Quasiparticle bound states in three-dimensional crystals
Abstract
The formation of quasiparticle bound states in crystals is considered for the case in which quadratic terms in the momentum components are absent from the expansion of the quasiparticle energy close to the edge of the energy band. This situation is possible if the effective mass of the quasiparticles depends on some external parameter, and becomes infinite for a certain value of this parameter as discussed earlier by Bar’yakhtar. It is shown that in this case, even in three-dimensional space, bound states are formed for arbitrarily small attractive quasiparticle-quasiparticle and quasiparticle-defect potentials. As an example, Heisenberg antiferromagnets in an external field are considered. The binding energy of the bound states is calculated, and the range of magnetic-field values in which these states are formed is determined for a given small value of the attractive potential.