Program

Abstract

We report the recent observation of a third-order nonlinear Hall effect in a quantum Hall state [1] and present theoretical frameworks that account for this experimental finding [2,3].  The experiment observed a finite third-order Hall response in graphene under strong magnetic fields, where the linear Hall resistance remains quantized and the third-order longitudinal response is suppressed.  This nonlinear response of a quantum Hall state is qualitatively distinct from previously reported nonlinear Hall effects in metallic or optical systems.

We develop complementary theories that explain nonlinear Hall response in the quantum Hall regime.  We first consider electron–electron interactions between counterpropagating quantum Hall edge channels [2].  We show that weakly nonlinear dispersion of the edge channels generates a finite third-order Hall response while the exact quantization of the linear Hall resistance remains intact.  Another picture is based on the Hall current through the incompressible bulk.  We then find that an inhomogeneous electric field induces nonlinear Hall response based on the hydrodynamic description [3].  This effect is analogous to the centrifugal force exerted on a curved current flow. 

Reference

[1] P. He, H. Isobe, G. K. W. Koon, J. Y. Tan, J. Hu, J. Li, N. Nagaosa, and J. Shen, Nat. Nanotechnol. 19, 1460 (2024).
[2] H. Isobe and N. Nagaosa, Sci. Adv. 10, eado2704 (2024).
[3] H. Isobe, Newton 100466 (2026).

Abstract

Under a strong magnetic field, when a Landau level is fractionally filled and electron-electron interactions dominate, the fractional quantum Hall effect emerges. This is a paradigmatic quantum many-body phenomenon characterized by topological order and anyonic excitations. In recent years, fractional Chern insulators—the zero-field counterparts of fractional quantum Hall states—have been observed in moiré systems such as twisted MoTe2 and are being actively studied. The realization of such states relies on band geometry: the Berry curvature and quantum metric of an isolated band must satisfy geometric conditions analogous to those of a Landau level. Bands satisfying these conditions are referred to as generalized Landau levels. In this talk, after reviewing recent progress on generalized Landau levels, I focus on generalized higher Landau levels, which are the analogs of higher Landau levels[1,2], and on generalized Landau levels with Chern number C>1[3]. I then show that both can be realized in twisted multilayer graphene.

Reference

[1] Manato Fujimoto, Daniel E. Parker, Junkai Dong, Eslam Khalaf, Ashvin Vishwanath, and Patrick Ledwith, Phys. Rev. Lett. 134, 106502 (2025).
[2] Zhao Liu, Bruno Mera, Manato Fujimoto, Tomoki Ozawa, and Jie Wang, Physical Review X 15, 031019  (2025).
[3] Manato Fujimoto, Naoto Nakatsuji, Ashvin Vishwanath, and Patrick Ledwith, arXiv:2510.02444 (2025).

Abstract

Characterizing material properties via the geometry and topology of electronic wavefunctions is a central paradigm in modern condensed matter physics, and its scope is broadening from linear response to nonlinear and nonequilibrium phenomena under strong external fields [1]. In this talk, we discuss quantum-geometric effects emerging in nonlinear phononics, a branch of physics focusing on resonant phonon excitations. 

When phonons are coherently excited by intense laser fields, nonlinear effects can dynamically alter the crystal structure. The field of controlling material properties through such processes is referred to as nonlinear phononics [2]. In conventional theoretical frameworks of nonlinear phononics, the electron dynamics are typically assumed to be adiabatic. However, this assumption generally breaks down under strong driving, and nonadiabatic corrections become essential.

We explore nonadiabatic effects in the phonon equations of motion by treating the electron dynamics under resonant phonon excitation beyond the adiabatic approximation. Our analysis reveals that quantum geometric contributions originating from electronic states give rise to unconventional forces on phonons. In particular, when we consider a circularly-polarized laser light, this force induces a coupling between the optical chirality and the crystal chirality of the material, with which we can dynamically alter an achiral crystal into a chiral crystal [3].

Reference

[1] T. Morimoto, S. Kitamura, and N. Nagaosa, J. Phys. Soc. Jpn. 92, 072001 (2023).
[2] A. S. Disa, T. F. Nova and A. Cavalleri, Nat. Phys. 17, 1087 (2021).
[3] S. Kitamura and T. Morimoto, in preparation.

Figure 1 (left panel)|
Calculated equilibrium crystal shapes for (a) a trivial insulator and (b) a TCI.
Figure 2 (right panel)|
Calculated crystal shape in the dynamical growth of (a) a HOTI and (b) a trivial insulator.  They have the same value of Df

Abstract

A quantum system coupled to external environment can often exhibit quantum phase transitions. An iconic, textbook example is the Schmid transition [1,2], a dissipative transition predicted to occur in the resistively shunted Josephson junction. Namely, early studies [3,4] based on perturbative RG and the duality argument predicted that the Josephson junction should exhibit the transition at the quantum resistance. I will talk about some of our attempts [5,6] to revisit this problem by employing nonperturbative RG analyses.

Reference

[1] A. Schmid, Phys. Rev. Lett. 51, 1506 (1983).
[2] N. Nagaosa, Quantum field theory in condensed matter physics (Springer Science & Business Media, 1999).
[3] C. L. Kane and M. P. A. Fisher, Phys. Rev. B 46, 15233 (1992).
[4] A. Furusaki and N. Nagaosa, Phys. Rev. B 47, 4631 (1993).
[5] K. Masuki, H. Sudo, M. Oshikawa and Y. Ashida, Phys. Rev. Lett. 129, 087001 (2022).
[6] T. Yokota, K. Masuki and Y. Ashida, Phys. Rev. A 107, 043709 (2023).

Abstract

Light-induced control of magnetism has attracted significant attention from both fundamental and technological perspective and has been actively studied. In particular, the double-exchange model, in which localized spins are strongly coupled to conduction electrons, has become a key platform in this field because it can host a variety of noncollinear and noncoplanar magnetic orders and enables efficient manipulation of magnetism via electronic excitations. In this talk, we discuss photoinduced magnetic phase transitions in double-exchange models on triangular and cubic lattices [1,2]. Based on numerical simulations and spin-wave dispersion calculations using the Floquet-Keldysh formalism [2,3], we elucidate their universal mechanisms as well as the nature and origin of transient magnetic states that emerge during the nonequilibrium dynamics.

Reference

[1] T. Inoue and M. Mochizuki, Phys. Rev. B 105, 144422 (2022).
[2] R. Hamano and M. Mochizuki, Phys. Rev. B 111, 214409 (2025).
[3] R. Hamano and M. Mochizuki, in preparation.