Fano resonances induced by the topological magnetoelectric effect

Abstract

We investigate the interaction between a topological insulator nanoparticle and a quantum dot in an impulse magnetic field. Since topological insulators are nonmagnetic, after the impulse has ended only the localised topological surface modes, which are quantised in terms of dipolar bosonic modes, thus coupling dipolarly to the quantum dot. Hence, the hybrid system can be treated as a single bosonic mode interacting with a two-level system, where the coupling strength is quantised in terms of the magnetoelectric polarizability. We implement the interaction of the hybrid with the environment through the coupling with a continuum reservoir of radiative output modes and a reservoir of phonon modes. Using the method of Zubarev's Green functions, we derive an expression for the optical absorption spectrum of the system. We find the emergence of Fano resonances which are direct manifestations of the $\mathbb{Z}_{2}$ invariant of topological insulators. We present numerical results for a topological insulator nanosphere made of TlBiSe$_2$ interacting with a CdSe quantum dot.