Identification of odd-frequency superconducting pairing in Josephson junctions

Optimal choice of spin polarization enables electron injection into the helical edge state at a precise position, despite the uncertainty principle, permitting access to specific nonlocal Green's functions. We show, within 1D effective description, that this fact facilitates a direct identification of odd-frequency pairing through parity measurement (under frequency reversal) of the nonlocal differential conductance in a setup comprising the Josephson junction on the helical edge state of a 2D topological insulator with two spin-polarized probes tunnel-coupled to the junction region. A 2D numerical simulation has also been conducted to confirm theoretical predictions as well as to demonstrate the experimental feasibility of the proposal.