  Starting from the Bogolubov - de Gennes theory describing the induced p-wave
superconductivity in the Majorana wire of an arbitrary shape, we predict a
number of intriguing phenomena such as the geometry-dependent phase battery (or
a phi-Josephson junction with the spontaneous superconducting phase difference)
and generation of additional quasiparticle modes at the Fermi level with the
spatial position tuned by the external magnetic field direction. This tuning
can be used to extend the capabilities of the braiding protocols in Majorana
networks.
