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We investigate the effects that a tilting of the magnetic field from theparallel direction has on the states of a 1D Majorana nanowire. Particularly,we focus on the conditions for the existence of Majorana zero modes, uncoveringan analytical relation (the sine rule) between the field orientation relativeto the wire, its magnitude and the superconducting parameter of the material.The study is then extended to junctions of nanowires, treated as magneticallyinhomogeneous straight nanowires composed of two homogeneous arms. It is shownthat their spectrum can be explained in terms of the spectra of two independentarms. Finally, we investigate how the localization of the Majorana mode istransferred from the magnetic interface at the corner of the junction to theend of the nanowire when increasing the arm length.

Effects of tilting the magnetic field in 1D Majorana nanowires