Superconducting proximity effect and Majorana fermions at the surface of a topological insulator (0707.1692v3)

Abstract: We study the proximity effect between an s-wave superconductor and the surface states of a strong topological insulator. The resulting two dimensional state resembles a spinless p_x+ip_y superconductor, but does not break time reversal symmetry. This state supports Majorana bound states at vortices. We show that linear junctions between superconductors mediated by the topological insulator form a non chiral 1 dimensional wire for Majorana fermions, and that circuits formed from these junctions provide a method for creating, manipulating and fusing Majorana bound states.

• The paper demonstrates that coupling s‑wave superconductors to topological insulator surfaces induces a p_x+ip_y‐like state supporting zero‑energy Majorana bound states at vortex cores.
• The paper employs rigorous Bogoliubov–de Gennes equation analyses to define the precise conditions under which Majorana modes form in superconducting junctions.
• The paper outlines experimental configurations for creating and manipulating Majorana fermions, advancing prospects for topologically protected quantum computation.

Superconducting Proximity Effect and Majorana Fermions on Topological Insulator Surfaces

The paper "Superconducting proximity effect and Majorana fermions at the surface of a topological insulator" by Liang Fu and C.L. Kane presents a detailed investigation into the interplay between $s$-wave superconductors and the surface states of strong topological insulators (TIs). This research explores the induction of superconductivity in a two-dimensional topological insulator surface state, resulting in a phase that emulates a spinless $p_x + ip_y$ superconductor without breaking time reversal symmetry. The significant outcome of this paper is the prediction that such a system can support Majorana bound states (MBSs) at vortex cores.

Major Findings

The authors provide a comprehensive theoretical framework for understanding the proximity effect within a system consisting of an $s$-wave superconductor coupled to the surface of a strong topological insulator. The emergent superconducting state shares characteristics with the $p_x + ip_y$ superconductor but uniquely retains time reversal symmetry. This state enables the localization of zero-energy Majorana bound states at vortex cores, which are quasiparticle excitations with non-Abelian statistics, offering potential avenues for topological quantum computation due to their robustness against local perturbations.

A further notable aspect of this work is the paper of linear superconducting junctions formed by two Superconductor-Topological Insulator-Superconductor (STIS) interfaces. These junctions enable the formation of one-dimensional non-chiral wires for Majorana fermions. The existence of MBSs within this framework holds promising implications for topological quantum computation. The paper also suggests that circuits constituted by these junctions allow for the creation, manipulation, and fusion of MBSs, processes critical to harnessing the computational potential of these excitations.

Strong Numerical and Theoretical Contributions

The paper provides rigorous solutions to the Bogoliubov-de Gennes (BdG) equations to confirm the existence of MBSs under different configurations. It thoroughly analyzes the boundary conditions that impact the singular nature of these states, including insights into the conditions under which Majorana modes in STIS line junctions are energetically favorable. Furthermore, the paper dissects the spectrum of the Andreev bound states for various superconducting phase differences and offers a phase diagram for tri-junctions demonstrating conditions for the emergence of MBSs.

The paper's analytical models, alongside proposed experimental configurations such as STIS and the associated tri-junctions, set the stage for potential empirical exploration into harnessing Majorana fermions. The boundary between theoretical predictions and realistic material constraints is poised for investigation, spurred by motivation to construct nontrivial quantum computing systems based on MBSs.

Implications and Future Directions

The implications of these findings extend into the further exploration of quantum systems that exhibit topological order and superconductivity. The proposed path for realizing non-Abelian excitations on the surface of topological insulators could revolutionize approaches to fault-tolerant quantum computation.

Practically, the development of materials with strong topological insulation and a robust superconducting proximity effect is paramount. The research invites the synthesis of experimental methods to observe these phenomena under realistic conditions, such as in recently discovered strong topological insulators like Bi$_{1-x}$Sb$_x$ and strained HgTe.

Toward future developments, focus should remain on refining the interfaces between superconductors and topological materials to optimize the proximity effect and the coupling necessary to observe Majorana physics. Experimentation with smaller-scale junctions and controlled manipulation of superconducting phases could yield transformative insights into scalable topological quantum computing architectures.

In conclusion, this paper contributes a critical theoretical foundation for understanding and potentially utilizing Majorana fermions in quantum information systems, offering a narrative poised to bridge a gap between abstract theoretical physics and applicable technological innovation.