Directly Detecting the Edge Current in a $p_x + ip_y$ Topological Superfluid

TL;DR

This paper proposes a gyroscopic measurement technique to directly detect edge currents in a $p_x + ip_y$ superfluid, providing a new way to identify topological superconductivity and observe phase transitions.

Contribution

It introduces a microelectromechanical system gyroscope capable of measuring edge currents in topological superfluids, enabling direct detection and study of topological phase transitions.

Findings

Proposed a gyroscopic method for edge current detection.

Demonstrated potential to observe topological phase transitions.

Enhanced sensitivity for measuring superfluid edge phenomena.

Abstract

Topological superconductors are one of the most actively studied materials these days. They are a promising candidate for hosting Majorana fermions either on their boundaries or in vortex cores. Detecting 1D edge current around the periphery of a 2D $p_x + ip_y$ superconductor would be a hallmark signature of topological superconductivity, but Majorana fermions are not amenable to electronic current measurements due to their charge neutral nature. Thermal conductivity measurements, such as thermal Hall effect, are alternatively proposed, but material synthesis must come first. Superfluid $^3$He-$A$, on the other hand, is a known $p_x + ip_y$ superfluid whose edge current can be measured with a gyroscopic technique. Here, we propose a microelectromechanical system based gyroscope that will not only have enough signal sensitivity to measure the edge current but also be used to observe dimensionality induced phase transitions between different topological superfluids.