二维狄拉克流体中的流体动力学反常霍尔效应
Hydrodynamic Anomalous Hall Effect in a Two-Dimensional Dirac Fluid
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中文总结 AI 辅助
本文针对二维大质量狄拉克费米液体建立动力学理论，研究电子-电子碰撞贡献的反常霍尔效应，发现其响应具有非平凡频率依赖性，且保留动量弛豫机制信息，贡献可与本征热修正比拟。
中文摘要 AI 辅助
在超洁净导体中，电子-电子碰撞可使输运呈现流体动力学特性；在具有贝里曲率的能带中，这类碰撞还会产生两粒子坐标偏移，在外加输运电场时会贡献反常霍尔电流。本文针对具有弱接触相互作用和弱短程无序的二维大质量狄拉克费米液体，建立了该贡献的动力学理论。计算得到的响应在玻恩近似主导阶下与相互作用强度无关，其对反常霍尔电导率的贡献可与本征反常霍尔电导率的热修正相比拟。电子-电子碰撞积分的动量零模的存在，导致本文所研究的反常霍尔响应具有非平凡的频率依赖性；特别地，零频率（直流）极限与零无序极限不可交换。在直流极限下，动量对输运场的响应随动量弛豫率的倒数增长，这使得任意弱的、与能量相关的杂质散射均可通过将守恒动量耦合到电子-电子散射弛豫的模式，产生有限的修正；若先取清洁极限再取零频率极限，该修正会消失。因此，即使整体无序强度趋于零，相互作用诱导的霍尔响应仍保留动量弛豫机制的信息。
英文摘要
In ultraclean conductors, electron-electron collisions can make transport hydrodynamic. In a Berry-curved band, these collisions can also produce two-particle coordinate shifts, which contribute to the anomalous Hall current in the presence of a transport electric field. We develop a kinetic theory of this contribution for a two-dimensional massive Dirac Fermi liquid with weak contact interactions and weak short-range disorder. The computed response is independent of interaction strength at leading Born order. Its contribution to the anomalous Hall conductivity is comparable to the thermal correction to the intrinsic anomalous Hall conductivity. The existence of the momentum zero mode of the electron-electron collision integral leads to a nontrivial frequency dependence of the anomalous Hall response considered in this work. In particular, the limits of vanishing frequency (dc) and vanishing disorder do not commute. In the dc limit, the momentum response to the transport field grows inversely with the momentum relaxation rate. This allows arbitrarily weak, energy-dependent impurity scattering to produce a finite correction by coupling conserved momentum to the modes relaxed by electron-electron scattering. This correction disappears when the clean limit is taken before the zero-frequency limit. As a result, the interaction-induced Hall response retains information about the mechanism of momentum relaxation even as the overall disorder strength tends to zero.
发表机构
- University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
- University of Virginia（弗吉尼亚大学）
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