Exciton-phonon interaction in the strong-coupling regime in hexagonal boron nitride

The temperature-dependent optical response of excitons in semiconductors is controlled by the exciton-phonon interaction. When the exciton-lattice coupling is weak, the excitonic line has a Lorentzian profile resulting from motional narrowing, with a width increasing linearly with the lattice temperature $T$. In contrast, when the exciton-lattice coupling is strong, the line shape is Gaussian with a width increasing sublinearly with the lattice temperature, proportional to $\sqrt{T}$. While the former case is commonly reported in the literature, here the latter is reported for hexagonal boron nitride. Thus the theoretical predictions of Toyozawa [Prog. Theor. Phys. 20, 53 (1958)] are supported by demonstrating that the exciton-phonon interaction is in the strong-coupling regime in this van der Waals crystal.

Figure 1

PL spectrum in hBN in the deep ultraviolet at 8 K (a), and at 100 K (b), showing the four dominant phonon replicas $X_{\mu }$ with $\mu$ the phonon type: experimental data (symbols), theoretical fit with a Gaussian line (green solid line), and with a Lorentzian line (dashed red line).

Figure 2

Temperature dependence of the PL spectrum in hBN as a function of temperature, from 8 to 300 K: experimental data (symbols); theoretical fit (solid line). The full width at half maximum $\mathrm{\Delta }$ of the phonon replicas is the same for the four types of phonon replicas (as shown in Fig. 1), and $\mathrm{\Delta }$ is the only varying parameter as a function of temperature.

Figure 3

Temperature dependence of the full width at half maximum $\mathrm{\Delta }$ of the phonon replicas, estimated from the quantitative interpretation performed in Fig. 2: experimental data (symbols); theoretical fit in the strong-coupling regime (green solid line), or in the weak-coupling regime (dashed red line). Inset: comparison between a commercial hBN sample from HQ Graphene and a crystal grown at Kansas State University (KSU) [27].