Electronic and Vibrational Properties of Layered Boron Nitride Polymorphs

Abstract: We present a comprehensive first-principles investigation of the structural, electronic, and vibrational properties of four layered boron nitride (BN) polymorphs--AA-stacked ($e$-BN), AA$^\prime$-stacked ($h$-BN), ABC-stacked ($r$-BN), and AB-stacked ($b$-BN). Using density functional theory and density functional perturbation theory with and without van der Waals (vdW) corrections, we quantify the impact of interlayer dispersion on lattice parameters, electronic band gaps, phonon frequencies, and infrared and Raman intensities. Our results demonstrate that vdW interactions are essential for reproducing experimental lattice constants and stabilizing interlayer phonon modes. The vibrational spectra exhibit distinct stacking-dependent features, enabling clear differentiation among polytypes. Notably, $b$-BN displays a direct band gap, while $r$-BN shows enhanced IR and Raman activity due to LO-TO splitting and symmetry breaking. These findings underscore the critical role of interlayer interactions in determining the physical properties of $sp^2$-bonded BN and offer insight into the experimental identification and functionalization of BN polytypes for electronic and photonic applications.