Influence of Magnetic Field on Surface Andreev Bound States in Superfluid $^3$He-B Studied by Mobility of Electron Bubble

TL;DR

This study investigates how a magnetic field affects surface Andreev bound states in superfluid $^3$He-B by examining the mobility of an electron bubble, revealing the impact of Zeeman gap opening on topological surface states.

Contribution

It provides experimental and theoretical insights into how magnetic fields influence the Zeeman gap and surface states in superfluid $^3$He-B, linking topological properties to magnetic effects.

Findings

Mobility increases more steeply at 0.25 T as temperature decreases.

Mobility is slightly smaller in magnetic field at higher temperatures.

Zeeman gap opening alters the density of states and distorts the superfluid gap.

Abstract

The B phase of superfluid $^\textrm 3$He ($^\textrm 3$He-B) is topologically nontrivial and the surface Andreev bound states formed on a surface are conceived as Majorana fermions. In a magnetic field, the surface Andreev bound states acquire a Zeeman gap. How the Zeeman gap opens when a magnetic field is applied is intimately related to how the topological properties are lost. In this article, we study the mobility of an electron bubble trapped under a free surface of $^\textrm 3$He-B in a magnetic field of 0.25 T to examine the influence of the magnetic field on the surface Andreev bound states. We observe experimentally and theoretically that, with decreasing temperature, the mobility at 0.25 T increases steeper than that in zero magnetic field when the thermal energy is comparable to the Zeeman energy, while the mobility is slightly smaller than that in zero magnetic field at higher temperatures. These features are understood by the opening of the Zeeman gap, the resulting change in the density of states within the bulk superfluid gap, and the distortion of the bulk superfluid gap by the magnetic field.