Anomalous Josephson current in quantum anomalous Hall insulator-based superconducting junctions with a domain wall structure*

Abstract

We theoretically study the Josephson effect in a quantum anomalous Hall insulator (QAHI) nanoribbon with a domain wall structure and covered by the superconductor. The anomalous Josephson current, the nonzero supercurrent at the zero superconducting phase difference, appears with the nonzero magnetization and the suitable azimuth angle of the domain wall. Dependent on the configuration of the domain wall, the anomalous current peaks in the Bloch type but disappears in the Néel type because the y-component of magnetization is necessary to break symmetry to arouse the anomalous current. The phase shift of the anomalous current is tunable by the magnetization, the azimuth angle, or the thickness of the domain wall. By introducing a bare QAHI region in the middle of the junction which is not covered by the superconductor, the anomalous Josephson effect is enhanced such that the phase shift can exceed π. Thus, a continuous change between 0 and π junctions is realized via regulating the configuration of the domain wall or the magnetization strength. As long as an s-wave superconductor is placed on the top of the QAHI with a domain wall structure, this proposal can be experimentally fabricated and useful for the phase battery or superconducting quantum bit.

The Progress of the Quantum Hall Effect

“…Additionally, for superconducting phases with Chern number being 0,1,2, corresponding to amplitude of magnetization 𝑀𝑀 =0.05,0.2 and 0.35, the anomalous Josephson current all appears, supporting that the anomalous Josephson current is independent of the superconducting phases. Furthermore, the current gets greater as M grows larger [12].…”

“…However, it's still hard to observe the anomalous current in realistic. Since the quantum anomalous Hall insulators (QAHI) can be transformed into a superconductor, scholars have constructed a domain wall structure based on QAHI [12]. Domain wall is the region where transition of the magnetization direction happens because of the difference of magnetization directions in the neighbouring regions.…”

“…Scholars analyzed the symmetry characters of this structure, they find that the condition for the existence of anomalous current is 𝑈𝑈𝐻𝐻 𝐵𝐵𝑑𝑑𝐵𝐵 (𝜑𝜑)𝑈𝑈 † = 𝐻𝐻 𝐵𝐵𝑑𝑑𝐵𝐵 (−𝜑𝜑) ( 8) and find that if the y-direction component 𝑀𝑀 𝑥𝑥 of the magnetization in domain wall is zero. 𝑀𝑀 and the azimuth angle 𝜑𝜑 𝑔𝑔𝑧𝑧 representing the configuration of the domain wall [12]. Through experiments, more findings are available.…”

“…Figure 8. The bottom is the QAHI-based Josephson junction with a domain wall structure and the top is the s-wave superconductor[12]. Seen from the sketch illustrated in Fig.8, the magnetization in the domain rotates gradually from +z to -z.…”

Spin-triplet superconductor$-$quantum anomalous Hall insulator$-$spin-triplet superconductor Josephson junctions: $0$-$π$ transition, $ϕ_{0}$ phase and switch effects

“…Various studies on the electrical transport have been carried out to detect or regulate the chiral Majorana edge modes produced in the composite system [4][5][6][7][8][9][10][11][12] . The Josephson junctions are also researched, which exhibit novel phase shift 13,14 , anomalous critical current 15 , tunable Majorana valve effect 16 or induced paring states 17 . However, the superconductors involved in the existing studies are limited to the spinsinglet pairing.…”