Antiparticle of exciton in semimetals

An emergent quantized field enriches quantum many-body systems. We propose an antiparticle analog of the exciton in semimetals as an emergent collective mode in interacting electron systems. We show that inter-band excitations in semimetals are generally comprised of both excitons and antiparticles of excitons. These two stand for two distinct inter-band collective modes in semimetals, having different energies and opposite conserved charges. The conserved charge here is a quantity conjugate to a joint U(1) symmetry of two electron's bands associated with the inter-band excitations. The opposite charges foster fertile scattering processes among the inter-band collective modes. In spin-polarized systems, they also suggest possible experimental detections of the antiparticles. We clarify that the effective theory of the inter-band excitations is given by a generalized Klein-Gordon theory. Our theory provides a comprehensive understanding of excitonic spectra in generic semimetals, bringing a new insight into electronic collective phenomena in solids.