Topological Phase Transitions in Multicomponent Superconductors.

Area of Science:

• Condensed Matter Physics
• Quantum Materials Science
• Topological Superconductivity

Background:

• Topological superconductors exhibit unique quantum phenomena.
• Understanding phase transitions is crucial for classifying topological phases.
• Symmetry and topology dictate the behavior of quantum materials.

Purpose of the Study:

• To investigate the phase transition between trivial and time-reversal-invariant topological superconductors.
• To analyze the role of symmetry, topology, and energetics in these transitions.
• To explore the existence and properties of topological defects and Majorana fermions.

Main Methods:

• Analysis of single-band superconductor models.
• Investigation of symmetry properties (inversion, rotational).
• Theoretical derivation of Majorana fermion dispersion.

Main Results:

• Phase transitions occur via intermediate phases with coexisting even- and odd-parity pairing.
• Inversion-symmetric systems show spontaneous time-reversal symmetry breaking.
• Noncentrosymmetric systems exhibit time-reversal breaking and preserving phases with topological line nodes.
• Emergent U(1)×U(1) symmetry leads to novel topological defects like half-vortex lines binding Majorana fermions.
• Analytically derived Majorana fermion dispersion shows energy-dependent velocities.

Conclusions:

• The study provides a theoretical framework for understanding topological superconductor phase transitions.
• Novel topological defects and Majorana fermion properties are predicted.
• The theory is relevant to materials like Cd_{2}Re_{2}O_{7} and half-Heusler compounds.