Band gaps induced by vacuum photons in closed semiconductor cavities

We consider theoretically a closed (zero-dimensional) semiconductor microcavity where a confined vacuum photonic mode is coupled to electrons in the valence band of the semiconductor. It is shown that vacuum-induced virtual electron transitions between valence and conduction bands result in renormalization of electron energy spectrum. As a consequence, vacuum-induced band gaps appear within the valence band. Calculated values of the band gaps are of sub-meV scale, which makes this QED effect measurable in state-of-the-art experiments.

Figure 1

(a) Sketch of the system under consideration: a bulk semiconductor (SC) embedded into a closed (zero-dimensional) microcavity formed by distributed Bragg reflectors (DBRs) with dimensions $(L_x,L_y,L_z)$. (b) Electron energy spectrum of the bulk semiconductor with vacuum-induced (virtual) interband electron transitions marked by arrows.

Figure 2

(a) The Dyson equation for renormalized electron Green's functions corresponding to the valence band. (b) The self-energy operator responsible for photon-induced dressing of the valence band. The dashed line corresponds to a virtual cavity photon and $g$ denotes the electron-photon coupling constant.

Figure 3

(a) Energy spectrum of dressed electrons within the approximation of a negligible small photon wave vector; (b) Exact energy spectrum of dressed valence electrons, calculated numerically for GaAs microcavity with dimensions $L_z=100$ nm and $L_x=L_y=500$ nm for the electron wave vector $\mathbf{k}=(k_x,k_y,k_z)$ with the components $k_x=k_y=k/\sqrt{2}$ and $k_z=0$.