Electrically Detected Interferometry of Majorana Fermions in a Topological Insulator

Majorana fermions are zero-energy quasiparticles that may exist in superconducting vortices and interfaces, but their detection is problematic since they have no charge. This is an obstacle to the realization of topological quantum computation, which relies on Majorana fermions to store qubits in a way which is insensitive to decoherence. We show how a pair of neutral Majorana fermions can be converted reversibly into a charged Dirac fermion. These two types of fermions are predicted to exist on the metallic surface of a topological insulator (such as ${\mathrm{Bi}}_2{\mathrm{Se}}_3$). Our Dirac-Majorana fermion converter enables electrical detection of a qubit by an interferometric measurement.

Figure 1

Three-dimensional topological insulator in proximity to ferromagnets with opposite polarization ($M_{\uparrow }$ and $M_{\downarrow }$) and to a superconductor ($S$). The top panel shows a single chiral Majorana mode along the edge between superconductor and ferromagnet. This mode is charge neutral, so it cannot be detected electrically. The Mach-Zehnder interferometer in the bottom panel converts a charged current along the domain wall into a neutral current along the superconductor (and vice versa). This allows for electrical detection of the parity of the number of enclosed vortices, as explained in the text.

Figure 2

Fabry-Pérot interferometer, allowing to measure the state of a qubit encoded in a pair of vortices. Black lines represent electron or hole modes at domain walls, gray lines represent Majorana modes at magnet-superconductor interface.