AI 中文总结
研究量子霍尔扫描探针图像，通过朗道能级投影等构建泛函，在不同传输 regime 得出结果，如强场 regime 中热电对比度关系等，还给出石墨烯几何形状的灵敏度等，将视觉解释转为定量可观测性测试。
AI 中文摘要
量子霍尔扫描图像常被解读为局部电势、温度或粘度的图谱，而探针记录的是传输算子的有限分辨率泛函。我们利用朗道能级投影、粒子数沃德恒等式、减去磁化的热电传输、流体动力学斯托克斯 - 欧姆反演和有限尖端费舍尔信息来构建此泛函。在强场、尖锐朗道能级 regime 中，光滑标量缺陷的缺陷诱导热电和电霍尔对比度满足特定关系，且热电对比度零点由能量加权确定。在流体动力学 regime 中，可测量的 \(q^2\) 张量振幅混合了多种通道，霍尔奇数图像本身并非霍尔粘度测量。对于代表性石墨烯几何形状，通过特定拟合在特定信噪比下有一定灵敏度，边界滑移是限制干扰因素。该框架将量子霍尔纳米显微镜的视觉解释转变为对电、热电和粘性响应通道的定量可观测性测试。
英文摘要
Quantum Hall scanning images are often read as maps of a local potential, temperature, or viscosity, whereas a probe records a finite-resolution functional of a transport operator. We formulate this functional using Landau-level projection, a particle-number Ward identity, magnetization-subtracted thermoelectric transport, a hydrodynamic Stokes-Ohm inversion, and finite-tip Fisher information. Two results follow in complementary transport regimes. In the strong-field, sharp-Landau-level regime, the defect-induced thermoelectric and electrical Hall contrasts of a smooth scalar defect obey $δα_{xy}^{tr}/δσ_{xy}=(E_c-μ)/(eT)$. At the retained long-wavelength order, the orbital form factor, defect geometry, and common tip kernel cancel after the heat-magnetization current is removed, so the zero of the thermoelectric contrast is pinned by energy weighting at $E_c=μ$ rather than by defect shape. In the hydrodynamic regime, the measurable $q^2$ tensor amplitudes mix Hall, longitudinal, transverse, boundary, electrothermal, and kinetic channels, so a Hall-odd image is not by itself a Hall-viscosity measurement. For a representative graphene geometry, a Schur-complement fit against the stated nuisance library yields a conditional one-standard-deviation sensitivity of approximately 68 square nanometers at SNR0 = 200, with boundary slip the limiting nuisance. The framework turns visual interpretation of quantum Hall nanoscopy into a quantitative observability test for electrical, thermoelectric, and viscous response channels.
CommentsComments: 18 pages, 5 figures; includes Supplemental Material
