  One-dimensional Majorana modes are predicated to form in Josephson junctions
based on three-dimensional topological insulators (TIs). While observations of
supercurrents in Josephson junctions made on bulk-insulating TI samples are
recently reported, the Fraunhofer patters observed in such TI-based Josephson
junctions, which sometimes present anomalous features, are still not well
understood. Here we report our study of highly gate-tunable TI-based Josephson
junctions made of one of the most bulk-insulating TI materials, BiSbTeSe2, and
Al. The Fermi level can be tuned by gating across the Dirac point, and the high
transparency of the Al/BiSbTeSe2 interface is evinced by a high characteristic
voltage and multiple Andreev reflections with peak indices reaching 12.
Anomalous Fraunhofer patterns with missing lobes were observed in the entire
range of gate voltage. We found that, by employing an advanced fitting
procedure to use the maximum entropy method in a Monte Carlo algorithm, the
anomalous Fraunhofer patterns are explained as a result of inhomogeneous
supercurrent distributions on the TI surface in the junction. Besides
establishing a highly promising fabrication technology, this work clarifies one
of the important open issues regarding TI-based Josephson junctions.
