Topological Majorana and Dirac zero modes in superconducting vortex cores

Area of Science:

• Condensed Matter Physics
• Topological Materials Science
• Superconductivity Theory

Background:

• Vortex cores in superconductors can host exotic quasiparticle states, including zero modes.
• Topological invariants are crucial for classifying phases of matter and predicting emergent phenomena.
• Understanding the conditions for protected zero modes is essential for topological quantum computing.

Purpose of the Study:

• To develop a general argument for the existence of protected zero modes in superconductor vortex cores.
• To establish the necessary and sufficient conditions for these zero modes across various symmetry classes.
• To provide a new perspective on zero modes in topological superconductors, particularly spinless p_x+ip_y types.

Main Methods:

• A flux insertion argument, analogous to a 2D index theorem, is employed.
• The approach is generalized to include disordered systems.
• Analysis is performed on superconductors with and without time-reversal and spin-rotational symmetry.

Main Results:

• Protected zero modes are shown to exist in vortex cores of superconductors with nontrivial topological invariants.
• The flux insertion argument is demonstrated to be applicable to disordered systems.
• A unified understanding of zero modes in different topological superconductor types is achieved.

Conclusions:

• The flux insertion method provides a robust framework for identifying protected zero modes in superconductor vortices.
• Symmetry properties play a critical role in determining the presence or absence of these zero modes.
• This work offers a pathway to engineer and detect protected zero modes in novel superconducting materials.