noncentrosymmetric

Noncentrosymmetric describes a crystal or material that lacks a center of symmetry, also known as an inversion center. In a centrosymmetric structure, for every point at coordinates (x, y, z) there is an equivalent point at (-x, -y, -z). If this inversion symmetry is absent, the structure is noncentrosymmetric. Such materials can be polar, possessing a spontaneous polarization, or nonpolar, and they belong to crystal classes that do not include an inversion center. Some noncentrosymmetric crystals are chiral and belong to Sohncke groups, which contain only proper rotations and translations and can exhibit optical activity.

The absence of inversion symmetry has important physical consequences. Noncentrosymmetric crystals can exhibit piezoelectricity, where mechanical stress induces electric polarization, and pyroelectricity, where temperature changes generate polarization. They also commonly display nonlinear optical effects, most notably second-harmonic generation, where incident light at a frequency is efficiently converted to light at twice that frequency. In contrast, centrosymmetric crystals generally suppress such dipole-allowed nonlinear effects.

In condensed matter physics, noncentrosymmetric superconductors lack inversion symmetry, leading to antisymmetric spin-orbit coupling. This coupling can enable mixing of spin-singlet and spin-triplet pairing, producing unconventional superconducting properties and responses to magnetic fields. Examples studied in research include certain intermetallic compounds and layered materials.

Overall, noncentrosymmetric materials are central to applications in nonlinear optics, electro-optics, and advanced superconducting systems, while also informing fundamental studies of symmetry in solid-state physics.