Effect of local Coulomb interaction on Majorana corner modes: Weak and strong correlation limits

Here we present an analysis of the evolution of Majorana corner modes realizing in a two-dimensional higher-order topological superconductor (HOTSC) on a square lattice under the influence of local Coulomb repulsion. Both weak- and strong-interaction regimes are studied. It is shown that in the homogeneous system, the weak repulsion widens the region of the topologically nontrivial phase on the phase diagram. The open-boundary effect, resulting in spatial inhomogeneity of the system, leads to the appearance of the ground-state crossover as the repulsion intensity increases. Before the crossover, concentration correlators are ${C}_{4}$ symmetric and spin independent, and the corner states have energies that are determined by the overlap of the excitation wave functions localized at the different corners. After the crossover, the concentration correlators are spin dependent and possess the spontaneously broken symmetry. In turn, the corner excitation energy is size independent and defined by the Coulomb repulsion intensity with a quadratic law. In the strong-repulsion regime we derive the effective HOTSC Hamiltonian in the atomic representation and found a rich variety of interactions induced by virtual processes between the lower and upper Hubbard subbands. It is shown that Majorana corner modes still can be realized in the limit of the infinite repulsion, although the boundaries of the topologically nontrivial phase are strongly renormalized by Hubbard corrections.