Researchers Uncover 17 Anomalous Transport Properties in 2D Materials, Breaking Major Symmetries

Recent discoveries of unusual transport behaviours, where a response appears at an angle to the force driving it, have sparked intense research into the fundamental symmetries governing material properties, and Elizabeth J. Dresselhaus, Sanjay Govindjee, and Kranthi K. Mandadapu, all from the University of California, Berkeley, now present a comprehensive framework for understanding these phenomena in two-dimensional materials. The team identifies these unexpected responses as part of a wider range of behaviours arising from broken symmetries, which they term “anomalous” properties, and develops a system for classifying them based on the material’s structure. This work reveals how specific symmetries constrain these responses, effectively grouping materials by their potential for exhibiting these unusual behaviours, and focuses on how this applies to electrical conductivity, as well as the material’s resistance to flow and deformation. These findings offer a powerful tool for predicting and understanding emergent properties in novel materials, with implications for diverse systems ranging from engineered textiles to twisted bilayer graphene.

Sensors frequently describe linear relations between fluxes and the gradients that drive them, particularly when parity and time-reversal symmetries are broken. This work identifies such odd properties as a subset of a broader class of symmetry-breaking behaviours, termed “anomalous. ” Researchers develop a classification of anomalous properties, described by second and fourth order tensors in anisotropic two-dimensional materials that maintain discrete rotational and reflection symmetries, characterised by the 17 wallpaper groups. To achieve this, the team presents representation theorems for these tensors, identifying which components are constrained for specific spatial symmetries and thereby allowing materials to be graded.

Tensor Symmetry and Viscosity Derivations

This is a remarkably detailed and comprehensive analysis of tensor symmetry in materials, specifically focusing on viscosity, but applicable to other tensors like elasticity. The work systematically derives the resulting tensor structures for viscosity based on the symmetry operations of various wallpaper groups. The approach uses complex representations of symmetry operations and then relates them back to real-valued components, a powerful and elegant technique. Detailed step-by-step derivations of tensor components for each symmetry group are presented, clearly explaining the use of complex components and their relation to real values.

The document correctly identifies the emergence of odd viscosity, or normal-shear coupling, in groups like C3 and C6, and the absence of such behavior in groups like D3 and D6. Isotropic materials, like those with D3 or D6 symmetry, exhibit isotropic behavior, fully determined by two independent parameters, with no normal-shear coupling. Anisotropic materials with C3 or C6 symmetry exhibit odd viscosity, characterized by normal-shear coupling terms, requiring three independent parameters. Higher symmetry groups impose more constraints on tensor components, reducing the number of independent parameters.

The methodology used to analyze viscosity can be extended to other tensors, providing a powerful tool for understanding material symmetry and behavior. While the analysis is thorough, some notation could be slightly more consistent, and adding diagrams illustrating the symmetry operations for each group would significantly enhance understanding. Explicitly stating that the methodology applies to other tensors, such as elasticity and piezoelectricity, would broaden the impact of the work.

Symmetry Dictates Anomalous Material Properties

Researchers have established a comprehensive classification of “anomalous” properties in two-dimensional materials, expanding beyond previously understood “odd transport” phenomena, and revealing a deeper connection between symmetry and material behavior. This work identifies that these unusual properties are not isolated instances, but rather a subset of behaviors arising from broken symmetries within materials. The team developed a system for categorizing these properties using order tensors, mathematical tools that describe how materials respond to external forces, and linked these tensors to the 17 distinct wallpaper groups which define spatial symmetries. The classification scheme allows scientists to predict which materials will exhibit anomalous responses based on their symmetry, grouping materials into classes that share similar behaviors.

This predictive power is demonstrated through analysis of electrical resistivity, viscosity, and elasticity, revealing how symmetry dictates a material’s response to stress and flow. Investigations into knitted fabrics and twisted bilayer graphene reveal how subtle structural arrangements can lead to significant anomalous properties. Specifically, the research suggests that the return point memory observed in knitted fabrics and the unconventional superconductivity in twisted bilayer graphene are both manifestations of these symmetry-breaking phenomena. This work provides a powerful new lens for understanding and designing materials with tailored, unusual properties, opening avenues for innovation in areas ranging from textiles to advanced electronics.

Symmetry Breaking Predicts Anomalous Material Responses

This research establishes a comprehensive classification of anomalous material properties, extending beyond previously observed odd transport phenomena, and applies it to two distinct two-dimensional materials. The team demonstrates that these anomalies are linked to the breaking of fundamental symmetries within materials, specifically relating to how they respond to applied forces or gradients. By utilizing the mathematical framework of wallpaper groups, which describe repeating patterns, researchers identified constraints on material behavior based on their underlying symmetry, allowing for the prediction of which materials might exhibit anomalous responses. The study highlights the potential for both twisted bilayer graphene and knitted fabrics to display these anomalies, though with important distinctions.

While twisted bilayer graphene, depending on its twist angle, can theoretically support a wide range of anomalous behaviors, the research demonstrates that fabrics are constrained by the laws of thermodynamics, specifically the second law. This limits the possibility of anomalous elasticity in fabrics, but does not preclude other anomalous behaviors like odd inelasticity, particularly in the presence of hysteresis, or path-dependent behavior, during deformation. The authors acknowledge that their analysis focuses on idealized materials and that real-world complexities could influence these predictions. Future research could explore the experimental verification of these theoretical predictions and investigate the potential for designing materials with tailored anomalous properties, particularly focusing on exploiting hysteretic behaviors in fabrics.