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Register a new userDeterministic creation and braiding of chiral edge vortices
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Majorana zero-modes in a superconductor are midgap states localized in the core of a vortex or bound to the end of a nanowire. They are anyons with non-Abelian braiding statistics, but when they are immobile one cannot demonstrate this by exchanging them in real space and indirect methods are needed. As a real-space alternative, we propose to use the chiral motion along the boundary of the superconductor to braid a mobile vortex in the edge channel with an immobile vortex in the bulk. The measurement scheme is fully electrical and deterministic: edge vortices ($pi$-phase domain walls) are created on demand by a voltage pulse at a Josephson junction and the braiding with a Majorana zero-mode in the bulk is detected by the charge produced upon their fusion at a second Josephson junction.
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Chiral $p$-wave superconductor is the primary example of topological systems hosting chiral Majorana edge states. Although candidate materials exist, the conclusive signature of chiral Majorana edge states has not yet been observed in experiments. Here we propose a smoking-gun experiment to detect the chiral Majorana edge states on the basis of theoretical results for the nonlocal conductance in a device consisting of a chiral $p$-wave superconductor and two ferromagnetic leads. The chiral nature of Majorana edge states causes an anomalously long-range and chirality-sensitive nonlocal transport in these junctions. These two drastic features enable us to identify the moving direction of chiral Majorana edge states in the single experimental setup.
Abrikosov vortices in Fe-based superconductors are a promising platform for hosting Majorana zero modes. Their adiabatic exchange is a key ingredient for Majorana-based quantum computing. However, the adiabatic braiding process can not be realized in state-of-the-art experiments. We propose to replace the infinitely slow, long-path braiding by only slightly moving vortices in a special geometry without actually physically exchanging the Majoranas, like a Majorana carousel. Although the resulting finite-time gate is not topologically protected, it is robust against variations in material specific parameters and in the braiding-speed. We prove this analytically. Our results carry over to Y-junctions of Majorana wires.
Using the tight binding model and the non-equilibrium Green function method, we study Andreev reflection in graphene-superconductor junction, where graphene has two nonequal Dirac Cones split in energy and therefore time reversal symmetry is broken. Due to the anti-chiral edge states of the current graphene model, an incident electron travelling along the edges makes distinct contribution to Andreev reflections. In a two-terminal device, because Andreev retro-reflection is not allowed for just the anti-chiral edges, in this case the mutual scattering between edge and bulk states is necessary, which leads that the coefficient of Andreev retro-reflection is always symmetrical about the incident energy. In a four-terminal junction, however, the edges are parallel to the interface of superconductor and graphene, so at the interface an incident electron travelling along the edges can be retro-reflected as a hole into bulk modes, or specularly reflected as a hole into anti-chiral edge states again. It is noted that, the coefficient of specular Andreev reflection keeps symmetric as to the incident energy of electron which is consistent with the reported results before, however the coefficient of Andreev retro-reflection shows an unexpected asymmetrical behavior due to the presence of anti-chiral edge states. Our results present some new ideas to study the anti-chiral edge modes and Andreev reflection for a graphene model with the broken time reversal symmetry.
After the recognition of the possibility to implement Majorana fermions using the building blocks of solid-state matters, the detection of this peculiar particle has been an intense focus of research. Here we experimentally demonstrate a collection of Majorana fermions living in a one-dimensional transport channel at the boundary of a superconducting quantum anomalous Hall insulator thin film. A series of topological phase changes are controlled by the reversal of the magnetization, where a half-integer quantized conductance plateau (0.5e2/h) is observed as a clear signature of the Majorana phase. This transport signature can be well repeated during many magnetic reversal sweeps, and can be tracked at different temperatures, providing a promising evidence of the chiral Majorana edge modes in the system.
We consider the one-dimensional (1D) topological superconductor that may form in a planar superconductor-metal-superconductor Josephson junction in which the metal is is subjected to spin orbit coupling and to an in-plane magnetic field. This 1D topological superconductor has been the subject of recent theoretical and experimental attention. We examine the effect of perpendicular magnetic field and a supercurrent driven across the junction on the position and structure of the Majorana zero modes that are associated with the topological superconductor. In particular, we show that under certain conditions the Josephson vortices fractionalize to half-vortices, each carrying half of the superconducting flux quantum and a single Majorana zero mode. Furthemore, we show that the system allows for a current-controlled braiding of Majorana zero modes.
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