Impurity-induced ferromagnetism in a doped triplet excitonic insulator

The theory of impurities in excitonic insulator is investigated in the light of the recent experiments on hexaborides. First, we study the bound state around the impurity and find that the bound-state emerges when $\mathrm{Re}\Delta$ is positive. Second, we study the continuum state using Abrikosov-Gor’kov’s approach. We find that the energy gap is reduced strongly when $\mathrm{Im}\Delta =0.\mathrm{}$ Finally, we solve Bogoliubov–de Gennes equations for excitonic insulator numerically. We get the results consistent with the analytic ones. We also find that incomplete ferromagnetism appears in doped triplet excitonic insulator with impurity. We make a short qualitative discussion on the ferromagnetism of doped hexaborides using our result.