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Motivated by experiments on the superfluid 3He confined in a thin slab, wedesign a concrete experimental setup for observing the Majorana surface states.We solve the quasi-classical Eilenberger equation, which is quantitativelyreliable, to evaluate several quantities, such as local density of states(LDOS), mass current for the A-phase, and spin current for the B-phase. Inconnection with realistic slab samples, we consider the upper and lowersurfaces and the side edges including the corners with several thicknesses.Consequently the influence on the Majorana zero modes from the spatialvariation of l-vector for the A-phase in thick slabs and the energy splittingof the zero-energy quasi-particles for the B-phase confined in thin slabs aredemonstrated. The corner of slabs in the B-phase is accompanied by the uniquezero-energy LDOS of corner modes. On the basis of the quantitative calculation,we propose several feasible and verifiable experiments to check the existenceof the Majorana surface states, such as the measurement of specific heat, edgecurrent, and anisotropic spin susceptibility.

Majorana surface states of superfluid 3He A- and B-phases in a slab