Orbital orders in correlated electron systems have attracted great attention in condensed matter. Recently, Pr-based materials (PrT2X20; T=Ti, V, etc.,X=Al ,etc.) have intensively studied, since they show orbital orders, non-Fermi liquids, and superconductivity. Their low-energy physics is attributed to the Γ3 non-Kramers crystalline-electric-field ground state doublet well separated from the excited states and have E quadrupole and A2 octuple moments in Td symmetry.
In this talk, we discuss two topics related to quadrupole orders. The first is magneto-electric (current) effects under antiferromagnetic quadrupole (AFQ) orders in a diamond structure [1]. Since the Pr ions form the diamond structure in the Pr-based materials, when AFQ takes place, the inversion symmetry is broken, which leads to finite magnetic response when electric field is applied and vice versa. This can be useful for identifying the order parameters, since the response strongly depends on the order parameters. In addition, we briefly discuss the way to generate (Kramers) Weyl points under the AFQs. The second is about unusual FQ order under magnetic fields in PrTi2Al20 [2]. Usually, when magnetic field is applied in z direction, 3z2-r2 type FQ domain is stabilized. However, this is not the case in this material [2]. We point out that magnetic-field induced quadrupole-quadrupole interactions are important for explaining the observed unusual FQ state in this compound and this situation is clear contrast to that in magnetic systems.

References:
[1] T. Ishitobi and KH, arXiv:1903.01103.
[2] T. Taniguchi et al., arXiv:1903.10215.