Antisymmetric Thermopolarization by Electric Toroidicity

TL;DR

This paper explores how electric toroidal dipole order induces an antisymmetric thermopolarization in insulating systems, revealing a vortex-like polarization pattern and emphasizing the role of orbital fluctuations.

Contribution

It introduces a two-dimensional three-orbital model to demonstrate the emergence of antisymmetric thermopolarization due to electric-toroidal dipole order, highlighting the importance of orbital fluctuations.

Findings

Vortex-type electric polarization configuration as ground state.

Nonzero antisymmetric thermopolarization linked to electric-toroidal order.

Orbital fluctuations significantly enhance the antisymmetric response.

Abstract

We investigate electric polarizations emergent perpendicular to an applied thermal gradient in insulating systems. The thermally-induced electric polarization, known as thermopolarization, has been studied conventionally in the case that an electric polarization appears along the thermal gradient. Here, we focus on the antisymmetric component of the thermopolarization tensor and reveal that it becomes nonzero owing to the ferro-type order for electric-toroidal dipole moments. To describe local electric polarizations originating from the disproportionation of localized electronic clouds, we introduce a two-dimensional three-orbital model with localized $s$ and two $p$ orbitals, where the electric polarization at each site interacts with the neighboring one as dipole-dipole interactions. We find that a vortex-type configuration of local electric polarizations appears as a mean-field ground state, corresponding to a ferro-type electric-toroidal dipole order. By taking account of collective modes from this ordered state, we calculate the coefficient of the thermopolarization based on the linear response theory. The antisymmetric component is nonzero in the presence of the electric-toroidal dipole order. We clarify that fluctuations in the $p$ orbitals are crucial in enhancing the antisymmetric thermopolarization. We discuss the appearance conditions based on the symmetry argument and the relevance to real materials.