发表机构
SISSA; Roma Tre University（的里雅斯特高等研究学院; 罗马三大）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对二维晶格无相互作用半金属电子系统，利用欧几里得多体形式主义推导拓扑相变处电导率矩阵的显式公式，计算相关量子霍尔流体模型的电导率矩阵，阐明其普适性或非普适性特征。
AI 中文摘要
针对晶格上的一类通用二维无相互作用半金属电子系统，我们利用欧几里得多体形式主义推导了完整电导率矩阵的显式公式。半金属相发生于两个布洛赫带在费米能处形成锥形交叉之时，通常出现在不同整数量子霍尔相的过渡阶段。与仅由费米能级处锥形形状决定的纵向电导率不同，横向电导率显著由能带的锥形结构以及两个相邻拓扑相的性质共同决定。一般而言，在半金属态中，纵向和横向电导率均不按通用电导率量子的整数倍量子化；然而，若假设费米点处线性哈密顿量呈现涌现旋转对称性，则电导率矩阵的普适性得以恢复。利用该公式，我们计算了多个与物理相关的拓扑相变处量子霍尔流体模型的电导率矩阵，展示了横向电导率按$e^2/h$的半整数倍量子化的情形，以及横向电导率连续依赖于外部应变参数的情形，从而阐明了其普适性或非普适性特征。
英文摘要
For a general class of two-dimensional non-interacting semi-metallic electron systems on a lattice, we derive an explicit formula for the whole conductivity matrix, by using Euclidean many-body formalism. The semi-metallic phase takes place whenever two Bloch bands touch at the Fermi energy with conical intersections and generally occurs at the transition between distinct integer quantum Hall phases. Unlike the longitudinal conductivity (which depends solely on the shape of the cones at the Fermi level), the transverse conductivity is remarkably determined both by the conical structures of the bands and by the nature of the two nearby topological phases. Generically, in the semi-metallic state, neither the longitudinal nor the transverse conductivities are quantized in integer multiples of a universal conductivity quantum; however, universality of the conductivity matrix is restored under the assumption of emergent rotational symmetry of the linearized Hamiltonian at the Fermi points. Using our formula, we compute the conductivity matrix for several physically relevant models of quantum Hall fluids at the topological phase transition, exhibiting cases where the transverse conductivity is quantized in half-integer multiples of $e^2/h$ and cases where it depends continuously on an external strain parameter, thus shedding light on its universality or non-universality features.
Comments47 pages, 5 figures, 2 ancillary Mathematica files
