Research

Hydrodynamic transports in strongly correlated electron systems

(under construction)

Effective higher-rank gauge fields in magnetic insulators

(under construction)

[Background]
Transport phenomena mediated by charge-neutral quasiparticles, such as magnons, are expected to enable dissipationless information transmission that is difficult to realize in conventional electron-based devices. Among them, the magnon thermal Hall effect is of particular importance as it serves not only as a platform for low-energy spintronic applications but also as a highly sensitive probe of exchange interactions and underlying spin textures.

Previous theoretical approaches to the magnon thermal Hall effect have largely been based on the U(1) gauge-field picture. In magnetic insulators, Dzyaloshinskii–Moriya interactions and noncoplanar spin textures often induce complex hopping for magnons, effectively generating a U(1) gauge flux. Although magnons are charge-neutral and do not feel the Lorentz force, their propagation can be deflected by the emergent magnetic field associated with the U(1) gauge flux, giving rise to the thermal Hall effect.

However, the U(1)-based framework imposes severe lattice-dependent constraints. In edge-sharing lattices such as square and triangular lattices, lattice symmetries enforce cancellation of the emergent magnetic fluxes, leading to an effective restoration of time-reversal symmetry and thereby forbidding the thermal Hall effect. This restriction, often referred to as a “no-go” condition, has posed a major obstacle in the search for magnon thermal Hall transport. Indeed, experimental observations have so far been limited almost exclusively to corner-sharing lattices such as kagome and pyrochlore networks.

[Research]
We propose a new mechanism that circumvents the no-go condition and allows for the emergence of the magnon thermal Hall effect. We demonstrate that the low-energy excitations in antiferromagnets are effectively described by magnons coupled to a higher-rank gauge field, and show that the non-Abelian nature of the gauge field breaks time-reversal symmetry even in edge-sharing lattices, thereby enabling a magnon thermal Hall effect. The sublattice degrees of freedom inherent to antiferomagnet endow magnons with internal degrees of freedom, and Dzyaloshinskii-Moriya interaction and topologically nontrivial spin texture translates magnon hopping processes into NxN transition matrices, i.e. SU(N) gauge links. The intrinsic noncommutativity of these matrices renders the magnon phase accumulation path-dependent, effectively generating additional gauge fluxes that break time-reversal symmetry. This framework naturally explains the finite thermal Hall conductivity recently observed in the antiferromagnetic skyrmion crystal phase of MnSc2S4.

(figure insertion test)

Strongly correlated electron systems with spin-orbit coupling

Developing numerical methods