Yasumasa Tsutsumi, Kazushige Machida
We propose a method utilizing edge current to observe Majorana fermions in the surface Andreev bound state for the superfluid $^3$He A- and B-phases. The proposal is based on self-consistent analytic solutions of quasi-classical Green's function with an edge. Local density of states and edge mass current in the A-phase or edge spin current in the B-phase can be obtained from these solutions. The edge current carried by the Majorana fermions is partially cancelled by the quasiparticles (QPs) in the continuum state outside the superfluid gap. The QPs contributing to the edge current in the continuum state are distributed in energy even away from the superfluid gap. The influence of the Majorana fermions emerges into the depletion of the edge current by temperature within a low temperature range. The observation of the reduction of the mass current as $T^2$-power in the A-phase or that of the spin current as $T^3$-power in the B-phase establishes the existence of the Majorana fermions. We also point out another possibility to observe the Majorana fermions by controlling surface roughness.
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http://arxiv.org/abs/1203.2722
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