  We investigate hybrid structures based on a bilayer quantum spin Hall system
in proximity to an s-wave superconductor as a platform to mimic time-reversal
symmetric topological superconductors. In this bilayer setup, the induced
pairing can be of intra- or inter-layer type, and domain walls of those
different types of pairing potentials host Kramers partners (time-reversal
conjugate pairs) of Majorana bound states. Interestingly, we discover that such
topological interfaces providing Majorana bound states can also be achieved in
an otherwise homogeneous system by a spatially dependent inter-layer gate
voltage. This gate voltage causes the relative electron densities of the two
layers to vary accordingly which suppresses the inter-layer pairing in regions
with strong gate voltage. We identify particular transport signatures
(zero-bias anomalies) in a five-terminal setup that are uniquely related to the
presence of Kramers pairs of Majorana bound states.
