边缘扩散的破坏
Breakdown of Diffusion on the Edge
摘要：
我们发现，肮脏的量子霍尔系统在其边缘表现出大的流体动力学波动，导致在Kardar-Parisi-Zhang普适性类$ω\simeq ck - i \mathcal D k^{3/2} $中的阻尼电荷激发。边缘的耗散光学电导率在低频$σ(ω) \sim 1/ω^{1/3}$处是奇异的。这些结果是直接后果的电荷连续性关系，手征异常，和热化的边缘-特别是平移不变性是不假定的。热的扩散也同样会破裂，其普适性取决于体热霍尔电导率是否消失。我们进一步建立了表面手性金属的波动流体力学理论，其中电荷波动对输运进行了对数修正。
英文摘要：
We show that dirty Quantum Hall systems exhibit large hydrodynamic fluctuations at their edge that lead to anomalously damped charge excitations in the Kardar-Parisi-Zhang universality class $ω\simeq ck - i \mathcal D k^{3/2} $. The dissipative optical conductivity of the edge is singular at low frequencies $σ(ω) \sim 1/ω^{1/3}$. These results are direct consequences of the charge continuity relation, the chiral anomaly, and thermalization on the edge -- in particular translation invariance is not assumed. Diffusion of heat similarly breaks down, with a universality class that depends on whether the bulk thermal Hall conductivity vanishes. We further establish the theory of fluctuating hydrodynamics for surface chiral metals, where charge fluctuations give logarithmic corrections to transport.
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