Abstract

We study planar Josephson junctions formed on the surface of a three-dimensional topological insulator (Fu-Kane proposal), motivated by recent experiments[1,2] which have reported low-temperature non-zero Josephson currents in states with an integer number of flux quanta threading the junction.
In the first part of the talk, we propose an explanation for the non-zero current, attributing it to (geometric) imperfections. We show that the low-temperature contributions to the current are provided by bound states with low but non-zero energy. We furthermore propose a clear experimental probe of the bound-state spectra based on microwave spectroscopy, revealing distinctive selection rules for vortex transitions.
In the second part of the talk, we examine the experimentally relevant parameter regimes in which the frequently used effective description in terms of two counter-propagating one-dimensional Majorana modes loses its validity. As parameters like the chemical potential or the width of the junction are tuned, instances of vanishing effective velocity of these modes mark the emergence of additional "Dirac cones" at zero energy and finite momentum. Josephson vortices may then bind a number of zero modes besides the topological Majorana mode. The ensuing presence of additional low-energy Andreev states can significantly contribute to the measured quantities discussed in the first part.

[1] G. Yue et al., PRB 109, 094511 (2024)
[2] J. Park et al., arXiv:2601.14384 (2026)