Orbital magnetic quadrupole moment in higher order topological phases
Orbital magnetic quadrupole moment in higher order topological phases
复制标题
高阶拓扑相中的轨道磁四极矩
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
T. Hughes
中科院分区：
文献类型：
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作者：
Jacopo Gliozzi;Mao Lin;T. Hughes
本文研究了三维高阶拓扑相中的轨道磁四极矩。很像电四极矩，这与有限样品边界上的电荷响应有关，MQM的对角分量表现为表面局部磁化和铰链电流。铰链电流一般不等于表面磁化的差异，相交的铰链，我们表明，这种不匹配是精确量化的散装MQM艾德。我们推导了一个量子力学公式的层分辨磁化板几何形状和使用它来定义系统的MQM间隙边界。我们的形式主义，然后应用到几个高阶拓扑相位，我们表明，MQM可以区分一些内在的和边界阻塞的高阶拓扑绝缘体的相位。然后，我们表明，衍生物的MQM相对于化学势可以作为量子化的拓扑不变量，类似于获得的二维陈数作为一个衍生物的磁化相对于化学势。这些不变量提供了一种新的方法来表征三维时间反转破坏绝缘子，具有消失的磁化。
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.