论文标题
轨道磁四极矩在高阶拓扑阶段
Orbital magnetic quadrupole moment in higher order topological phases
论文作者
论文摘要
我们在三维高阶拓扑阶段研究轨道磁四极矩（MQM）。就像电动四极矩与有限样品的边界上的电荷响应相关的电动矩一样，MQM的对角线成分表现为表面定位的磁化和铰链电流。铰链电流通常不等于在铰链处相交的表面磁化的差，并且我们表明该不匹配是由大量MQM精确量化的。我们在平板几何形状中得出了用于层分辨磁化的量子机械公式，并使用它来定义具有间隙边界的系统的MQM。然后，我们的形式主义被应用于几个高阶拓扑阶段，我们表明MQM可以区分某些内在和边界的高阶拓扑绝缘子中的阶段。然后，我们证明MQM相对于化学电位的衍生物可以用作量化的拓扑不变性，类似于获得2D Chern数作为磁化剂相对于化学电位的衍生物。这些不变性提供了一种表征3D时间反转破坏绝缘子的新方法，这些绝缘子的磁化化消失了。
We study the orbital magnetic quadrupole moment (MQM) in three dimensional higher-order topological phases. Much like electric quadrupole moment, which is associated with a charge response on the boundaries of a finite sample, the diagonal components of the MQM manifest as surface-localized magnetization and hinge currents. The hinge current is generally not equal to the difference of surface magnetizations that intersect at the hinge, and we show this mismatch is precisely quantified by the bulk MQM. We derive a quantum mechanical formula for the layer-resolved magnetization in slab geometries and use it to define the MQM of systems with gapped boundaries. Our formalism is then applied to several higher-order topological phases, and we show that the MQM can distinguish phases in some intrinsic and boundary-obstructed higher-order topological insulators. We then show that derivatives of the MQM with respect to the chemical potential can act as quantized topological invariants, similar to obtaining the 2D Chern number as a derivative of the magnetization with respect to the chemical potential. These invariants provide a new way to characterize 3D time-reversal breaking insulators that have vanishing magnetization.
