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

Motivated by experiments on the superfluid He-3 confined in a thin slab, we design a concrete experimental setup for observing the Majorana surface states. We solve the quasiclassical Eilenberger equation, which is quantitatively reliable, to evaluate several quantities, such as local density of states (LDOS), mass current for the A phase, and spin current for the B phase. In connection with realistic slab samples, we consider the upper and lower surfaces and the side edges including the corners with several thicknesses. Consequently, the influence on the Majorana zero modes from the spatial variation of the l vector for the A phase in thick slabs and the energy splitting of the zero-energy quasiparticles for the B phase confined in thin slabs are demonstrated. The corner of slabs in the B phase is accompanied by the unique zero-energy LDOS of corner modes. On the basis of the quantitative calculation, we propose several feasible and verifiable experiments to check the existence of the Majorana surface states, such as the measurement of specific heat, edge current, and anisotropic spin susceptibility.