Electrically detected interferometry of Majorana fermions in a topological insulator (0903.2196v1)

Abstract: We show how a chiral Dirac fermion (a massless electron or hole) can be converted into a pair of neutral chiral Majorana fermions (a particle equal to its own antiparticle). These two types of fermions exist on the metallic surface of a topological insulator, respectively, at a magnetic domain wall and at a magnet-superconductor interface. Interferometry of Majorana fermions is a key operation in topological quantum computation, but the detection is problematic since these particles have no charge. The Dirac-Majorana converter enables electrical detection of the interferometric signal.

• The paper introduces a method using a Dirac-Majorana converter on topological insulators to electrically detect Majorana fermions through interferometry.
• It demonstrates that the interferometer produces zero conductance for even vortex parity and 2e²/h conductance for odd parity, confirming charge parity effects.
• This approach paves a viable route for integrating Majorana-based devices into fault-tolerant quantum computing architectures.

Electrically Detected Interferometry of Majorana Fermions in Topological Insulators

The paper "Electrically Detected Interferometry of Majorana Fermions in a Topological Insulator" by Akhmerov, Nilsson, and Beenakker presents a comprehensive analysis of how Majorana fermions on the surface of a topological insulator can be electrically detected. The authors explore the intricate process of converting a chiral Dirac fermion into a pair of neutral chiral Majorana fermions, offering a pathway to overcome the challenges Majorana fermions' charge neutrality presents to electrical detection.

Background and Motivation

Majorana fermions have garnered significant interest due to their potential applications in fault-tolerant quantum computation. These particles, which are their own antiparticles, harbor unique properties that are promising for quantum information storage and manipulation, notably in the form of topological qubits. The $5/2$ fractional quantum Hall effect (FQHE) has contextualized the existence and utility of such excitations, but there remain substantial hurdles in effective electrical manipulation and readout due to the absence of charge.

Experimental and Theoretical Framework

The authors propose the use of a Dirac-Majorana converter within a topological insulator—a system readily accessible in materials such as ${\rm Bi}_{2}{\rm Se}_{3}$. Specifically, they detail a device architecture involving a combination of magnetic domain walls and superconducting interfaces to accomplish this conversion. The integration is meticulously designed, ensuring the coherent conversion of a Dirac fermion into two Majorana modes via interaction with a magnet-superconductor junction.

The process leverages the unique electronic properties of the topological insulator surface, where magnetization and superconducting order parameters introduce chiral modes. The technological novelty here lies in the configuration of the converter, where an electron splits into two Majorana modes at a magnet-superconductor interface and recombines back into a charged particle. This setup culminates in a Mach-Zehnder interferometer setup, which facilitates this conversion and potential measurements of the parity of enclosed vortices.

Results and Implications

The paper presents a detailed theoretical analysis leading to a significant result—the electrical conductance is sensitive to the parity of the total number of Majorana fermions enclosed in the interferometer loop. Specifically, an even number of enclosed vortices result in zero conductance, whereas an odd number yields a conductance of $2e^{2}/h$. These results are derived within the context of unitarity and electron-hole symmetries, resulting in a robust mechanism where charge measurements yield insights into the Majorana configurations.

This methodology not only addresses the immediate challenge of detecting such exotic modes but also proposes a viable route for their application in quantum computing circuits. The practical implementation of this interferometry concept has implications for the further miniaturization and integration of quantum computational components.

Future Directions

The prospects for future research following this work are multifaceted. Experimentally, the realization of such converters and their integration into operable circuits is a logical first step. Moreover, the exploration of different material systems that can host such states, alongside further theoretical expansion into error rates and decoherence in these systems, would enrich the understanding and application of Majorana states in quantum computing.

In conclusion, this paper contributes substantively to the field by introducing a feasible method for electrically detecting Majorana fermions. It opens up new avenues for the application of topological states in quantum computing, drawing a closer linkage between theoretical predictions and experimental realizability.