On June 30, the top Chinese journal Science Bulletin published a paper titled "Angle-dependent planar thermal Hall effect by quasi-ballistic phonons in black phosphorus" by the Extreme Quantum Transport Team in the Wuhan National High Magnetic Field Center. HUST served as the primary institution for the paper. Associate Professor Li Xiaokang is the first and co-corresponding author, doctoral student Guo Xiaodong is the second author, Professor Zhu Zengwei and Professor Kamran Behnia (ESPCI) are the co-corresponding authors.

Figure 1: Schematic for measuring planar thermal Hall effect (left) and

angle-dependent behavior of planar thermal Hall effect in black phosphorus (right).

Thermal conductivity, as a key physical quantity describing thermal transport properties, is a second-order tensor that connects heat flux density and temperature gradient. Within this tensor, the thermal Hall effect corresponds to the off-diagonal components. The generation of the traditional thermal Hall effect requires the direction of the magnetic field to be perpendicular to the plane defined by the heat flow and temperature gradient. In contrast, the planar thermal Hall effect (PTHE) exhibits a unique geometric feature: the heat flow vector, the transverse temperature gradient vector, and the magnetic field vector are coplanar (as shown in the left panel of Figure 1). It is worth noting that this effect is usually forbidden by theory due to symmetry restrictions. However, it has recently been observed in several insulating materials, all of which are magnetic, such as the quantum spin liquid  candidate α-RuCl₃. The generation mechanism is explained as symmetry breaking caused by magnetic order or structural defects.

In this study, building on previous work (Nat. Commun. 14, 1027 (2023)), the team conducted research on the planar thermal Hall effect and its angular characteristics in the non-magnetic elemental black phosphorus, using a self-built high-sensitivity angular thermal transport measurement system. The main findings are as follows: (i) Significant planar thermal Hall signals were observed in two different PTHE configurations where the magnetic field was parallel to either the heat flow or the transverse temperature gradient. And the planar Hall thermal conductivity follows Onsager's reciprocity relations. (ii) In angular measurements of the planar thermal Hall effect, the signals were enhanced and annihilated along the two diagonal axes within the plane, indicating that the PTHE signals consist of two sinusoidal components contributing along high-symmetry axes (as shown in the right panel of Figure 1). (iii) The study points out that anharmonicity and the torque exerted by the magnetic field on the electric dipole waves accompanying phonon propagation could be the key ingredient leading to the observed PTHE signals.

This work was supported by the National Key Research and Development Program of China, the National Science Foundation of China and the Fundamental Research Funds for the Central Universities, and the Hubei Provincial Natural Science Foundation of China.

Link: https://doi.org/10.1016/j.scib.2025.03.052