Topological superconductivity and Majorana fermions in hybrid structures involving cuprate high-Tcsuperconductors

Abstract

The possibility of inducing topological superconductivity with cuprate high-temperature superconductors (HTSC) is studied for various heterostructures. We first consider a ballistic planar junction between a HTSC and a metallic ferromagnet. We assume that inversion symmetry breaking at the tunnel barrier gives rise to Rashba spin-orbit coupling in the barrier and allows equal-spin triplet superconductivity to exist in the ferromagnet. Bogoliubov-de Gennes equations are obtained by explicitly modeling the barrier, and taking account of the transport anisotropy in the HTSC. By making use of the self-consistent boundary conditions and solutions for the barrier and HTSC regions, an effective equation of motion for the ferromagnet is obtained where Andreev scattering at the barrier is incorporated as a boundary condition for the ferromagnetic region. For a ferromagnet layer deposited on a (100) facet of the HTSC, triplet p-wave superconductivity is induced. For the layer deposited on a (110) facet, the induced gap does not have the p-wave orbital character, but has an even orbital symmetry and an odd dependence on energy. For the layer on the (001) facet, an exotic f -wave superconductivity is induced. We also consider the induced triplet gap in a one-dimensional half-metallic nanowire deposited on a (001) facet of a HTSC. Due to the breaking of translational symmetry in the direction perpendicular to the wire axis, the expression for the gap receives contributions from different perpendicular momentum eigenstates in the superconductor. We find that for a wire axis along the a-axis, these different contributions constructively interfere and give rise to a robust triplet p-wave gap. For a wire oriented 45• away from the a-axis the different contributions destructively interfere and the induced triplet p-wave gap vanishes. For the appropriately oriented wire, the induced p-wave gap may give rise to Majorana fermions at the ends of the half-metallic wire. In light of the recent experimental progress in the quest for realizing Majorana fermions, we also discuss inducing superconductivity in the spin-orbit coupled nanowire using a HTSC. Based on our result, topological superconductivity in a semi-conductor nanowire may be possible given that it is oriented along the a-axis of the HTSC.

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.…”

Majorana zero modes and topological quantum computation

“…The inherent energy scales of present MZM systems are on the order of 1 K≈20 GHz so there is room to do much better. In fact, to combine the two frontiers one might envision exploiting exotic superconductors with very large (~100 K) energy gap, pnictides or cuprates, 133,134 in conjuction with semiconductor wires to increase the gap protecting Majorana systems and clock rates by an order of magnitude.…”

Geometrical lattice engineering of complex oxide heterostructures: a designer approach to emergent quantum states

“…Another interesting theory proposal is the study on the interface between (100)-oriented high-temperature superconducting cuprate YBa 2 Cu 3 O 7 (YBCO) and colossal magnetoresistance manganite La x Ca 1−x MnO 3 (LCMO). [98] Compared to the extensively investigated (001) YBCO/LCMO interface [99] where the nodes of Cu d x2-y2 orbital are in the a-b plane, the (100)-oriented YBCO has nodes of the d x2-y2 orbital out of the CuO 2 plane (see Fig. 9, left panel on the bottom).…”