Spontaneous breaking of space inversion symmetry in itinerant electron system. Unconventional multipole ordering and spin-valley splitting, non-diagonal response

This paper takes up the lattice system with broken space inversion symmetry that is hidden in the system with inversion center, and introduces the latest theoretical studies on unconventional multipole ordering and non-diagonal response brought about by the spontaneous breaking of symmetry in an electron system. Firstly, as general theory, it describes the antisymmetric spin-orbit interaction and odd parity multipoles lurking in sublattice. Then, it discusses the following items: (1) peculiar electronic state accompanied by toroidal ordering in metal, and non-diagonal response such as Hall effect and electromagnetic effect, under the conditions where three-fold rotational symmetry was broken at each lattice point on honeycomb lattice in the odd crystal field, and (2) relationship between antisymmetric spin-orbit interaction and non-diagonal response induced by various charges / spins / orbit ordering of the electronic system on honeycomb lattice. Finally, it describes with expectations for the future research, whether there is a possibility that the ordering state accompanied by odd parity multipoles, which was mentioned above, and the specific electronic state and non-diagonal response associated with the above ordering state lurk in some kinds of substance groups. (A.O.)