Electron-hole liquid in the hexaborides

We investigate the energetics of the electron-hole liquid in stoichiometric divalent-metal hexaborides. The ground-state energy of an electron-hole plasma is calculated using the random-phase approximation and Hubbard schemes and compared to the binding energy of a single exciton. Intervalley scattering processes play an important role in increasing this binding energy and stabilizing a dilute Bose gas of excitons. The remarkable discovery of the high-temperature weak ferromagnetism in La-doped CaB6 , SrB6, and BaB6 has opened a new page in the physics of magnetism. 1 In our previous work 2 we attributed this effect to an unusual ground state of undoped divalent hexaborides. This so-called excitonic insulator is characterized by a condensation of bound electron-hole pairs ~excitons!. An excitonic instability in narrow gap semiconductors or semimetals was predicted 3 and studied theoretically in the mid-1960s. 4 However, its occurrence in any real compound is still controversial. Bandstructure calculations 5,6 predict a small direct overlap in divalent-metal hexaborides between a boron-derived valence band and a cation-derived conduction band at three equivalent X points in the cubic Brillouin zone. This feature, together with absence of direct electric-dipole transitions between the two bands, is extremely favorable for electron-hole pairing and leads to the excitonic instability. Weak ferromagnetism develops, then, in a triplet excitonic insulator due to spontaneous time-reversal symmetry breaking under