Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule
Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule
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DOI：
10.1103/physrevlett.123.246602
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发表时间：
2019-12-12
影响因子：
8.6
通讯作者：
Sodemann, I.
中科院分区：
文献类型：
--
作者：
Matsyshyn, O.;Sodemann, I.
众所周知，在布洛赫带中运动的电子会获得与带的贝里曲率成正比的异常霍尔速度，这是导致具有破时间反转对称性的材料中的固有线性霍尔效应的原因。在这里，我们证明了电子加速度也有一个与Berry曲率偶极子成正比的异常修正，这是最近在具有破逆对称性的材料中发现的非线性霍尔效应的原因。这使我们能够揭示Berry曲率偶极子作为德鲁德权重的非线性版本的更深层次的含义，德鲁德权重作为金属中破碎反转对称性的可测量的阶参数。通过证明整流电导率的频率积分仅取决于Berry连接而不取决于能带能量，我们还推导出了时间反转不变材料中的量子整流和规则。该和规则的带内谱权由Berry曲率偶极子类德鲁德峰耗尽，带间谱权也完全由Berry连接控制。这个求和规则打开了一扇门，寻找基于Berry几何波段的替代光伏技术。我们还描述了Weyl半金属的整流性质，这是研究这些效应的一个有希望的平台。
Electrons moving in a Bloch band are known to acquire an anomalous Hall velocity proportional to the Berry curvature of the band which is responsible for the intrinsic linear Hall effect in materials with broken time-reversal symmetry. Here, we demonstrate that there is also an anomalous correction to the electron acceleration which is proportional to the Berry curvature dipole and is responsible for the nonlinear Hall effect recently discovered in materials with broken inversion symmetry. This allows us to uncover a deeper meaning of the Berry curvature dipole as a nonlinear version of the Drude weight that serves as a measurable order parameter for broken inversion symmetry in metals. We also derive a quantum rectification sum rule in time reversal invariant materials by showing that the integral over frequency of the rectification conductivity depends solely on the Berry connection and not on the band energies. The intraband spectral weight of this sum rule is exhausted by the Berry curvature dipole Drude-like peak, and the interband weight is also entirely controlled by the Berry connection. This sum rule opens a door to search for alternative photovoltaic technologies based on the Berry geometry of bands. We also describe the rectification properties of Weyl semimetals which are a promising platform to investigate these effects.