Effective Potential for Emergent Majorana Fermions in Superconductor Systems

Abstract

Majorana fermions cannot be found in nature as a free fundamental particle. Nevertheless, in condensed matter systems, they can emerge as a collective excitation. In this work, using functional integration techniques, we calculated the effective potential for emergent Majorana fermions in the Kitaev chain. In this case, we have shown how the superconductor parameter behaves as a function of temperature. Furthermore, we considered surface-induced superconductivity in a Topological Insulator and calculated the effective potential for emergent Majorana fermions in this system. In the case of an s-wave superconductor, we obtained a gap equation equivalent to that one appearing in a quasi-two-dimensional Dirac electronic system, a candidate to explain high-Tc superconductivity. Finally, for the p-wave superconductor, we have obtained a critical value of the electronelectron interaction in the surface of the Topological Insulator, determining the existence or not of induced superconductivity, a remarkable result to guide experiments

arXiv comment6 pages, 3 figures, Accepted in Physics Letters A

References in corpus (16)

• Topological Insulators
• Topological insulators and superconductors
• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Comments on the Sachdev-Ye-Kitaev model
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Introduction to topological superconductivity and Majorana fermions
• Quantum Computing with Majorana Fermion Codes
• Quantum Criticality and Superconductivity in Quasi-Two-Dimensional Dirac Electronic Systems
• Majorana representation for dissipative spin systems
• Tuning of heat and charge transport by Majorana fermions
• Temperature vs. doping phase diagram of cuprate superconductors
• Antiferromagnetic phase diagram of the cuprate superconductors
• Pb induces superconductivity in Bi2Se3 analyzed by point contact spectroscopy