Topological transitions in multi-band superconductors

• Published in: Annals of physics Vol. 348; pp. 1 - 14
• Main Authors: Continentino, Mucio A., Deus, Fernanda, Padilha, Igor T., Caldas, Heron
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01-09-2014; Elsevier BV
• Subjects: ANGULAR MOMENTUM; BCS THEORY; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; FERMIONS; Hybridization; Insulation; L-S COUPLING; MAGNETIC FIELDS; MAJORANA THEORY; METALS; Multi-band superconductors; Orbits; PARITY; PHASE TRANSFORMATIONS; Quantum phase transition; Spin–orbit coupling; SUPERCONDUCTORS; SYMMETRY; T INVARIANCE; Topological manifolds; Topological transitions; TOPOLOGY; Multi-band superconductors; Spin–orbit coupling; Quantum phase transition; Hybridization; Topological transitions; BCS theory
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2014.05.008

The search for Majorana fermions has been concentrated in topological insulators or superconductors. In general, the existence of these modes requires the presence of spin–orbit interactions and of an external magnetic field. The former implies in having systems with broken inversion symmetry, while the latter breaks time reversal invariance. In a recent paper, we have shown that a two-band metal with an attractive inter-band interaction has non-trivial superconducting properties, if the k-dependent hybridization is anti-symmetric in the wave-vector. This is the case, if the crystalline potential mixes states with different parities as for orbitals with angular momentum l and l+1. In this paper we take into account the effect of an external magnetic field, not considered in the previous investigation, in a two-band metal and show how it modifies the topological properties of its superconducting state. We also discuss the conditions for the appearance of Majorana fermions in this system.