Andreev reflection via the zero-energy bound states at the superconducting skyrmion crystal–normal skyrmion crystal interface

Abstract

In this work, we used the double exchange model and studied the transport properties of the electronic states across the superconducting skyrmion crystal (SkX)–normal SkX interface. By calculating the energy dispersion and the real-space wave function of the electronic states we found topologically protected edge zero modes in the superconducting SkX nanoribbon. By consideration of the symmetry of the Hamiltonian of the bulk superconducting SkX and its nanoribbon, we found that they belong to the symmetry class D and support Majorana edge modes. To demonstrate the transport properties of these zero edge modes, we used the Green's function method and calculated the Andreev reflection coefficients of the electronic states across the superconducting SkX–normal SkX interface. Zero-mode-induced Andreev reflection peaks are demonstrated and also reflected in the tunneling current. Single-channel conductance is quantized at 2e2/h and 4e2/h for two-fold and four-fold degenerate Majorana bound states, respectively.