Optical signatures of parity anomaly in a gapped graphene-like system.

Parity anomaly refers to the violation of coordinate reflection symmetry induced by the quantum fluctuations. It is proposed to exist in a graphene-like system with a finite bare mass for Dirac fermions, and manifests itself as a parity-violating quantum correction to the current of each species of fermions. Coulomb interaction greatly increases the fermion mass, and produces various types of excitons. Of particular interest is the ρ-exciton, which is directly connected to parity anomaly and can be generated by absorbing a specific photon. The exciton is a particle-hole bound state, and can be regarded as condensed-matter analogue of meson composed of quark-anti-quark pair. By virtue of this correspondence, we analyze the optical conductivity and calculate the mass of ρ-exciton by employing the Shifman-Vainshtein-Zakharov sum rule method that is widely used in the studies of hadron phenomenology. We show that ρ-exciton leads to a sharp peak in the optical conductivity, which is observable in optical experiments. Moreover, we study the impact of scalar-like excitons on two-photon processes by computing the decay amplitude, and also find peaks in the Raman spectra.