![Fig. 1 Schematic image of spin-split Fermi surfaces of ferromagnetism, d-wave altermagnetism, and p-wave magnetism [2].](attachment:8a12d3a6-dd78-4c1f-bfab-03d2350c89c2:image.png)
In my research, I theoretically investigate what novel and exotic phenomena “superconductivity” —a state in which electrical resistance arises when a material is cooled to extremely low temperatures—can give rise to. In particular, I focus on “topological superconductivity” —where localized states exist at the surface and edges due to the bulk material possessing a topological number—as well as the surface and interface states and transport phenomena in “superconducting junctions,” which are formed by combining a superconductor to a normal metal or two superconductors.
In the theory of superconductivity, the fundamental principles are understood solely in terms of the spin degrees of freedom of electrons (single orbital model), as seen in single-element metals and copper-oxide superconductors. However, there are also superconductors—such as the Sr₂RuO₄ superconductor [1]—that require consideration of “intrinsic degrees of freedom” of the system, such as the orbital degrees of freedom; these intrinsic degrees of freedom give rise to novel and exotic phenomena that cannot be explained by the existing single orbital model. Furthermore, while unique phenomena in superconductivity—such as topological superconductivity and superconducting spintronics—can be manifested and controlled by “magnetism” (such as ferromagnetism), superconductivity has the potential problem of being destroyed by ferromagnetism (pair breaking). Recent theoretical and experimental research has identified new class of magnetism (unconventional magnetism) known as “altermagnetism” and “p-wave magnetism” [2], which are believed to solve this problem (Fig. 1). Since unconventional magnetism is without net magnetization, they are believed to be less likely to disrupt superconductivity than ferromagnetism. Therefore, combining these unconventional magnetism with superconductivity may enable the realization of novel phenomena, in addition to those already known from combinations with ferromagnetism [3].
Fig. 1 Schematic image of spin-split Fermi surfaces of ferromagnetism, d-wave altermagnetism, and p-wave magnetism [2].
Based on the above, I focus on developing theoretical frameworks for novel and exotic quantum properties by investigating quantum phenomena in superconductivity that arise from intrinsic degrees of freedom — such as the orbital degrees of freedom of electrons —and from unconventional magnetism (Fig. 2).
Fig. 2 Image of my research field
[1] Y. Maeno, et al., Nature (London) 372, 532 (1994).
[2] M. Naka, et al., Nat. Commun. 10, 4305 (2019), S. Hayami, et al., J. Phys. Soc. Jpn. 88, 123702 (2019), L. Šmejkal, et al., Phys. Rev. X 12, 031042 (2022), etc.
[3] Y. Fukaya, B. Lu, K. Yada, Y. Tanaka, J. Cayao, J. Phys.: Condens. Matter 37, 313003 (2025).
I calculate numerically by using Fortran90 programming. While my calculations involve tight-binding models, I also occasionally work with continuum models. Then I numerically calculate Green’s functions for tight-binding models to investigate surface/interface states, as well as transport phenomena in superconducting junctions.
Below, I present my major research achievements to date.
The study of what kind of superconducting state can emerge upon a phase transition to superconductivity is referred to as the “pairing mechanism.” Superconductivity is a many-body problem caused by interactions between electrons, and determining how to solve this many-body problem is crucial.
I investigated the pairing symmetries that arise from Coulomb repulsion between electrons in a honeycomb lattice—a regular hexagonal structure typified by graphene—within the framework of the Random Phase Approximation (RPA) [4]. Since this honeycomb lattice system possesses intrinsic degrees of freedom other than electron spin—known as the sublattice (Fig. 3)—it is necessary to perform calculations using a model that accounts for these sublattice degrees of freedom. Furthermore, by introducing spin-orbit coupling into the honeycomb lattice system (Kane-Mele model [5]), we can investigate the pairing mechanism that also takes into account the spin-orbit coupling. When the spin-orbit coupling is small, spin-singlet d-wave pairing with inter-sublattice is stabilized by the spin fluctuation. However, when the spin-orbit coupling becomes strong, the spin fluctuations that stabilize the spin-singllet d-wave pairing are suppressed; consequently, the spin-triplet f-wave pairing with intra-sublattice becomes more stable than the spin-singlet d-wave pairing with inter-sublattice.
Fig. 3 Schematic illustration of honeycomb lattice systems. Red and blue circles indicate the sublattice A and B, respectively.
[4] Y. Fukaya, K. Yada, A. Hattori, Y. Tanaka, J. Phys. Soc. Jpn. 85, 104704 (2016).
[5] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005).