Since the first observation of odd and even high-order harmonics generated from ZnO crystals in 2011, the dependence of the harmonic yields on the orientation of the laser polarization with respect to the crystal axis has never been properly interpreted. This failure has been traced to the lack of a correct account of the phase of the transition dipole moment between the valence band and the conduction band. Using a simple one-dimensional two-band model, here we demonstrate that the observed odd harmonics is directly related to the orientation dependence of the magnitude of the transition dipole, while even harmonics is directly related to the phase of the transition dipole. Our result points out the essential role of the complex transition dipole moment in understanding harmonic generation from solids that has long been overlooked so far.

Bilayer ZrS ₂ -based vdW heterostructures are proposed as efficient photocatalysts for water splitting under visible light.

Since the turn of the new century, the increasing demand for high-performance energy storage systems has generated considerable interest in rechargeable ion batteries (IBs). However, current IB technologies are not entirely satisfactory, especially the electrodes. We report here, via density functional theory calculations and first principles molecular dynamics simulations, that a borophene anode material has the fascinating properties of ultrahigh energy storage and ultrafast ion diffusion in metal (Li, Na, K, Mg, Al) IBs. Particularly for Li IBs with a borophene anode, a specific density of 3306 mA h g⁻¹ and a high charging voltage of 1.46 V can be maintained at room temperature. Furthermore, non-ideal borophene anodes, including those with defects or oxidation and nanoribbon samples, still possess good properties for practical applications. This theoretical exploration will provide helpful guidance in searching for available or novel boron nanosheets as promising anode materials to advance commercial IB technology.

We carry out a combined theoretical and experimental investigation on the population distributions in the ground and excited states of tunnel-ionized nitrogen molecules at various driver wavelengths in the near- and midinfrared range. Our results reveal that efficient couplings (i.e., population exchanges) between the ground ${\mathrm{N}}_2^{+}(X^2{\mathrm{\Sigma }}_g^{+})$ state and the excited ${\mathrm{N}}_2^{+}(A^2{\mathrm{\Pi }}_u)$ and ${\mathrm{N}}_2^{+}(B^2{\mathrm{\Sigma }}_u^{+})$ states occur in strong laser fields. The couplings result in a population inversion between the ${\mathrm{N}}_2^{+}(X^2{\mathrm{\Sigma }}_g^{+})$ and ${\mathrm{N}}_2^{+}(B^2{\mathrm{\Sigma }}_u^{+})$ states at wavelengths near 800 nm, which is verified by our experimental observation of the amplification of a seed at $\sim 391\mathrm{nm}$. The result provides insight into the mechanism of free-space nitrogen ion lasers generated in remote air with strong femtosecond laser pulses.