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In condensed matter physics, various types of phase transitions have been observed and their nature has been clarified by intensive experimental and theoretical studies. However, the order parameter of the phase below critical temperature T₀ = 17.5 K in URu₂Si₂ has still been uncovered since its discovery in 1985 despite many efforts by several researchers. With the latest and high-resolution experiments, such as nuclear magnetic resonance, muon spin relaxation, and resonant X-ray scattering measurements, the symmetry of local environment of ions has been narrowed down. This enigmatic ordered phase is called the hidden order. Meanwhile, the candidate order parameter compatible with known experimental facts has recently been clarified from the symmetry aspect by Kambe et al. [Phys. Rev. B 97, 235142 (2018)], although its microscopic object and experimental identification have still been unclear.

In the present study, we theoretically propose that a staggered alignment of chiral charge, that appears in association with electron motion in crystals, corresponds to the hidden order parameter in URu₂Si₂, satisfying all the symmetry conditions accumulated by many experiments. The chiral charge represents composite degrees of freedom consisting of a spin and a hybridization between orbitals with different orbital angular momenta that can be regarded as a pseudoscalar monopole distinct from conventional electric and magnetic monopoles. Because it only locally breaks the mirror and inversion symmetries, the observation using microscopic probes is difficult; therefore, the order parameter is still hidden. By considering the minimal effective d-f hybridized model on the itinerant picture, we propose the methods to observe the hidden order parameter in experiments. One is an electric-field-induced static rotational deformation in bulk. The other is the observation of states at the surface or domain boundary that can be detected by state-of-the-art experimental methods such as nuclear quadrupole resonance and scanning transmission electron microscopy combined with convergent-beam electron diffraction under an electric field and circularly polarized second harmonic generation microscopy. Our result may provide the last information to resolve the hidden order parameter in URu₂Si₂.

(Written by Satoru Hayami on behalf of all authors.)