标题： 各向异性二维材料的异常张量性质 显示英文标题

标题： Anomalous tensorial properties of anisotropic 2D materials

摘要： 奇输运现象——定义为与施加的梯度正交的通量响应——最近在各向同性系统中被观察到，已有大量提出的模型和实验来研究这些效应。 奇输运体现在描述驱动它们的通量和梯度之间线性关系的张量中，尤其是在宇称和时间反演对称性被破坏时。 在本工作中，我们将这些奇性质识别为更广泛的主对称性破坏行为的一个子集，我们将其称为“异常”。 我们开发了一种分类方法，用于描述各向异性二维材料中由$2^\mathrm{nd}$和$4^\mathrm{th}$阶张量所描述的异常性质，这些材料保持离散旋转和反射对称性，由17种墙纸群表征。 为此，我们提出了这些张量的表示定理，确定了在特定空间对称性下哪些分量受到约束，从而允许将材料分为表现出异常响应或不表现出异常响应的类别。 我们重点讨论电导率背景下$2^\mathrm{nd}$阶张量以及粘度和弹性背景下$4^\mathrm{th}$阶张量。 这些发现广泛适用于研究新型涌现材料性质。 为了说明这一点，我们讨论了这些发现对两种截然不同的二维材料的影响，这两种材料最近在凝聚态物理领域引起了关注：编织织物和扭曲双层石墨烯。 显示英文摘要

摘要： Odd transport phenomena -- defined as a flux response orthogonal to an applied gradient -- have been recently observed in isotropic systems, with a multitude of proposed models and experiments to study these effects. Odd transport manifests in tensors that describe linear relations between fluxes and gradients that drive them, particularly when parity and time-reversal symmetries are broken. In this work, we identify such odd properties to be a subset of a broader class of major-symmetry-breaking behaviors, which we term ``anomalous." We develop a classification of anomalous properties described by $2^\mathrm{nd}$ and $4^\mathrm{th}$ order tensors in anisotropic 2D materials that maintain discrete rotational and reflection symmetries, characterized by the 17 wallpaper groups. To this end, we present representation theorems for these tensors, identifying which components are constrained for specific spatial symmetries and thereby allowing materials to be grouped into classes that exhibit anomalous responses or not. We focus our discussion on $2^\mathrm{nd}$ order tensors in the context of electrical resistivity and on $4^\mathrm{th}$ order tensors in the context of viscosity and elasticity. These findings are broadly applicable to the study of novel emergent material properties. To illustrate this, we discuss implications of our findings for two very different 2D materials that have recently garnered attention in condensed matter physics: knitted fabrics and twisted bilayer graphene.