Abstract
Josephson junctions based on three-dimensional topological insulators offer intriguing possibilities to realize unconventional $p$-wave pairing and Majorana modes. Here, we provide a detailed study of the effect of a uniform magnetization in the normal region: We show how the interplay between the spin-momentum locking of the topological insulator and an in-plane magnetization parallel to the direction of phase bias leads to an asymmetry of the Andreev spectrum with respect to transverse momenta. If sufficiently large, this asymmetry induces a transition from a regime of gapless, counterpropagating Majorana modes to a regime with unprotected modes that are unidirectional at small transverse momenta. Intriguingly, the magnetization-induced asymmetry of the Andreev spectrum also gives rise to a Josephson Hall effect, that is, the appearance of a transverse Josephson current. The amplitude and current phase relation of the Josephson Hall current are studied in detail. In particular, we show how magnetic control and gating of the normal region can enable sizable Josephson Hall currents compared to the longitudinal Josephson current. Finally, we also propose in-plane magnetic fields as an alternative to the magnetization in the normal region and discuss how the planar Josephson Hall effect could be observed in experiments.
Highlights
The helical spin structure of the surface states of threedimensional topological insulators (3D TIs) offers intriguing possibilities of tailoring the surface-state properties by various proximity effects
We have studied Josephson junctions realized on three-dimensional topological insulators which are subject to a Zeeman term in the normal topological insulator region
We have found that the interplay between the spin-momentum locking of the topological insulator surface state, superconductivity, and an in-plane Zeeman field in the normal region gives rise to a net transverse Josephson Hall current
Summary
The helical spin structure of the surface states of threedimensional topological insulators (3D TIs) offers intriguing possibilities of tailoring the surface-state properties by various proximity effects. The combination of 3D TIs with both proximity-induced superconductivity and magnetism can prove even more interesting [11,40,41,42], and could point to novel possibilities for superconducting spintronics [43,44] Motivated by this prospect [45] as well as by phenomena found in nonsuperconducting TI tunneling junctions, such as the tunneling planar Hall effect [38], we study 3D TI-based Josephson junctions with a ferromagnetic tunneling barrier [see Fig. 1(c)].
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