual aid, to more clearly distinguish the bands. To make the localized states at the top and bottom of the grain boundary more visible, the middle part of the LDOS plots has been removed. Here, we set the order parameter to Δp = 0.75t, the inter-sublattice distance between edge dislocations to d = 12a, and the slip between sublattices to l = 5d/12 in the parent SC Hamiltonian (1). Additional plots showing the entire geometry are available in Supplementary Note 2, see Supplementary Fig. 3.
