标题： 异常平面输运中$d$波反铁磁体的近似半整数量子化 显示英文标题

标题： Approximate half-integer quantization in anomalous planar transport in $d$-wave altermagnets

摘要： 我们研究在最近发现的一类共线磁性材料中出现的异常平面输运现象，这类材料被称为$d$波交替磁体。 异常的平面效应在一种配置中表现出来，当施加的电场/温度梯度、磁场和测量的霍尔电压都在同一平面内，但平面磁场在破坏$d$波交替磁体的$\hat{C}_{4z}\hat{\mathcal{T}}$对称性中起关键作用，其中$\hat{\mathcal{T}}$是时间反演算符，导致在偏移的狄拉克节点处出现泽曼能隙和非零的贝里曲率单极子。 我们证明这些系统在低温下表现出几乎半量子化的异常平面霍尔效应和平面热霍尔效应，并且在一定范围的磁场下持续存在。 平面输运的角度依赖性显示出对磁场方向的$\cos2\phi$依赖性，其中$\phi$是磁场形成的方位角。 我们还讨论了异常的平面能斯特效应，或横向热电势，并证明当化学势位于诱导的泽曼能隙之外时，能斯特电导率达到峰值，并在能隙内消失。 我们进一步探讨了当磁场在完整的$3D$空间中旋转时，所有三个系数与磁场的极角和方位角的依赖关系。 我们的结果揭示了在平面内磁场的一定范围内存在大约半量子化的异常平面热霍尔平台，而无需拓扑超导性和传导马约拉纳模式，并且可以在$d$-波交替磁体的实验中进行探测。 显示英文摘要

摘要： We investigate anomalous planar transport phenomena in a recently identified class of collinear magnetic materials known as $d$-wave altermagnets. The anomalous planar effects manifest in a configuration when the applied electric field/temperature gradient, magnetic field, and the measured Hall voltage are all co-planar, but the planar magnetic field is instrumental in breaking $\hat{C}_{4z}\hat{\mathcal{T}}$ symmetry of the $d$-wave altermagnet, where $\hat{\mathcal{T}}$ is the time reversal operator, resulting in a Zeeman gap at a shifted Dirac node and a nonzero Berry curvature monopole. We demonstrate that these systems exhibit nearly half-quantized anomalous planar Hall and planar thermal Hall effects at low temperatures that persist over a range of magnetic fields. The angular dependence of the planar transport reveals a $\cos2\phi$ dependence on the magnetic field direction, where $\phi$ is the azimuthal angle made by the magnetic field. We also discuss the anomalous planar Nernst effect, or transverse thermopower, and demonstrate that the Nernst conductivity peaks when the chemical potential lies just outside the induced Zeeman gap and vanishes within the gap. We further explore the dependence of all three coefficients on the polar and the azimuthal angle of the magnetic field when it is rotated in the full $3D$ space. Our results reveal the presence of approximately half-quantized anomalous planar thermal Hall plateau for a range of in-plane magnetic fields without requiring topological superconductivity and conducting Majorana modes, and can be probed in experiments in $d$-wave altermagnets.