Ab Initio Finite-Temperature Excitons

The coupling with the lattice vibrations is shown to drastically modify the state-of-the-art picture of the excitonic states based on a frozen-atom approximation. The zero-point vibrations renormalize the bare energies and optical strengths. Excitons acquire a nonradiative lifetime that decreases with increasing temperature. The optical brightness turns out to be strongly temperature-dependent such as to induce bright to dark (and vice versa) transitions. The finite-temperature experimental optical absorption spectra of bulk Si and hexagonal BN are successfully explained without using any external parameter.

Figure 1

Optical absorption of bulk Si (upper frames) for several temperatures and of $h$-BN (lower frames) at room temperature. The experimental spectra [3, 15] (circles) are compared with the BS equation (solid line) and with the independent-particle approximation (dotted-dashed line). In the insets, the exciton-phonon spectral functions $\mathrm{Re}[g^2{F}_{\lambda }(\omega ,T=0)]$ are shown for the $E_1$ (Si) and $B_1$ ($h$-BN) peaks (see text). The width of the absorption peaks reflects the damping of the excitons due to the scattering with phonons. No additional numerical damping is included. The excitonic energies obtained within the frozen-atom BS equation (represented by the vertical dashed lines) are redshifted in Si and blueshifted in $h$-BN.

Figure 2

Temperature dependence of the energies and oscillator strengths of the near-gap excitons (bound and resonant) in $h$-BN. The dashed line indicates the energy position of the optical gap in the independent-particle approximation. The sizes of the circles are proportional to the excitonic optical strength. The darker circles at $T=0$ is the result obtained neglecting exciton-phonon coupling. At $T=0$ we observe a 30% reduction of the $B_1$ exciton binding energy due to the zero-point lattice vibrations. The $B_2$ and $R_1$ excitons, instead, undergo a bright to dark (and vice versa) transition at room temperature (see text).