Laboratoire de Physique Théorique

de la Matière Condensée

Pascal Simon (LPS Orsay)

Majorana zero modes around skyrmionic  textures

Recent scanning tunneling spectroscopy measurements on a superconducting monolayer of lead(Pb) with nanoscale cobalt islands, have revealed puzzling quasiparticle in-gap states [1] which demand a better understanding of two-dimensional superconductivity in presence of spin-orbit coupling and magnetism.  Thus motivated, we theoretically study a model of two-dimensional s-wave superconductor with a fixed configuration of exchange field and spin-orbit coupling terms allowed by symmetry. Using analytics and exact diagonalization of tight-binding models, we find that a vortex-like defect in the Rashba spin-orbit coupling binds a single Majorana zero-energy (mid-gap) state. In contrast to the case of a superconducting vortex [2], our spin-orbit defect does not create a tower of in-gap excitation states and our findings match the puzzling features observed in the experiment.  Additionally, these properties indicate that the system realizes a pair of well-protected Majorana zero mode (MZM) localized at the core and the rim of the defect [3]. We also discuss how the quasiparticle states of the defect relate to the states of superconductors on top of magnetic textures, such as skyrmions. Magnetic skyrmions are nanoscale particle-like spin configurations that are efficiently created and manipulated. They hold great promises for next-generation spintronics applications. I will focus on the theoretical analysis of magnetic skyrmions proximitized by conventional superconductors. I will show that a topological superconducting phase can emerge in these systems and uncover a whole almost flat band of these modes on the edge of the magnetic texture, in contrast to a previously reported MZM in the core of the skyrmion [4]. I will discuss in details the origin of these MZMs by relating this problem to the the extensively-studied Rashba nanowire model. We have found that these modes are remarkably stable to electronic and geometric perturbations which we investigate by a combination of analytical arguments and numerical tight-binding calculations. Additionally, this analysis reveals that the number of MZMs on the edge scales linearly with its perimeter [5].

[1] G.C. Ménard et al., Nature Comm. 8, 2040 (2017).

[2] C. Caroli, P.G. de Gennes, and J. Matricon, Physics Letters 9, 307(1964).

[3]  G. C. Ménard, et al., arXiv:1810.09541, Nature Comm. 10, 2587 (2019).

[4] G. Yang, P. Stano, J. Klinovaja & D. Loss, PRB 93, 224505 (2016).

[5] M. Garnier, A. Mesaros, P. Simon, arXiv:1909.1267, Comm. in Physics 2, 1 (2019).