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Proximity coupled spin-orbit quantum wires have recently been shown to support midgap Majorana states at critical points.
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Strictly speaking, the system is in class D \mathrm{D} or B \mathrm{B} depending on whether a Majorana is absent or present. We stick to the designation ’ D \mathrm{D} ’ for simplicity
Cited in the paper.
N = 1 N=1 is a special case. For abruptly varying control parameters (an ’interface’), the system then supports only one level below the bulk gap, and our analysis does not apply. For smoothly varying parameters Anderson localization on length scales l ∼ τ v F l\sim\tau v_{F} may become an issue. Although the detailed analysis is beyond the scope of this paper, a band center peak should be observable also in this case
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D. Bagrets and A. Altland to be published
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The point is that each mode, a a , is described by an Hamilton operator obeying the symmetry [ \mathaccentV h a t 05 E H , σ 1 ] + = 0 [\mathaccentV{hat}05EH,\sigma_{1}]_{+}=0 . This chirality implies that all eigenstates of non-vanishing energy come in degenerate pairs. For gap functions Δ eff \Delta_{\mathrm{eff}} possessing a critical point, Δ eff ( 0 ) = 0 \Delta_{\mathrm{eff}}(0)=0 , the channel supports a non-degenerate zero energy state, i.e. the total number of states, N a N_{a} , is odd
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