  Topological insulators (TIs) hold great promise for realizing zero-energy
Majorana states in solid-state systems. Recently, several groups reported
experimental data suggesting that signatures of Majorana modes in topological
insulator Josephson junctions (TIJJs) have -- indeed -- been observed. To
verify this claim, one needs to study the topological properties of low-energy
Andreev-bound states (ABS) in TIs of which the Majorana modes are a special
case. It has been shown theoretically that topologically non-trivial low-energy
ABS are also present in TIJJs with doped topological insulators up to some
critical level of doping at which the system undergoes a topological phase
transition. Here, we present first experimental evidence for this topological
transition in the bulk band of a doped TI. Our theoretical calculations, and
numerical modeling link abrupt changes in the critical current of top-gated
TIJJs to moving the chemical potential in the charge-accumulation region on the
surface of the doped TI across a band-inversion point. We demonstrate that the
critical-current changes originate from a shift of the spatial location of
low-energy ABS from the surface to the boundary between topologically-trivial
and band-inverted regions after the transition. The appearance of a decay
channel for surface ABS is related to the vanishing of the band effective mass
in the bulk and thus exemplifies the topological character of surface ABS as
boundary modes. Importantly, the mechanism suggest a means of manipulating
Majorana modes in future experiments.
