GoKawiilStrain engineering has long been recognized as a powerful means to tailor material functionalities24,25,26,27. Well-established examples, such as piezoelectricity28 and piezomagnetism29, have been extensively studied and led to widespread applications30. However, the linear coupling of strain to chirality has not yet been investigated. Whereas strain, polarization and magnetization are directional quantities, chirality is a non-directional pseudoscalar that reverses sign under inversion symmetry31. This distinction makes the coupling between strain and chirality elusive.
The piezochiral effect is defined here as the induction of chirality in a system by the application of strain (Fig. 1a). Mathematically, the effect can be written as
$$C=\sum _{{ij}}{T}_{{ij}}{\varepsilon }_{{ij}}$$ (1)
in which C denotes the strain-induced chirality, ε ij is the strain tensor and T ij is the piezochiral tensor, which we introduce here to describe the coupling between strain and chirality (Supplementary Information). Notably, in contrast to many conventional rank-2 tensors, such as the strain tensor, which are even under spatial inversion, the piezochiral tensor changes sign under this symmetry operation.
Fig. 1: The piezochiral effect. Full size image a, An achiral system at equilibrium develops chirality under strain. Switching between tensile strain and compressive strain reverses the handedness of the induced chirality. b, Piezochiral coupling forms. From left to right, four achiral point groups supporting coupling between strain and chirality, their respective coupling forms, visualization of the coupling forms and representative materials. a.u., arbitrary units.
In this study, we focus on the piezochiral effect in achiral systems, in which reversing the sign of strain by switching between compressive and tensile strain allows controlled generation of both left- and right-handedness, analogous to the reversed electric polarization and magnetization in piezoelectricity and piezomagnetism, respectively. Building on this formalism, we performed a systematic group theory analysis. We enumerated all of the achiral crystallographic point groups and identified the cases in which the piezochiral effect is symmetry-allowed (Fig. 1b). For each allowed group, we derived the explicit form of the piezochiral coupling consistent with the symmetry constraints (Supplementary Tables 1–4) and found that it breaks all of the rotoinversion operations to drive the transition from an achiral to a chiral state (Supplementary Table 5).
As a clear example, we consider the point group \(\bar{4}2m\) (D2d), which is achiral in its unstrained equilibrium state. When external strain is applied, the symmetry of the system is lowered to a subgroup in which chirality becomes allowed. In this case, the induced chirality can be described by the coupling
$$C=\theta ({\varepsilon }_{{xx}}-{\varepsilon }_{{yy}})$$ (2)
in which θ is a material-specific coupling coefficient and ε xx and ε yy represent externally applied strain components.
This coupling relation suggests that chirality can be induced in this point group by applying uniaxial strain along either the x or the y direction. Because ε xx and ε yy enter the coupling with opposite signs, applying the same type of strain (compressive or tensile) along the two directions induces chirality of opposite handedness.
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