Rotation, Electric-Field Responses, and Absolute Enantioselection in Chiral Crystals

On the Definition of Chirality and Enantioselective Fields

“…The typical example of the elemental tellurium is found in ref. [19]. It is notable that G 0 term in chiral tellurium is quite large with respect to other terms in the Hamiltonian.…”

“…, and so on where Q a; b; c and M a; b are the independent electric and magnetic dipoles, respectively. It is interesting to see, in a physical point of view, that such a structure indeed appears both in the Hamiltonian of tellurium as a lattice-spin coupling, R • (l × σ), [19] and in the parity-violation term due to weak interaction of elementary particles (see next section), which is a source of chiral response.…”

“…In general, $${{G}_{0}}$$ can be decomposed into $${{{\bf Q}}_{a}\cdot{}\left({{\bf Q}}_{b}\times {{\bf Q}}_{c}\right)}$$ , $${{{\bf Q}}_{a}\cdot{}\left({{\bf M}}_{a}\times {{\bf M}}_{b}\right)}$$ , and so on where $${{{\bf Q}}_{a,\ b,\ c}}$$ and $${{{\bf M}}_{a,\ b}}$$ are the independent electric and magnetic dipoles, respectively. It is interesting to see, in a physical point of view, that such a structure indeed appears both in the Hamiltonian of tellurium as a lattice‐spin coupling, R ⋅ ( l × σ ), [19] and in the parity‐violation term due to weak interaction of elementary particles (see next section), which is a source of chiral response.…”

Symmetry-adapted modeling for molecules and crystals

“…In this sense, the symmetry-adapted modeling as Eq. ( 33) is also useful to analyze various linear and nonlinear response functions, which bridges the gap between the phenomenological approaches and DF computations [14,23]. The systematic analysis method for response functions proposed in Ref.…”

Cluster Toroidal Multipoles Formed by Electric-Quadrupole and Magnetic-Octupole Trimers: A Possible Scenario for Hidden Orders in Ca$_5$Ir$_3$O$_{12}$

“…Among them, the odd-parity toroidal multipoles, i.e., the odd-rank MT and even-rank ET multipoles, have been extensively studied, since they give rise to physical phenomena related to the spatial-parity breaking, such as the magnetoelectric effect under the MT dipole, [8][9][10][11][12][13][14][15][16][17] nonlinear (spin) transport [18][19][20][21][22][23][24][25] and nonreciprocal magnon excitations under the MT dipole and octupole, [26][27][28][29][30][31] and Edelstein effect and rotation-field induced electric polarization under the ET monopole and quadrupole. [32][33][34][35][36][37] These unconventional electronic orderings have been proposed and identified in metallic materials, such as the MT dipole orderings in UNi 4 B, 12,[38][39][40][41][42][43][44] Ce 3 TiBi 5 , [45][46][47][48] and CeCoSi 36,[49][50]…”