Abstract
We theoretically investigate the crystalline anisotropy of topological phase transitions in phase-controlled planar Josephson junctions (JJs) subject to spin-orbit coupling and in-plane magnetic fields. It is shown how topological superconductivity (TS) is affected by the interplay between the magnetic field and the orientation of the junction with respect to its crystallographic axes. This interplay can be used to electrically tune between different symmetry classes in a controlled fashion and thereby optimize the stability and localization of Majorana bound states in planar Josephson junctions. Our findings can be used as a guide for achieving the most favorable conditions when engineering TS in planar JJs and can be particularly relevant for setups containing non-collinear junctions which have been proposed for performing braiding operations on multiple Majorana pairs.
Highlights
Majorana bound states (MBSs) are localized zero-energy quasiparticle excitations at the boundaries of topological superconductors [1,2,3,4,5]. These states are of tremendous interest for fundamental research, and because their non-Abelian statistics makes them ideal building blocks for fault-tolerant quantum computation [6,7,8]
Among the various proposals for 2D setups hosting MBSs [14,32,33,34,35,36,37,38,39], those based on phase-controlled planar Josephson junctions (JJs) [Fig. 1(a)] appear auspicious [14,37,38]
We theoretically investigate crystalline anisotropic topological superconductivity (TS) (CATS) in a planar JJ, i.e., how TS is affected by the orientation of the junction with respect to a fixed crystallographic axis
Summary
Majorana bound states (MBSs) are localized zero-energy quasiparticle excitations at the boundaries of topological superconductors [1,2,3,4,5]. Magnetoanisotropic effects due to the coexistence of Rashba and Dresselhaus SOC in planar JJs [50,63] and their relevance for the realization of TS have recently been theoretically investigated [50]. Understanding the properties of CATS is crucial for the optimal experimental design of planar JJs. in dependence of the crystallographic orientation, a top gate tuning the Rashba SOC strength can be used for controlling TS [40,41]
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