Negative Poisson's Ratio in Two-Dimensional Materials

Materials characterised by a negative Poisson’s ratio (NPR), often termed auxetic materials, exhibit the counterintuitive behaviour of expanding laterally when stretched and contracting when compressed. In the realm of two-dimensional (2D) systems, this phenomenon arises not only from engineered re-entrant or hinged geometries but also from intrinsic electronic and bonding features. Since graphene’s isolation, a diverse family of atomically thin crystals has been shown to host auxetic responses, driven by mechanisms ranging from orbital hybridisation to anisotropic lattice architectures. These 2D auxetic materials promise enhanced shear resistance, superior energy absorption and tunable electromechanical properties. They hold potential for flexible electronics, adaptive sensors, nanomechanical actuators and advanced metamaterials. Recent advances have unveiled new classes of 2D oxides, transition metal dichalcogenides and group-V layered materials with intrinsic NPR, as well as metamorphic superlattices and origami-inspired architectures with programmable auxeticity. The interplay of strain, electronic structure and interlayer interactions continues to guide the discovery and design of next-generation auxetic 2D materials with tailored mechanical and multifunctional performance.

Research from Nature Portfolio

Recent theoretical predictions have identified a suite of nonlayered oxide monolayers exhibiting exceptionally high dielectric constants and intrinsic NPR. Computational screening uncovered more than fifty exfoliable oxide monolayers, among which GeO₂ stands out with a Poisson’s ratio below zero, ultra-high κ values and compatibility with prototypical 2D semiconductors in heterostructures. Another seminal study revealed that monolayer crystals of transition-metal dichalcogenides in the 1T phase intrinsically exhibit in-plane auxetic behaviour. This discovery attributes the NPR to strong coupling between metal d-orbitals and chalcogen p-orbitals within a triangular pyramid motif, demonstrating that auxeticity can originate from pure electronic effects rather than geometric re-entrance. Earlier foundational work on a 2D Be₅C₂ monolayer showcased quasi-planar pentacoordinate carbon units and unexpected negative Poisson’s ratio, highlighting how unconventional bonding topologies in atomically thin materials yield unique mechanical and electronic functionalities.

Negative Poisson's Ratio in Two-Dimensional Materials publication trend

The graph below shows the total number of articles in negative poisson's ratio in two-dimensional materials across all publications each year (not limited to Nature Index journals).

Technical terms

Poisson’s ratio: A dimensionless parameter describing the transverse strain response of a material to uniaxial stress.

Auxetic effect: The phenomenon in which a material exhibits a negative Poisson’s ratio, expanding laterally when stretched.

Two-dimensional materials: Crystalline solids consisting of a single layer or few atomic layers, with strong in-plane bonds and weak out-of-plane interactions.

Strain engineering: The deliberate application of mechanical deformation to modify a material’s structural, electronic or optical properties.

References

1. Prediction of nonlayered oxide monolayers as flexible high-κ dielectrics with negative Poisson’s ratios. Nature Communications (2023).
2. Multiscale functionalized graphene origami metamaterials enable programming thermoelectric performance of flexible energy harvesters. Carbon (2024).
3. Intralayer Negative Poisson's Ratio in 2D Black Arsenic by Strain Engineering. Small Structures (2023).
4. Semi-metallic Be5C2 monolayer global minimum with quasi-planar pentacoordinate carbons and negative Poisson’s ratio. Nature Communications (2016).
5. Negative Poisson’s ratio in 1T-type crystalline two-dimensional transition metal dichalcogenides. Nature Communications (2017).
6. Negative Poisson’s ratio in two-dimensional honeycomb structures. npj Computational Materials (2020).
7. Tunable Negative Poisson’s Ratio in Van der Waals Superlattice. Research (2021).