整数量子霍尔效应中的准局域输运：绝热分离、局域欧姆定律与非压缩条带的焦耳热
Quasilocal transport in the integer quantised Hall effect: adiabatic separation, local Ohm's law, and Joule heating of the incompressible strips
- Vocational School, Atlas University（阿特拉斯大学职业学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过分离快速回旋运动与慢速引导中心景观，建立准局域欧姆模型，揭示非压缩条带吸引电流并产生焦耳热，且热效应受损失定律限制。
AI中文摘要：
我们围绕一个核心思想重新审视整数量子霍尔输运的半经典路径：将快速、量子化的回旋运动与缓慢、自洽屏蔽的引导中心景观分离。正则作用的玻尔-索末菲量子化确定了朗道能谱；平滑的约束将其转化为具有绝热参数$\ell|\nabla V|/\hbar\omega_c$的玻恩-奥本海默曲面；屏蔽提供了自洽场。输运是准局域的，$R_H=\int\rho_Hj_y\\,dx/\int j_y\\,dx$，其中$j_y\propto1/\rho_l$，因此在正则化的局域欧姆模型中，非压缩条带按权重吸引电流，计算出的焦耳功率分布跟随电流分布。在线性响应中，冻结剖面模型的内禀静电交流修正是无功的，$\mathrm{Im}\\,R_H\propto\omega$，在$2$~MHz以下，$\mathrm{Re}\\,R_H-R_H^{\rm DC}\propto\omega^{2}$低于$10^{-9}$。当电流在$1$--$5\\,\mu$A下反馈回静电学中（此时霍尔压降为一个到五个回旋能隙），驱动边界条件破坏了条的反射对称性，霍尔压降集中在一个条带中（在电流反转时交换至$10^{-9}$），平台从其低场侧变窄，而对于所研究的GaAs参数，其高场边缘保持在$\nu(0)=2$。受Akera启发的局域横向热闭合，作为冻结剖面上的后处理过程，采用两种声子损失定律进行评估，表明低场侧的窄载流条带可能加热到晶格温度的量级；采用激活热容闭合时，冷条带在模型相关的$0.3$--$2\\,\mu$A电流下失去其稳态解。热结论受损失定律和冻结剖面的限制，作为估计呈现。
英文摘要：
We reassess the semiclassical route to integer quantum Hall transport around one idea: the separation of fast, quantised cyclotron motion from a slow, self-consistently screened guiding-centre landscape. Bohr--Sommerfeld quantisation of the canonical action fixes the Landau spectrum; smooth confinement turns it into Born--Oppenheimer surfaces with adiabatic parameter $\ell|\nabla V|/\hbarω_c$; screening supplies the self-consistent field. Transport is quasilocal, $R_H=\intρ_Hj_y\,dx/\int j_y\,dx$ with $j_y\propto1/ρ_l$, so within the regularised local Ohm model the incompressible strips attract the current by weight and the computed Joule-power profile follows the current profile. In linear response the intrinsic electrostatic AC correction of the frozen-profile model is reactive, $\mathrm{Im}\,R_H\proptoω$, with $\mathrm{Re}\,R_H-R_H^{\rm DC}\proptoω^{2}$ below $10^{-9}$ up to $2$~MHz. With the current fed back into the electrostatics at $1$--$5\,μ$A, where the Hall drop is one to five cyclotron gaps, the driven boundary condition breaks the reflection symmetry of the bar, the Hall drop concentrates in one strip (interchanged to $10^{-9}$ under current reversal), and the plateau narrows from its low-field flank while, for the GaAs parameters studied, its high-field edge stays at $ν(0)=2$. A local transverse thermal closure inspired by Akera, evaluated as a post-process on the frozen profile with two phonon-loss laws, indicates that the narrow current-carrying strips of the low-field flank may heat by of order the lattice temperature; with the activated-heat-capacity closure the cold strip loses its stationary solution at model-dependent currents of $0.3$--$2\,μ$A. The thermal conclusions are bounded by the loss law and by the frozen profile, and are presented as estimates.
