Electronic and optical properties of materials are affected by atomic motion through the electron–phonon interaction: not only band gaps change with temperature, but even at absolute zero temperature, zero-point motion causes band-gap renormalization. We present a large-scale first-principles evaluation of the zero-point renormalization of band edges beyond the adiabatic approximation. For materials with light elements, the band gap renormalization is often larger than 0.3 eV, and up to 0.7 eV. This effect cannot be ignored if accurate band gaps are sought. For infrared-active materials, global agreement with available experimental data is obtained only when non-adiabatic effects are taken into account. They even dominate zero-point renormalization for many materials, as shown by a generalized Fröhlich model that includes multiple phonon branches, anisotropic and degenerate electronic extrema, whose range of validity is established by comparison with first-principles results.

Black phosphorus (BP) is unique among layered materials because of its homonuclear lattice and strong structural anisotropy. While recent investigations on few-layer BP have extensively explored the in-plane (a, c) anisotropy, much less attention has been given to the out-of-plane direction (b). Here, the optical response from bulk BP is probed using polarizationresolved photoluminescence (PL), photoluminescence excitation (PLE), and resonant Raman scattering along the zigzag, out-ofplane, and armchair directions. An unexpected b-polarized luminescence emission is detected in the visible, far above the fundamental gap. PLE indicates that this emission is generated through b-polarized excitation at 2.3 eV. The same electronic resonance is observed in resonant Raman with the enhancement of the A g phonon modes scattering efficiency. These experimental results are fully consistent with DFT calculations of the permittivity tensor elements and demonstrate the remarkable extent to which the anisotropy influences the optical properties and carrier dynamics in black phosphorus.

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After reports of high mobility and a tunable bandgap covering a wide spectral range from the visible to the mid-infrared region, layered black phosphorus (BP) has emerged as a promising 2D material for high performance electronic and optoelectronic devices. Owing to its orthorhombic crystallographic structure, black phosphorus expresses strong anisotropic properties. While recent investigations on few-layers crystals have extensively explored the in-plane anisotropy, much less attention has been given to the out-of-plane direction. In this work, we use polarization-resolved photoluminescence (PL) and Raman spectroscopies to investigate the band structure anisotropy of bulk BP along the in-plane (zigzag, armchair) and out-of-plane directions. An unexpected room-temperature luminescence is detected in the visible, and strongly polarized in the out-of-plane direction. This emission, detected at 1.75 eV far above the band gap (0.3 eV), is surprising as it violates Kasha's rule which favors light emission from the lowest energy states. To elucidate its origin, we have systematically examined the characteristics of this luminescence as a function of polarization, temperature and excitation energy. These results reveal an unreported out-of-plane resonance at 2.3 eV in both the PL and Raman responses. Polarization selection rules and density functional theory (DFT) calculations of the complex dielectric permittivity are used to understand the origin of the strongly polarized optical response and demonstrate the remarkable extent to which the anisotropy influences the optical properties and carrier dynamics in black phosphorus.