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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.
A chiral $p_x+ip_y$ superconductor on a square lattice with nearest and next-nearest hopping and pairing terms is considered. Gap closures, as various parameters of the system are varied, are found analytically and used to identify the topological ph
The total angular momentum associated with the edge mass current flowing at the boundary in the superfluid $^3$He A-phase confined in a disk is proved to be $L=Nhbar/2$, consisting of $L^{rm MJ}=Nhbar$ from the Majorana quasi-particles (QPs) and $L^{
We propose a method utilizing edge current to observe Majorana fermions in the surface Andreev bound state for the superfluid $^3$He A- and B-phases. The proposal is based on self-consistent analytic solutions of quasi-classical Greens function with
Motivated by a recent experiment on the superfluid 3He A-phase with a chiral p-wave pairing confined in a thin slab, we propose designing a concrete experimental setup for observing the Majorana edge modes that appear around the circumference edge re
We establish a criterion for characterizing superfluidity in interacting, particle-number conserving systems of fermions as topologically trivial or non-trivial. Because our criterion is based on the concept of many-body fermionic parity switches, it