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We investigate the occurrence of Majorana modes in semiconductor quantumwires in close proximity with a superconductor and when both, Rashbainteraction and magnetic field, are present. We consider long, but finite,multiband wires (namely, planar wires with dimensions $L_x\gg L_y$). Ourresults demonstrate that interband mixing coming from Rashba spin orbit termhybridizes Majorana pairs originating from different transverse modes whilesimultaneously closing the effective gap. Consequently, multiple Majorana modesdo not coexist in general. On the contrary, Majorana physics is robust providedthat only one single transverse mode contributes with a Majorana pair. Finally,we analyse the robustness of Majorana physics with respect to magnetic orbitaleffects.

Magnetic-field instability of Majorana modes in multiband quantum wires