Proposal for Measuring the Parity Anomaly in a Topological Superconductor Ring

Area of Science:

• Condensed Matter Physics
• Quantum Materials
• Superconductivity

Background:

• Topological superconductors possess unique properties stemming from their electronic band structure.
• A key characteristic is the fermion parity switch in the ground state, linked to the "parity anomaly."
• This fundamental property has yet to be experimentally verified.

Purpose of the Study:

• To propose a definitive experimental method for detecting the fermion parity switch in topological superconductor rings.
• To establish a link between thermodynamic and transport properties and the topological invariant.

Main Methods:

• Extending the Ambegaokar-Eckern-Schön formalism to include Coulomb charging energy in superconductor rings.
• Analyzing the flux periodicity of two-terminal conductance.
• Investigating the dependence on charging energy, temperature, and tunnel barrier transparency.

Main Results:

• Demonstrating that the fermion parity switch can be detected via conductance measurements.
• Establishing explicit relationships between macroscopic properties and the topological invariant.
• Showing that the topological signal can be distinguished from non-topological Aharonov-Bohm oscillations.

Conclusions:

• The proposed method offers a viable route for the experimental observation of a defining property of topological superconductors.
• This work bridges the gap between theoretical predictions and experimental verification of topological phenomena.
• It paves the way for exploring novel applications of topological superconductivity.