Edge-induced pairing states in a Josephson junction through a spin-polarized quantum anomalous Hall insulator

TL;DR

This paper investigates the pairing states and Josephson effect in a junction involving a spin-polarized quantum anomalous Hall insulator, revealing equal-spin triplet pairings, finite momentum states, and disorder sensitivity of the critical current.

Contribution

It provides a detailed analysis of the pairing symmetry and Josephson current in a QAHI-based junction, highlighting the presence of equal-spin triplet and finite-momentum pairing states.

Findings

Induced pairing states are equal-spin triplet with mixed even- and odd-frequency components.

Finite-momentum pairing states are confirmed by spatial Green's function analysis.

Disorder affects the critical current and phase difference due to interference effects.

Abstract

Despite the robustness of the chiral edge modes of quantum Hall systems against the superconducting proximity effect, Cooper pairs can penetrate into the chiral edge channels and carry the Josephson current in an appropriate setup. In our work, the Josephson junction of a spin-polarized quantum anomalous Hall insulator (QAHI) with a Chern number $\nu=1$ connecting conventional superconductors is studied from the perspective of pairing symmetry consistent with the chiral edge mode. Induced pairing states are equal-spin triplet, a combination of the even- and odd-frequency components, nonlocally extended, and have a finite momentum $2k_F$. The signature of the equal-spin triplet pairings is confirmed via the dependence on the interface-magnetization direction, and that of the finite-momentum pairing states via the spatial profile of the anomalous Green's function. In the presence of disorder, the robustness of the chiral edge mode leads to high sensitivity of the critical current and the equilibrium phase difference to disorder configurations, which is resulting from the interference of current-carrying channels. The numerical calculations on a lattice model are also examined by a simplified analytical model.