Department of Applied Physics, The University of Tokyo, Bunkyo-ku, Tokyo, 113-8656, Japan.
RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama, 351-0198, Japan.
Phys Rev Lett. 2019 Dec 20;123(25):255901. doi: 10.1103/PhysRevLett.123.255901.
A mechanism for the phonon Hall effect (PHE) in nonmagnetic insulators under an external magnetic field is theoretically studied. PHE is known in (para)magnetic compounds, where the magnetic moments and spin-orbit interaction play an essential role. In sharp contrast, we here discuss that the PHE also occurs in nonmagnetic band insulators subject to the magnetic field. We find that a correction to the Born-Oppenheimer approximation gives rise to a Raman-type interaction between the magnetic field and the phonons; this interaction gives rise to the Berry curvature of a phonon band. This Berry curvature results in the finite thermal Hall conductivity κ_{H} in nonmagnetic band insulators. The value of κ_{H} is calculated for square and honeycomb lattices. The order of the magnitude estimation for κ_{H} is given for Si at room temperature.
理论研究了在外磁场中非磁性绝缘体中声子霍尔效应（PHE）的机制。已知 PHE 存在于（顺磁）化合物中，其中磁矩和自旋轨道相互作用起着至关重要的作用。相比之下，我们在这里讨论的是，在磁场作用下，非磁性能带绝缘体中也会发生 PHE。我们发现，Born-Oppenheimer 近似的修正导致磁场和声子之间产生 Raman 型相互作用；这种相互作用导致声子能带的 Berry 曲率。这种 Berry 曲率导致非磁性能带绝缘体中有限的热霍尔电导率κ_{H}。计算了方晶格和蜂窝晶格的κ_{H}值。给出了室温下 Si 的κ_{H}量级的估算值。
