Superconductivity as a Probe of Altermagnetism: Critical Temperature, Field, and Current

Abstract

We study thin films that host coexisting collinear $d$-wave altermagnetic and superconducting orders in the presence of an external magnetic field that fully penetrates the films. We use the Ginzburg-Landau functional to analyze the response of the films to magnetic fields and an in-plane supercurrent. We demonstrate that the interplay between superconductivity and altermagnetism induces characteristic fourfold anisotropies in the critical temperature, parallel critical field, and critical current density of the films. These results establish experimentally accessible signatures of altermagnetism in superconducting films and in superconductor/altermagnetic insulator heterostructures.

Figures (2)

• Figure 1: (a): Altermagnetic superconducting film realized as a bilayer composed of a conventional $s$-wave superconductor (SC) and an altermagnetic insulator (AMI). Although the Néel vector $\boldsymbol{N}$ may point in an arbitrary direction, the spin splitting occurs in the $\hat{\boldsymbol{x}}$--$\hat{\boldsymbol{y}}$ plane, resulting in an altermagnetic tensor $K_{jk}$ with the only two non-vanishing components which we set as $K_{xx} = -K_{yy} = K$. The film is subjected to the external magnetic field $\boldsymbol{H} = (H_\parallel \cos\phi, H_\parallel \sin\phi, H_\perp)$. (b): Ferromagnetic insulator/SC/AMI trilayer. The ferromagnetic insulator induces an exchange field $\boldsymbol{h}$ in the superconductor coupled to the altermagnetic Néel vector $\boldsymbol{N}$ given by the AMI film. (c): Cross-shaped SC/AMI structure suitable for detecting the critical-current anisotropy $I_{cx} \neq I_{cy}$ induced by the external magnetic field $\boldsymbol{H}$.
• Figure 2: (a), (b): Critical temperature and parallel critical field for the setup shown in Fig. \ref{['fig:setup']}(a), obtained from Eqs. \ref{['eq:Tc']} and \ref{['eq:Hc_simple']}, respectively. Here, $\xi^{(0)} = \xi(T=0)$ and $H_{c2}^{(0)} = H_{c2}(T=0)$, with $\xi^2 = [2m^* \alpha |T_{c0}-T|]^{-1}$ and $H_{c2} = \Phi_0/(2\pi \xi^2)$. (c): Critical current density modulation for the setup shown in Fig. \ref{['fig:setup']}(b), according to Eqs. \ref{['eq:j_c_theta']} and \ref{['eq:phi_theta']}. Here, the notation $\overline{q}$ is used to denote averaging of $q$ over the angle $\phi$ between applied parallel magnetic field or supercurrent and one of the crystallographic axes with maximal spin-splitting.