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

TL;DR

This paper proposes an experimental setup to observe Majorana surface states in superfluid 3He phases, using quantitative calculations of local density of states and currents to identify measurable signatures of these exotic states.

Contribution

It provides a detailed theoretical framework and specific experimental proposals for detecting Majorana surface states in superfluid 3He confined in a slab geometry.

Findings

Majorana zero modes are influenced by slab thickness and surface geometry.

Zero-energy LDOS at slab corners indicates localized Majorana modes.

Proposed experiments include specific heat, edge current, and spin susceptibility measurements.

Abstract

Motivated by experiments on the superfluid 3He confined in a thin slab, we design a concrete experimental setup for observing the Majorana surface states. We solve the quasi-classical 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 l-vector for the A-phase in thick slabs and the energy splitting of the zero-energy quasi-particles 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.