Orientation-dependent transport in junctions formed by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>d</mml:mi> </mml:math> -wave altermagnets and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>d</mml:mi> </mml:math> -wave superconductors

Abstract

We investigate de Gennes-Saint-James states and Josephson effect in hybrid junctions based on $d$-wave altermagnet and $d$-wave superconductor. Even though these states are associated to long junctions, we find that the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ altermagnet in a normal $\text{metal/altermagnet/}d$-wave superconductor junction forms de Gennes-Saint-James states in a short junction due to an enhanced mismatch between electron and hole wave vectors. As a result, the zero-bias conductance peak vanishes and pronounced resonance spikes emerge in the subgap conductance spectra. By contrast, the ${d}_{xy}$ altermagnet only features de Gennes-Saint-James states in the long junction. Moreover, the well-known features such as V-shape conductance for ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairings and zero-biased conductance peak for ${d}_{xy}$ pairings are not affected by the strength of ${d}_{xy}$ altermagnetism in the short junction. We also study the Josephson current-phase relation $I(\ensuremath{\varphi})$ of $d$-wave $\text{superconductor/altermagnet/}d$-wave superconductor hybrids, where $\ensuremath{\varphi}$ is the macroscopic phase difference between two $d$-wave superconductors. In symmetric junctions, we obtain anomalous current phase relation such as a $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition by changing either the orientation or the magnitude of the altermagnetic order parameter and dominant higher Josephson harmonics. Interestingly, we find the first-order Josephson coupling in an asymmetric ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}\text{\ensuremath{-}}\text{superconductor/altermagnet/}{d}_{xy}$-superconductor junction when the symmetry of altermagnetic order parameter is neither ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ nor ${d}_{xy}$ wave. We present the symmetry analysis and conclude that the anomalous orientation-dependent current-phase relations are ascribed to the peculiar feature of the altermagnetic spin-splitting field.

Topics & Concepts