Collective modes in the loop-current-ordered phase of cuprates

Abstract

Recently two branches of weakly dispersive collective modes have been discovered in underdoped cuprates by inelastic neutron scattering. Polarization analysis reveals that the modes are magnetic excitations. They are visible only for temperatures below the transition temperature to a broken symmetry phase, which was discovered earlier, and their intensity increases as temperature is further decreased. The broken symmetry phase itself has symmetries consistent with ordering of orbital current loops within a unit cell without breaking translational symmetry. In order to calculate the collective modes of such a state we add quantum terms to the Ashkin-Teller model with which the classical loop current order has been described. We derive that the mean-field ground state of the quantum model is a product over all unit cells of linear combination of the four possible classical configurations of the loop current order in each unit cell. The collective modes are calculated by using a generalized Holstein-Primakoff boson representation of orbital moment operators and lead to three branches of gapped weakly dispersive collective modes. The experimental results are consistent with the two lower-energy branches; the third mode is at a higher energy than looked for by present neutron-scattering experiments and might also be overdamped. Implications of the discovery of the collective modes are discussed.