Microscopic theory for a ferromagnetic nanowire/superconductor heterostructure: Transport, fluctuations, and topological superconductivity

Abstract

Motivated by the recent experiment of Wang et al. [Nature Physics 6, 389 (2010)], who observed a highly unusual transport behavior of ferromagnetic Cobalt nanowires proximity-coupled to superconducting electrodes, we study proximity effect and temperature-dependent transport in such a mesoscopic hybrid structure. It is assumed that the asymmetry in the tunneling barrier gives rise to the Rashba spin-orbit-coupling in the barrier that enables induced p-wave superconductivity in the ferromagnet to exist. We first develop a microscopic theory of Andreev scattering at the spin-orbit-coupled interface, derive a set of self-consistent boundary conditions, and find an expression for the p-wave mini-gap in terms of the microscopic parameters of the contact. Second, we study temperature-dependence of the resistance near the superconducting transition and find that it should generally feature a fluctuation-induced peak. The upturn in resistance is related to the suppression of the singleparticle density of states due to the formation of fluctuating pairs, whose tunneling is suppressed. In conclusion, we discuss this and related setups involving ferromagnetic nanowires in the context of one-dimensional topological superconductors. It is argued that to realize unpaired end Majorana modes, one does not necessarily need a half-metallic state, but a partial spin polarization may suffice. Finally, we propose yet another related class of material systems -ferromagnetic semiconductor wires coupled to ferromagnetic superconductors -where direct realization of Kitaev-Majorana model should be especially straightforward.

Spin-orbit coupling as a source of long-range triplet proximity effect in superconductor-ferromagnet hybrid structures

“…On the other hand, the lack of inversion symmetry can also occur at the interface between two different materials inducing an interfacial SO coupling. [37][38][39][40][42][43][44][45] This might be the scenario in some of the structures used in the experiments on SFS junctions. It is not straightforward to estimate the strength of the SO coupling for a given hybrid interface.…”

“…34 A finite SO coupling can result from either an intrinsic property of materials without inversion symmetry 35 or from geometrical constraints such as low dimensional structures or interfaces between different materials. [36][37][38][39][40][42][43][44][45] Specifically, Ref. 34 presented a unified view of the singlet-triplet conversion which connects the magnetic inhomogeneous mechanism with the one based on SO coupling.…”

Substrate-induced Majorana renormalization in topological nanowires

“…Experimental evidence in the form of a weak and broad zero-bias peak seems to provide some support to this hypothesis [21]. Several theoretical calculations [14,[30][31][32][33] have shown that as a matter of principle Majorana modes can emerge in ferromagnetic wires in superconductors, as had been suggested in more mesoscopic geometries [11,12,34,35]. Motivated by earlier STM works [36,37], some of the theoretical works [13,33,38,39] have modeled the system to be a chain of magnetic atoms (i.e.…”

“…We now turn to the physical realization [8-10, 29-33, 40, 47] of TS in a ferromagnetic nanowire in contact with a bulk s-wave superconductor. We note that the minimal model for the ferromagnetic wire proximity-coupled to a superconductor [30,31,34], as used in [21], is formally the same as the corresponding semiconductor nanowire TS system introduced in [8][9][10]47] with the only constraint being that the spin-splitting is arising from intrinsic exchange splitting in the ferromagnetic system whereas it is induced as a Zeeman splitting by an externally applied magnetic field in the semiconductor case. This has already been pointed out by Dumitrescu et al [31].…”

Local spin excitations in the rectangular ferromagnetic semiconductor nanowires

“…Although progress has been made in the understanding magnetic nanostructured materials studies of magnetic semiconductors nanotubes and nanowires (NWs) are still at a nascent stage [5][6][7]. Ferromagnetic semiconductors NWs can bring interesting applications to future magnetic recording media and electronic devices.…”