Phase diagram and collective excitation in excitonic insulator: from the orbital physics viewpoint

TL;DR

This paper investigates excitonic insulators through orbital physics, deriving an effective model from the two-orbital Hubbard model, analyzing phase diagrams, and exploring collective excitations and magnetic orders.

Contribution

It introduces a new effective model capturing excitonic phases and their excitations, highlighting the role of orbital physics and symmetry breaking in excitonic insulators.

Findings

Identification of two excitonic insulating phases with distinct magnetic orders

Classification of the excitonic transition as an Ising-like transition

Observation of active spin excitation modes in excitonic phases

Abstract

Excitonic insulating system is studied from the viewpoints of the orbital physics in strongly correlated electron systems. An effective model Hamiltonian for low-energy electronic states is derived from the two-orbital Hubbard model with a finite energy difference corresponding to the crystalline field splitting. The effective model is represented by the spin operators and the pseudo-spin operators for the spin-state degrees of freedom. The ground state phase diagram is analyzed by the mean-field approximation. In addition to the low-spin state and high-spin state phases, two kinds of the excitonic insulating phases emerge as a consequence of the competition between the crystalline field effect and the Hund coupling. The excitonic transition is classified to be an Ising-like transition reflecting a spontaneous breaking of the $Z_2$ symmetry. Magnetic structures in the two excitonic insulating phases are different from each other; an antiferromagnetic order and a spin nematic order. Collective excitations in each phase are examined by using the generalized spin-wave method. The Goldstone modes in the excitonic insulating phases appear in the dynamical correlation functions for the spins and pseudo-spin operators. Both the transverse and longitudinal spin excitation modes are active in the two excitonic insulating phases in contrast to the low-spin state and high-spin state phases. Connections of the present results to the perovskite cobalt oxides are discussed.