Modification of topological corner excitations at the interplay of boundary geometry and Coulomb interaction

The effect of Coulomb interaction on the 2D second order topological superconductor is investigated taking into account different geometries of the boundary in the mainframe of the mean-field approximation. The spontaneous symmetry breaking, described earlier in Aksenovet al(2023Phys. Rev.B107125401), is found to be robust against the boundary deformation. Meanwhile, the details of the state with spontaneously broken symmetry is found to be dependent on the specific boundary geometry. Considering different types of the boundary of the 2D system, it is demonstrated that the deviation of the electron density in the broken symmetry state is determined by the position of the zero-dimensional (second-order) excitations with nearly zero energy. The critical value of the Coulomb interaction, at which the transition occurs, is found to be determined by the energy of these excitations, which is non-zero due to overlapping of the wave-functions at different corners.