Majorana fermions from Shiba states in an antiferromagnetic chain on top of a superconductor

We propose a new mechanism for topological superconductivity based on an antiferromagnetically ordered chain of magnetic atoms on the surface of a conventional superconductor. In a weak Zeeman field, a supercurrent in the substrate generates a staggered spin current, which converts the preexisting topologically unprotected Shiba states into Majorana fermions (MFs). The two experimental knobs can be finely tuned providing a platform with enhanced functionality for applications. Remarkably, the electronic spin polarization of the arising edge MF wavefunctions depends solely on the parity of the number of magnetic moments, which can serve as a distinctive signature of the MFs. We introduce the basic concepts within a minimal model and make contact with experiments by a microscopic analysis based on the Shiba states.

Figure 1

Antiferromagnetic chain on top of a superconductor. The simultaneous presence of a weak in-plane Zeeman field $B$ ($yz$ plane) and a supercurrent flow $J$ ($z$ direction), convert the Shiba states into a single spin-filtered MF per edge. Inset: Mapping to Kitaev's model with unpaired MFs ${\gamma }_{nA,B}$.

Figure 2

Results based on the lattice version of the minimal model, Eq. (3): (a) Ground-state (g) and first-excited-state (e) energies, as a function of $J$ for ${\mu }_{B}B/\Delta =0.08$, $M/\Delta =0.99$, and $t/\Delta =0.1$. (b) Ground-state energy in color scale depending on $J$ and $B$. The red line, $\tilde{M}+\left|\Lambda \right|=\Delta$, corresponds to the analytically derived critical value for entering the TSC phase. The value ${\mu }_{B}B/\Delta =0.08$ used in panel (a) is indicated by the black dashed line ($N=160$ lattice sites).

Figure 3

Results based on the lattice version of the minimal model, Eq. (3): (a) Majorana wavefunctions for an odd ($N=60$) or even ($N=61$) number of sites. Parameters are the same as in Fig. 2 with $Ja/\pi =0.4$. Depending on the parity of $N$ the right-edge Majorana wavefunction is ${\gamma }_{\mathrm{even},B}$ ($N=60$) or ${\gamma }_{\mathrm{odd},B}$ ($N=61$). (b) Corresponding electronic spin texture.

Figure 4

Results based on the lattice version of the microscopic model, Eq. (15): (a) Energies of the ground state (g, red) and excited state (e, black). The corresponding topological invariant $\mathcal{M}$ is shown by the blue line. (b) Majorana wavefunctions in the topologically nontrivial regime.