Abstract: The Hall effect [1] is widely used to probe the electronic structure of materials and has found applications in various electronic devices. Research on the Hall effect has expanded to include related phenomena such as the anomalous Hall effect, the spin Hall effect, and the quantum Hall effect. More recently, these studies have been extended to the nonlinear regime [2].
For superconductors, many of previous studies on the Hall effect have focused on the responses in the presence of magnetic fields generated by vortex motion [3], where normal carriers in vortex cores give rise to dissipative currents. This raises the question of whether it is possible to realize a dissipationless Hall current (i.e., transverse supercurrent flow) in superconductors. While the corresponding divergent Hall conductivity does not appear in the linear response regime near equilibrium, it can emerge in the nonlinear regime [4], and we refer to this phenomenon as the superconducting nonlinear Hall effect (SNHE).
In this seminar, we present our recent work proposing a mechanism for the SNHE in s-wave superconductors without magnetic fields [5]. The key ingredient is a quantum geometric phase (i.e., the Aharanov-Bohm (AB) phase). To demonstrate the mechanism, we study a honeycomb lattice model that incorporates two types of AB phases: one attached to single-particle hoppings, similar to that of the Haldane model, and another associated with two-particle hoppings. By calculating with the Keldysh Green's functions, which incorporate the effect of dissipation microscopically, we reveal a robust divergence in the DC limit of the nonlinear Hall conductivity. We also discuss the SNHE from the Ginzburg–Landau framework, and point out that SNHEs are classified with higher-order Lifshitz invariants, which are symmetry invariants containing odd-order spatial derivatives. Furthermore, we conduct real-time simulation under a light drive to show that the SNHE leads to the divergently strong rectification in the Hall current. We will provide further details on the methodologies and candidate materials for its experimental realization during the presentation.
[1] E. H. Hall, Am. J. Math. 2, 287 (1879).
[2] Z. Z. Du, H.-Z. Lu, and X. C. Xie, Nat. Rev. Phys. 3, 744 (2021).
[3] e.g., G. Blatter et al., Rev. Mod. Phys. 66, 1125 (1994),
[4] H. Watanabe et al., Phys. Rev. B 105, 024308 (2022); H. Tanaka et al., Phys. Rev. B 107, 024513 (2023); H. Tanaka et al., Phys. Rev. B 110, 014520 (2024); O. Matsyshyn et al., arXiv:2410.21363.
[5] KT, N. Tsuji, arXiv:2503.14589.