Unpaired Majorana fermions in quantum wires

TL;DR

The paper shows that unpaired Majorana fermions can arise as boundary states in a one-dimensional superconducting wire when the bulk spectrum is gapped and the system's parity is nontrivial. It analyzes a toy Kitaev-like chain to illustrate end Majorana modes and ground-state degeneracy, then derives a general Majorana number invariant that predicts when end modes occur in 1D systems. It ends with speculative pathways for physical realization, including spin-selective gaps and Josephson-junction geometries that could reveal a 4pi periodic Josephson effect and phase-slip–driven end-state dynamics, highlighting potential routes to robust quantum memory devices.

Abstract

Certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length $L$ possesses two ground states with an energy difference proportional to $\exp(-L/l_0)$ and different fermionic parities. Such systems can be used as qubits since they are intrinsically immune to decoherence. The property of a system to have boundary Majorana fermions is expressed as a condition on the bulk electron spectrum. The condition is satisfied in the presence of an arbitrary small energy gap induced by proximity of a 3-dimensional p-wave superconductor, provided that the normal spectrum has an odd number of Fermi points in each half of the Brillouin zone (each spin component counts separately).

Figures (5)

• Figure 1: A piece of "quantum wire" on the surface of 3-dimensional superconductor.
• Figure 2: Two types of pairing.
• Figure 3: Reconnecting closed chains.
• Figure 4: An electron spectrum in the presence of magnetic field and CDW.
• Figure 5: A Josephson junction made of quantum wire.