Effects of Disorder in Planar Topological Josephson Junctions

Topological properties of planar Josephson junctions, which recently emerged as promising systems for topological superconductivity [1], depend sensitively on disorder and impurities in the materials. While planar Josephson junctions may be a viable platform to demonstrate fusion and non-Abelian statistics of Majorana bound states [2], the role of disorder in these proposals is unclear. We analytically and numerically investigate the effect of disorder in these systems and give limits of the amount of disorder on experimental setups in order to achieve nontrivial topological phases [3]. We demonstrate reentrant behavior of topological properties on planar Josephson junctions and conclude that an intermediate disorder may be beneficial to establishing topological phases [4-6].

[1] J. Shabani et al., Phys. Rev. B 93, 155402 (2016).

[2] T. Zhou, M.C. Dartiailh, K. Sardashti, J.E. Han, A. Matos-Abiague, J. Shabani, and I. Žutic, Nat Commun 13, 1 (2022).

[3] M.C. Dartiailh, W. Mayer, J. Yuan, K. S. Wickramasinghe, A. Matos-Abiague, I. Žutic, and J. Shabani, Phys. Rev. Lett. 126, 036802 (2021).

[4] B. Pekerten, A. Teker, Ö. Bozat, M. Wimmer, and I. Adagideli, Physical Review B 95, (2017).

[5] B. Pekerten, A.M. Bozkurt, and I. Adagideli, Phys. Rev. B 100, 235455 (2019).

[6] A. Haim and A. Stern, Phys. Rev. Lett. 122, 126801 (2019).