Seminar: Theory of superconductor/unconventional magnet junctions

Recently, a new class of magnetic materials known as unconventional magnets (UMs)—including altermagnets and p-wave magnets—has been discovered [1,2]. These materials exhibit unique characteristics that combine features of both ferromagnets and antiferromagnets: they possess zero net magnetization while displaying nonrelativistic spin splitting of energy bands, akin to ferromagnets. This duality leads to anisotropic spin-polarized Fermi surfaces. A particularly intriguing property of UMs is that their magnetic order can be either even or odd with respect to momentum. Representative examples include d-wave altermagnets and p-wave magnets. From this perspective, d-wave altermagnets and p-wave magnets can be viewed as magnetic counterparts to unconventional d-wave and p-wave superconducting states, respectively. Exploring the novel phenomena that emerge from the interplay between UMs and superconductivity has become a rapidly growing area of research [3]. In this talk, we present our recent work about basic properties about tunneling effect and Josephson effect on UM/superconductor (SC) junctions.

We have studied Josephson current SC/altermagnet/SC and SC/p-wave magnet/SC junctions [4,5]. It has been demonstrated the existence of φ-junction behavior in the Josephson current through SC/altermagnet/SC junction while it is absent in SC/p-wave magnet/SC junctions [4]. Here, φ-junction is an exotic junction where free energy minima of the junctions locates neither 0 nor π with phase difference of two superconductors φ [5]. These junctions reveal a rich variety of pairing symmetries, including odd-frequency pairing [6]. We have also investigated tunneling spectroscopy in p-wave magnet/superconductor junctions, considering various pairing symmetries of the superconducting side [7-8]. A notable feature arises in junctions with helical p-wave superconductors, where the surface Andreev bound states (ABS) exhibit dispersion. Furthermore, we have studied ABS in hybrid junctions composed of d-wave altermagnets and d-wave superconductors. Our results show that the orientation of the d-wave altermagnet’s crystal axis significantly affects the ABS and the resulting tunneling conductance [9].

The study of UMs with proximity-induced superconductivity is another compelling direction. We have completed a comprehensive classification of all allowed Cooper pair symmetries in such systems, including odd-frequency components [10]. Additionally, we explore how tailored altermagnetic fields can be used to realize and control subgap states in unconventional superconductors. When the symmetries of altermagnetism and unconventional superconductivity are aligned, we find that bulk zero-energy flat bands can emerge, leading to a pronounced zero-bias conductance peak [11]. Most recently, we have discovered that exotic surface Andreev bound states can arise in three-dimensional altermagnets coupled to chiral d-wave superconductors. These systems exhibit crossed surface flat bands, a consequence of the underlying symmetries. These flat bands appear at zero energy on surfaces normal to the z-axis, due to the presence of superconducting nodal lines in the xy-plane. The number of corners in these flat bands is determined by the crystal symmetry of the altermagnet [12].

[1] L. Šmejkal, J. Sinova, and T. Jungwirth, Phys. Rev. X 12, 040501 (2022).

[2] A. B. Hellenes, T. Jungwirth, R. Jaeschke-Ubiergo, A. Chakraborty, J. Sinova, L. Šmejkal, arXiv:2309.01607 (2024).

[3] Y. Fukaya, B. Lu, K. Yada, Y. Tanaka and J. Cayao, J. Phys. Condens. Matter 37 (2025) 313003.

[4] B. Lu, K. Maeda, H. Ito, K. Yada, and Y. Tanaka, Phys. Rev. Lett. 133 226002 (2024).

[5] Y. Tanaka and S. Kashiwaya, Phys. Rev. B 56 892 (1997).

[6] Y. Fukaya , K. Maeda , K. Yada, J. Cayao, Y. Tanaka, and Bo Lu, Phys. Rev. B 111 064502 (2025).

[7] K. Maeda, B. Lu, K. Yada, and Y. Tanaka, J. Phys. Soc. Jpn. 93, 114703 (2024).

[8] Y. Fukaya, K. Yada and Y. Tanaka, J. Superconductiviy and Novel Magnetism 38 228, (2025).

[9] W. Zhao, Y. Fukaya, P. Burset, J. Cayao, Y. Tanaka, and B. Lu, Phys. Rev. B 111, 184515, (2025).

[10] K. Maeda, Y. Fukaya, K. Yada, B. Lu, Y. Tanaka, and J. Cayao, Phys. Rev. B 111 144508 (2025).

[11] B. Lu, P. Mercebach, P. Burset, K. Yada, J. Cayao, Y. Tanaka, Y. Fukaya, arXiv:2508.03364.

[12] Y. Fukaya, B. Lu, K. Yada, Y. Tanaka, J. Cayao, arXiv:2510.14724.