We study the excitonic phase and low-energy excitation spectra of perovskite cobalt oxides. Constructing the five-orbital Hubbard model defined on the three-dimensional cubic lattice for the 3d bands of Pr0.5Ca0.5CoO3, we calculate the excitonic susceptibility in the normal state in the random-phase approximation (RPA) to show the presence of the instability toward excitonic condensation. On the basis of the excitonic ground state with a magnetic multipole obtained in the mean-field approximation, we calculate the dynamical susceptibility of the excitonic phase in the RPA and find that there appear a gapless collective excitation in the spin-transverse mode (Goldstone mode) and a gapful collective excitation in the spin-longitudinal mode (Higgs mode). The experimental relevance of our results is discussed.The Bose-Einstein condensation of fermion pairs is one of the most intriguing phenomena in condensed matter physics. The excitonic phase (EP) is representative of such a pair condensation, [1][2][3][4] where holes in valence bands and electrons in conduction bands spontaneously form pairs owing to attractive Coulomb interaction. After Mott's prediction of the EP half a century ago, 5) a number of candidate materials for this phase have come to our attention. Among them are the transition-metal chalcogenides 1T -TiSe 2 6-8) and Ta 2 NiSe 5 , 9-11) where the electrons and holes on different atoms are considered to form spin-singlet pairs to condense into the EP, which is accompanied by lattice distortion.
12)Another class of materials includes the perovskite cobalt oxides, [13][14][15] where the valence-band holes and conduction-band electrons form spin-triplet pairs in different orbitals on the same atoms. Pr 0.5 Ca 0.5 CoO 3 (PCCO) is an example in which the "metal-insulator" phase transition is observed at T c ≃ 80 K, which is associated with a sharp peak in the temperature dependence of the specific heat and a drop in the magnetic susceptibility below T c , 16) together with a valence transition of Pr ions.17, 18) Some results of experiments indicate that the resistivity is in fact small and nearly temperature independent below T c , 19) suggesting that the bands may not be fully gapped. Note that no local magnetic moments are observed, but the exchange splitting of the Pr 4+ Kramers doublet occurs, 19) the result of which may therefore be termed as a hidden order, and also that no clear signatures of the spin-state transition are observed in the X-ray absorption spectra.
19, 20)Kuneš and Augustinsky argued that the anomalies of PCCO can be attributed to the EP transition,
13)whereby they applied the dynamical-mean-field-theory calculation to the two-orbital Hubbard model defined on * t.yamaguchi@chiba-u.jp a two-dimensional square lattice and claimed that the anomalous behaviors of the specific heat, dc conductivity, and spin susceptibility can be explained. They also performed the LDA+U band-structure calculation and showed that the magnetic multipole ordering occurs in PCCO as a result of the excitonic con...