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The concept of the Majorana fermion has been postulated more than eightyyears ago; however, this elusive particle has never been observed in nature.The non-local character of the Majorana fermion can be useful for topologicalquantum computation. Recently, it has been shown that the 3He-B phase is atime-reversal invariant topological superfluid, with a single component ofgapless Majorana fermion state localized on the surface. Such a Majoranasurface state contains half the degrees of freedom of the single Dirac surfacestate recently observed in topological insulators. We show here that theMajorana surface state can be detected through an electron spin relaxationexperiment. The Majorana nature of the surface state can be revealed though thestriking angular dependence of the relaxation time on the magnetic fielddirection, $1/T_1 \propto sin^2 \theta$ where $\theta$ is the angle between themagnetic field and the surface normal. The temperature dependence of the spinrelaxation rate can reveal the gapless linear dispersion of the Majoranasurface state. We propose a spin relaxation experiment setup where we inject anelectron inside a nano-sized bubble below the helium liquid surface.

Detecting the Majorana fermion surface state of $^3$He-B through spin relaxation