Locally gauge-invariant spin response of ${}^3$He-$B$ films with Majorana surface states

Abstract

A locally gauge-invariant theory of the spin response of a thin film of ${}^3$He-$B$ film is given that describes fluctuation effects arising from the coupled dynamics of the superconducting order parameter (the collective mode) and in-gap Majorana surface states. In contrast to a mean-field calculation of the spin response, which predicts a nonzero imaginary longitudinal spin susceptibility at frequencies inside the bulk gap due to absorption from the Majorana states, our gauge-invariant theory shows that this response is strongly suppressed above the collective mode frequency and vanishes if dipole-dipole interactions are neglected. In the presence of dipole-dipole interactions, in sufficiently thin films, and at ultra-low temperatures, the Majorana states lead to a distinctive magnetic-field- and temperature-dependent damping of the collective mode, a feature that may be observable in longitudinal NMR experiments.

arXiv commentPublished version. 8 pages, 3 figures

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Cited by in corpus (3)

• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Power-law Temperature Dependence of the Penetration Depth in a Topological Superconductor due to Surface States
• Quasiclassical theory of spin dynamics in superfluid ${}^3$He: kinetic equations in the bulk and spin response of surface Majorana states