Switch effect and 0- π transition in Ising superconductor Josephson junctions

Abstract

We theoretically study the Josephson current in Ising superconductor−half-metal−Ising superconductor junctions. By solving the Bogoliubov-de Gennes equations, the Josephson currents contributed by the discrete Andreev levels and the continuous spectrum are obtained. For very short junctions, because the direct tunneling of the Cooper pair dominates the Josephson current, the current-phase difference relation is independent of the magnetization direction, which is the same as the conventional superconductor-ferromagnet-superconductor junctions. On the other hand, when the length of the half-metal is similar to or greater than the superconducting coherence length, the spin-triplet Josephson effect occurs and dominates the Josephson current. In this case, the currentphase difference relations show the strong magnetoanisotropic behaviors with the period π. When the magnetization direction points to the ±z directions, the current is zero regardless of the phase difference. However, the current has a large value when the magnetization direction is parallel to the junction plane, which leads to a perfect switch effect of the Josephson current. Furthermore, we find that the long junctions can host both the 0-state and π-state, and the 0-π transitions can be achieved with the change of the magnetization direction. The physical origins of the switch effect and 0-π transitions are interpreted from the perspectives of the spin-triplet Andreev reflection, the Ising pairing order parameter and the Ginzburg-Landau type of free energy. In addition, the influences of the chemical potential, the magnetization magnitude and the strength of the Ising spin-orbit coupling on the switch effect and 0-π transitions are also investigated. Furthermore, the two-dimensional Josephson junctions are also investigated and we show that the spin-triplet Josephson effect can exist always. These results provide a convenient way to control the Josephson critical current and to adjust the junctions between the 0-state and π-state by only rotating one magnetization.PACS numbers:

Ising pairing in atomically thin superconductors

“…In a similar spirit, spin triplet Andreev reflection was proposed to occur between a ferromagnet-Ising superconductor junction [30]. An in-plane junction made of Ising superconductor-ferromagnet-Ising superconductor may further allow the spin triplet Josephson current to pass [67]. However, constructing such an in-plane junction may require technical ingenuity.…”

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

“…When a ferromagnetic middle layer with large exchanging interactions is inserted between superconducting electrodes, the π junction forms with I = I c sin(ϕ + π). [6][7][8][9][10][11] In addition, the anomalous Josephson junction can carry supercurrent even if there is no superconducting phase difference between two leads, that is, I = I c sin(ϕ + δ ), also named as the δ junction. [12][13][14][15] This anomalous junction could not only be a natural phase shifter or a phase battery in the superconducting circuits but also be crucial for the superconducting quantum computation.…”

Controlling charge and spin transport in an Ising-superconductor Josephson junction

“…In particular, ferromagnetic Josephson junctions have been fabricated and the coexistence of 0 and π states in the junction region has been demonstrated which can be used to construct φ-phase Josephson junctions [16,17]. Transport properties of Ising superconductors have also been theoretically investigated in ferromagnet-Ising-superconductor junctions [29,30] and Josephson junctions with a half-metal barrier [31]. These theoretical works focused on phenomena arising from spintriplet Andreev reflection at the interfaces.…”

“…Thus, a 0-π transition can be achieved by changing the magnitudes or the relative orientation of the exchange fields for weak impurity scattering and low temperature. Typically, π-states are realized in Josephson junctions with a ferromagnetic barrier between two superconductors [31,[45][46][47][48][49][50][51][52]. Here, its appearance is due to the interplay of the supercurrents induced by singlet and triplet pairing correlations.…”