Robust topological superconductivity in weakly coupled nanowire-superconductor hybrid structures

We investigate the role of the coupling between a spin-orbit coupled semiconductor nanowire and a conventional $s$-wave superconductor on the emergence of the topological superconducting phase with Majorana bound states in an applied magnetic field. We show that when the coupling is strong, the topological phase transition point is very sensitive to the size of the superconductor and in order to reach the topological phase a strong magnetic field is required, which can easily be detrimental for superconductivity. Moreover, the induced energy gap separating the Majorana bound states and other quasi-particles in the topological phase is substantially suppressed compared to the gap at zero field. In contrast, in the weak coupling regime, we find that the situation is essentially the opposite, with the topological phase emerging at much lower magnetic fields and a sizable induced energy gap in the topological phase, that can also be controlled by the chemical potential of the superconductor. Furthermore, we show that the weak coupling regime does not generally allow for the formation of topologically trivial zero-energy states at the wire end points, in stark contrast to the strong coupling regime where such states are found for a wide range of parameters. Our results thus put forward the weak coupling regime as a promising route to mitigate the most unwanted problems present in nanowires for realizing topological superconductivity and Majorana bound states.Comment: 8 pages, 5 figures + 2 pages, 3 figures of Appendice

Superconductivity and magnetism in the surface states of ABC-stacked multilayer graphene

ABC-stacked multilayer graphene (ABC-MLG) exhibits topological surface flat bands with a divergent density of states, leading to many-body instabilities at charge neutrality. Here, we explore electronic ordering within a mean-field approach with full generic treatment of all spin-isotropic, two-site charge density and spin interactions up to next-nearest neighbor (NNN) sites. We find that surface superconductivity and magnetism are significantly enhanced over bulk values. We find spin-singlet $s$ wave and unconventional NNN bond spin-triplet $f$ wave to be the dominant superconducting pairing symmetries, both with a full energy gap. By establishing the existence of ferromagnetic intra-sublattice interaction, $(J_2<0)$ we conclude that the $f$-wave state is favored in ABC-MLG, in sharp contrast to bulk ABC-graphite where chiral $d$- or $p$-wave states, together with s-wave states, display stronger ordering tendencies albeit not achievable at charge neutrality. We trace this distinctive surface behavior to the strong sublattice polarization of the surface flat bands. We also find competing ferrimagnetic order, fully consistent with density functional theory (DFT) calculations. The magnetic order interpolates between sublattice ferromagnetism and antiferromagnetism, but only with the ratio of the sublattice magnetic moments ($R$) being insensitive to the DFT exchange correlation functional. We finally establish the full phase diagram by constraining the interactions to the $R$-value identified by DFT. We find $f$-wave superconductivity being favored for all weak to moderately strong couplings $J_2$ and as long as $J_2$ is a sufficiently large part of the full interaction mix. Gating ABC-MLG away from charge neutrality further enhances the $f$-wave state over the ferrimagnetic state, establishing ABC-MLG as a strong candidate for $f$-wave superconductivity.Comment: 20 pages, 11 figures + supplementary (1 page). Minor corrections implemente

Mitigating disorder-induced zero-energy states in weakly-coupled semiconductor-superconductor hybrid systems

Disorder has appeared as one of the main mechanisms to induce topologically trivial zero-energy states in superconductor-semiconductor systems, thereby challenging the detection of topological superconductivity and Majorana bound states. Here we demonstrate that, for disorder in any part of the system, the formation of disorder-induced trivial zero-energy states can be to a large extent mitigated by keeping the coupling between semiconductor and superconductor weak. Furthermore, we find that the topological phase in this weak coupling regime is robust against disorder, with a large and well-defined topological gap which is highly beneficial for topological protection. Our work shows the advantages and disadvantages of weak and strong couplings under disorder, important towards designing superconductor-semiconductor hybrid structures.Comment: 8 pages, 4 figures + 3 pages, 2 figures of Supplementary Informatio