Probing Neutral Majorana Fermion Edge Modes with Charge Transport

We propose two experiments to probe the Majorana fermion edge states that occur at a junction between a superconductor and a magnet deposited on the surface of a topological insulator. Combining two Majorana fermions into a single Dirac fermion on a magnetic domain wall allows the neutral Majorana fermions to be probed with charge transport. We will discuss a novel interferometer for Majorana fermions, which probes their $Z_2$ phase. This setup also allows the transmission of neutral Majorana fermions through a point contact to be measured. We introduce a point contact formed by a superconducting junction and show that its transmission can be controlled by the phase difference across the junction. We discuss the feasibility of these experiments using the recently discovered topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$.

Figure 1

An interferometer for Majorana fermions. Magnetic (M) and superconducting (SC) materials are deposited on a topological insulator. Chiral Majorana fermion edge states (denoted by a single arrow) circle the outer boundary of the superconductor, and chiral Dirac fermion edge states (denoted by the double arrow) are confined to the magnetic domain wall connected to a source (S) and drain (D). A return path between the drain and source is shown with the dashed line. When a voltage is applied to the source electrons are split into two Majorana fermions, allowing their $Z_2$ interference phase $\pm 1$ to be probed by measuring the current in the drain.

Figure 2

(a) A point contact for neutral Majorana fermions characterized by reflection and transmission amplitudes $t$ and $r$ formed by a junction between two superconductors. Each superconductor is connected to a source and drain by chiral fermions at a magnetic domain wall, allowing $t$ to be measured with charge transport. (b) Zero energy transmission of the point contact as a function of phase $\varphi$ for different coupling strengths. The insets indicate the limits of a weakly coupled point contact (right) and a long line junction (left).