Considerations on the symmetry of loop order in cuprates

The loop-current state discovered in the pseudogap phase of cuprates breaks time reversal symmetry and lowers the point group symmetry of the crystal. The order parameter and the magnetic structure within each unit cell which is associated with it can be described by a toroidal moment parallel to the copper-oxide planes. We discuss lattice point group symmetry of the magnetic structure. As an application, we discuss a few effects that necessarily accompany order parameter in the pseudogap phase. The magnitude estimated for these specific effects makes them hard to observe because they rely on the small magnetic fields associated with the order parameter. Effects, associated with the electronic energies are much larger. Some of them have already been discussed.