Majorana fermions, exotic quasiparticles that are their own antiparticles, have emerged as a promising platform for topological quantum computing due to their non-Abelian braiding statistics. In 2D topological insulators and hybrid semiconductor-superconductor systems, these zero-energy modes can be engineered and manipulated, offering a pathway toward fault-tolerant quantum information processing. This article examines their formation, braiding properties, and experimental detection in semiconductor-based low-dimensional systems.

Theoretical foundations of Majorana fermions in 2D systems stem from the interplay between spin-orbit coupling, superconductivity, and magnetic fields. In materials like Bi2Se3 monolayers, the helical edge states—where spin and momentum are locked—provide a natural host for Majorana modes when proximity-coupled to an s-wave superconductor. The superconducting pairing potential induces a gap in the edge states, except at domain walls or vortices where zero-energy Majorana bound states localize. Hybrid systems, such as semiconductor nanowires with strong spin-orbit interaction (e.g., InSb or InAs) coupled to superconductors (e.g., Nb or Al), similarly satisfy the conditions for Majorana formation under applied magnetic fields. The topological phase transition in these systems is characterized by the closing and reopening of the superconducting gap, with Majorana modes appearing at the ends of 1D nanowires or at defects in 2D structures.

Braiding statistics of Majorana fermions are central to their application in quantum computing. Unlike fermions or bosons, Majoranas obey non-Abelian statistics, meaning their wavefunctions transform in a non-commutative manner when particles are exchanged. In a 2D system, adiabatically moving Majoranas around one another generates unitary operations on the degenerate ground state manifold, forming the basis for topological quantum gates. Theoretical proposals for braiding involve networks of nanowires or patterned 2D electron gases with superconducting islands. For instance, a T-junction geometry of semiconductor nanowires allows Majoranas to be swapped by tuning gate voltages to control their positions. The resulting braiding operations are inherently robust against local perturbations, as they depend only on the topological properties of the path taken.

Experimental detection of Majorana fermions relies on several key signatures. The most direct evidence is a zero-bias conductance peak (ZBCP) in tunneling spectroscopy, measured using superconducting leads coupled to the suspected Majorana host. The peak arises from resonant Andreev reflection at the Majorana energy level. In hybrid nanowires, ZBCPs with heights close to 2e²/h have been reported under specific conditions, though alternative explanations like disorder or Andreev bound states require careful exclusion. Additional confirmation comes from observing the predicted quantized conductance plateau or its response to magnetic field orientation. In 2D topological insulators, scanning tunneling microscopy (STM) can spatially resolve Majorana modes localized at vortex cores in the superconducting proximity layer. Coulomb blockade spectroscopy in hybrid islands provides another method, where the 1e-periodic conductance oscillations (distinct from the 2e-periodicity of conventional superconductors) signal the presence of Majorana zero modes.

Challenges remain in unambiguously proving the existence of Majorana fermions and achieving scalable braiding. False positives from trivial bound states necessitate stringent experimental checks, such as varying system parameters to test robustness or probing the predicted topological invariance. Fabrication imperfections in 2D materials—like inhomogeneous proximity coupling or edge disorder—can obscure Majorana signatures. For braiding, maintaining phase coherence during operations and minimizing quasiparticle poisoning are critical hurdles. Recent advances in epitaxial superconductor-semiconductor interfaces and ultra-clean 2D material growth have improved the reproducibility of Majorana-like signals.

The potential impact of Majorana-based quantum computing lies in its error-resistant architecture. Topological qubits encoded in Majorana pairs are protected from decoherence by their non-local storage of information. While conventional qubits require extensive error correction, Majorana systems could achieve fault tolerance with fewer physical resources. Practical implementations will require advances in material quality, nanoscale control, and integration with existing quantum hardware. Ongoing research focuses on optimizing hybrid systems, developing scalable braiding protocols, and refining detection techniques to move from fundamental physics to functional devices.

In summary, 2D topological insulators and hybrid semiconductor-superconductor structures offer a viable platform for realizing and manipulating Majorana fermions. Their unique braiding properties hold promise for topological quantum computing, though experimental verification and scalable control demand continued innovation in materials science and nanofabrication. The pursuit of Majorana-based technologies represents a convergence of fundamental physics and engineering, with the potential to revolutionize quantum information processing.