Quantification of chirality based on electric toroidal monopole

Quantification of chirality based on electric toroidal monopole

22 February 2024 | A. Inda, R. Oiwa, S. Hayami, H. M. Yamamoto, and H. Kusunose
The paper proposes a method to quantify chirality using electric toroidal monopoles (ETMs), which are practical entities reflecting time-reversal even pseudoscalar objects. The authors analyze twisted methane at the quantum-mechanical level, demonstrating that ETMs serve as quantitative indicators for chirality. They find that the handedness of chirality corresponds to the sign of the expectation value of the ETM, with spin-dependent imaginary hopping between hydrogen atoms being the most crucial factor. The relativistic spin-orbit coupling within carbon atoms is found to be irrelevant for chirality in this context. The study provides a microscopic understanding of chirality and suggests that the approach can be applied to other chiral molecules and crystals.The paper proposes a method to quantify chirality using electric toroidal monopoles (ETMs), which are practical entities reflecting time-reversal even pseudoscalar objects. The authors analyze twisted methane at the quantum-mechanical level, demonstrating that ETMs serve as quantitative indicators for chirality. They find that the handedness of chirality corresponds to the sign of the expectation value of the ETM, with spin-dependent imaginary hopping between hydrogen atoms being the most crucial factor. The relativistic spin-orbit coupling within carbon atoms is found to be irrelevant for chirality in this context. The study provides a microscopic understanding of chirality and suggests that the approach can be applied to other chiral molecules and crystals.
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