Phase-shifted Andreev levels in an altermagnet Josephson junction
C. W. J. Beenakker, Tereza Vakhtel
Abstract
We compute the effect of a $d$-wave magnetization (altermagnetism) on the spectrum of bound states (Andreev levels) in a junction between two $s$-wave superconductors (gap ${\mathrm{\ensuremath{\Delta}}}_{0}$ and phase difference $\ensuremath{\phi}$). Compared to a nonmagnetic junction, the $\ensuremath{\phi}$ dependence of the spectrum is shifted by an offset $\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}\ensuremath{\phi}$, dependent on the spin direction, so that the Andreev levels become spin polarized. In a planar junction, oriented along the crystalline axis of ${d}_{xy}$-wave symmetry, the excitation energies are determined by the normal-state transmission probability $T$ according to $E={\mathrm{\ensuremath{\Delta}}}_{0}\sqrt{1\ensuremath{-}T\phantom{\rule{0.16em}{0ex}}{sin}^{2}\frac{1}{2}(\ensuremath{\phi}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}\ensuremath{\phi})\phantom{{}^{0}}}$. We calculate the corresponding Josephson energy and supercurrent, recovering the 0-$\ensuremath{\pi}$ transition of related studies.