Abstract
Certain one-dimensional Fermi systems have anenergy gap in the bulk spectrum while boundary states aredescribed by one Majorana operator per boundary point. Afinite system of length L possesses two ground states with anenergy difference proportional to exp(-L/l0) and differentfermionic parities. Such systems can be used as qubits sincethey are intrinsically immune to decoherence. The property of asystem to have boundary Majorana fermions is expressed as acondition on the bulk electron spectrum. The condition issatisfied in the presence of an arbitrary small energy gapinduced by proximity of a three-dimensional p-wave superconductor, provided that the normal spectrum has an oddnumber of Fermi points in each half of the Brillouin zone (eachspin component counts separately).
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