发表机构
Facultad de Ingeniería y Ciencias Agrarias, Pontificia Universidad Católica Argentina; Departamento de Física Teórica de Interacciones Fundamentales y Sistemas Complejos, Laboratorio Tandar, Comisión Nacional de Energía Atómica（阿根廷天主教宗座大学工程与农业科学学院; 阿根廷国家原子能委员会基础相互作用与复杂系统理论物理部坦达实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于二维费米海的拓扑分类，发现密度矩阵呈现各向异性弗里德尔振荡，并建立动量空间填充与电导率间的等周参数标度关系，揭示拓扑输运特征。
AI 中文摘要
本文探讨了基于离散对称群 $\Gamma$ 的平坦轨道流形 $\mathbb{R}^2/\Gamma$ 对自由粒子二维费米海进行近期拓扑分类的两个物理后果。第一个后果是对费米长度与（无限）热长度所围介观窗口内空间密度行为的研究。研究表明，单粒子密度矩阵表现出尖锐的方向各向异性，编码了实空间衍射图案，即费米海的夫琅禾费型图样，以各向异性弗里德尔振荡的形式揭示背景晶格 $\Gamma$ 的点群对称性。作为示例，详细处理了 $p4m$ 和 $p6m$ 晶体学平坦轨道流形的特例。第二个物理后果是建立了动量空间填充与电输运之间的显式几何对应关系。利用几何测度论，提出了纵向电导率 $\sigma_{xx}$ 作为占据轨道域等周参数 $\cal{I}$ 函数的平均场表达式，满足标度律 $ \sigma_{xx} \propto 1/\sqrt{\cal{I}}$。该拓扑输运公式自然包含了先前描述的“几何绝缘体”中电导率消失（$\sigma_{xx} \to 0$）的情况，将等周参数提升为导体中拓扑和几何相的有效描述符。
英文摘要
Two physical consequences of the recent topological classification of 2d Fermi seas for free particles based on flat orbifolds $\mathbb{R}^2/Γ$ of discrete symmetry $Γ$, are explored. The first is an study of the spatial density behavior inside the mesoscopic window enclosed by the Fermi and (infinite) thermal lengths. It is shown that the single-particle density matrix exhibits a sharp directional anisotropy, encoding a real space diffraction pattern, {\it i.e.}, a Fraunhofer-like diagram of the Fermi sea, that reveals the point-group symmetries of the background lattice $Γ$ in the form of anisotropic Friedel oscillations. As examples, the special cases of the $p4m$ and $p6m$ crystallographic flat orbifolds are treated in some detail. The second physical consequence is the establishment of an explicit geometric correspondence between momentum-space packing and electrical transport. A mean-field expression for the longitudinal electrical conductivity $σ_{xx}$ as a function of the {\it isoperimetric parameter} $\cal{I}$ of the occupied orbifold domain by utilizing geometric measure theory is presented, satisfiying the scaling law $ σ_{xx} \propto 1/\sqrt{\cal{I}}$. The topological transport formula naturally incorporates the vanishing conductivity ($σ_{xx} \to 0$) of the previously described ``geometric insulators,'' promoting the isoperimetric parameter as an efficient descriptor for topological and geometric phases in conductors.
Comments22 pages, 2 figures
