Majorana quasiparticles in condensed matter (1711.00011v2)

Abstract: In the space of less than one decade, the search for Majorana quasiparticles in condensed matter has become one of the hottest topics in physics. The aim of this review is to provide a brief perspective of where we are with strong focus on artificial implementations of one-dimensional topological superconductivity. After a self-contained introduction and some technical parts, an overview of the current experimental status is given and some of the most successful experiments of the last few years are discussed in detail. These include the novel generation of ballistic InSb nanowire devices, epitaxial Al-InAs nanowires and Majorana boxes, high frequency experiments with proximitized quantum spin Hall insulators realised in HgTe quantum wells and recent experiments on ferromagnetic atomic chains on top of superconducting surfaces.

• The paper presents a comprehensive review of theoretical models and experimental setups aimed at detecting Majorana quasiparticles in condensed matter systems.
• It details how topological superconductivity and engineered platforms such as semiconducting nanowires facilitate the emergence of robust Majorana zero modes.
• The review outlines future research directions to overcome challenges like disorder and finite-size effects, advancing prospects for fault-tolerant quantum computing.

Majorana Quasiparticles in Condensed Matter

The paper "Majorana quasiparticles in condensed matter" by Ramón Aguado offers an extensive overview of the quest to realize Majorana quasiparticles within condensed matter systems. It meticulously discusses the theoretical underpinnings, experimental realizations, and future directions in identifying and leveraging these exotic quasiparticles for technological applications.

Key Concepts and Theoretical Foundations

The paper roots its exploration in the historical and theoretical context, introducing the Majorana equation as a real wave function solution to the Dirac equation that implies particles which are their own antiparticles. This property sets the foundation for Majorana fermions, particularly in high energy physics. However, their realization within condensed matter systems brings about novel manifestations known as Majorana zero modes (MZMs).

A significant fraction of the work pivots on the notion of topological superconductivity. This distinct phase of matter supports quasiparticle excitations that can be described by the Bogoliubov-de Gennes (BdG) framework, intrinsically linked to the Majorana fermions through particle-hole symmetry. Topological superconductors host boundary-bound MZMs, which are robust against local perturbations, making their detection and potential utilization in fault-tolerant quantum computing a compelling pursuit.

Experimental Platforms and Observations

The review encapsulates several pioneering models and experiments aimed at realizing MZMs. It contrasts intrinsic $p$-wave superconductors, which are rare, against engineered systems leveraging proximitized $s$-wave superconductors, spin-orbit coupling, and broken time-reversal symmetry. Semiconducting nanowires with strong spin-orbit coupling and topological insulator surfaces are particularly emphasized due to their experimental accessibility and potential to host MZMs at relatively manageable conditions.

Recent experiments have reported zero-bias conductance peaks in transport measurements, indicative of MZMs. Noteworthy implementations include InSb and InAs nanowires, subjected to superconducting proximity effects and external magnetic fields, to induce the topological phase transition necessary for Majorana excitation. These systems demonstrate the characteristic zero-bias anomaly in conductance, albeit with nuances due to impurities and quantum confinement.

Theoretical Implications and Future Prospects

From a theoretical perspective, the paper highlights the implications of non-Abelian statistics, showcased in MZMs, and how these can underpin topological quantum computation. The elegance of Majorana braiding lies in their topological protection against decoherence, a nontrivial attribute owed to their quantum statistical properties.

Looking ahead, the review speculates on the integration of Majorana-based qubits within scalable quantum computing architectures, contingent on overcoming present challenges such as disorder, finite-size effects, and measurement precision. Further explorations into high-frequency dynamics, interferometric techniques for braiding, and improved heterostructures are suggested to bolster the robustness of Majorana detection and manipulation.

Conclusion

This comprehensive take on Majorana quasiparticles in condensed matter emphasizes both the remarkable progress and significant hurdles faced in this vibrant field. While the practical realization of topological quantum computers remains distant, the synthesis of theory and experiment has provided a fertile ground for uncovering new quantum phenomena and technologies. The review ultimately serves as a crucial reference for ongoing and future research aimed at exploiting these quasiparticles' potential to revolutionize quantum information science.