Majorana states and longitudinal NMR absorption in $^3$He-B film

TL;DR

This paper investigates how Majorana surface states in superfluid $^3$He-B influence longitudinal NMR absorption, revealing a distinct signature when the NMR frequency exceeds the Larmor frequency.

Contribution

It introduces the theoretical prediction of NMR absorption signatures caused by Majorana surface states in $^3$He-B films, linking topological surface states to measurable magnetic resonance effects.

Findings

Surface states cause non-zero NMR absorption above Larmor frequency.

Transitions between surface state branches produce detectable signals.

Majorana states influence the magnetic response of $^3$He-B films.

Abstract

The topological superfluid $^3$He-B supports massless Dirac spectrum of surface bound states which can be described in terms of the self-conjugated Majorana field operators. We discuss here the possible signature of surface bound states in nuclear magnetic resonance absorption spectrum in a $^3$He-B film. It is shown that transitions between different branches of the surface states spectrum lead to the non-zero absorption signal in longitudinal NMR scheme when the frequency is larger than the Larmour one.