Grain boundary band structure engineering in a topological superconductor

Ubiquitous in all crystalline materials is the presence of grains, within which the crystal lattice is oriented in a certain direction. Neighboring grains do not necessarily align, giving rise to a lattice mismatch at their interface, also known as a grain boundary. This extended lattice defect can consist of an array of edge dislocations, which in topologically non-trivial materials can, in turn, yield bands for momenta along the grain boundary.

In our work we study the band structure of the Bogoliubov quasiparticles emerging at the grain boundary formed by a misalignment of two square lattices in a two-dimensional topological superconductor. The misalignment consists of a relative angle, and a relative shift. We find that by tuning only the chemical potential, a large variety of band structures can be generated, ranging from fully gapped, to semimetallic, and finally almost completely flat ones. Furthermore, by applying an in-plane magnetic field, additional tunability is obtained, as the presence or absence of a gap in the band structure may be controlled by the orientation of the magnetic field in a counterintuitive way. Finally, I will discuss the physical mechanism behind these results based on an effective lattice model along the grain boundary.