Manipulating and braiding Majorana corner modes on a kagome lattice

Demonstrating the braiding of Majorana modes remains an unsolved problem in condensed matter physics because of platform-specific challenges. In this paper, we propose a two-dimensional (2D) kagome lattice with $s$-wave and $d$-wave superconductors as an effective platform for manipulating and braiding Majorana modes. Our findings reveal that the topological phase is highly sensitive to the application of uniaxial strain or variations in chemical potential, enabling real-space manipulation of Majorana modes. In proximity to an $s$-wave superconductor, we design the kagome lattice with only $C/B$-type sublattice terminations, and exchange the position of Majorana corner modes (MCMs) along the boundary. We further develop a porous kagome lattice to host and braid multiple MCMs, as experimentally measurable braiding requires at least four Majorana modes. When substituting the $s$-wave superconductor with a $d$-wave superconductor, we observe the emergence of Majorana Kramers pairs (MKPs). Importantly, the positions of the Dirac mass domain walls that bind the MKPs are sensitively dependent on the local boundary topology. By building a kagome lattice featuring solely $C/B$-type sublattice terminations and manipulating the local boundary topology, we can therefore exchange the positions of MKPs through applying inhomogeneous chemical potential and/or nonuniform uniaxial strain.