KPROJ: A program for unfolding electronic and phononic bands

We introduce a program named KPROJ that unfolds the electronic and phononic band structure of materials modeled by supercells. The program is based on the k-projection method, which projects the wavefunction of the supercell onto the k-points in the Brillouin zone of the artificial primitive cell. It allows for obtaining an effective “local” band structure by performing partial integration over the k-projected wavefunctions, e.g., the unfolded band structure with layer-projection for interfaces and the weighted band structure in the vacuum for slabs. The layer k-projection is accelerated by a scheme that combines the Fast Fourier Transform (FFT) and the inverse FFT algorithms. It is now interfaced with several first-principles codes based on plane waves such as VASP, Quantum Espresso, and ABINIT. In addition, it also has interfaces with ABACUS, a first-principles simulation package based on numerical atomic basis sets, and PHONOPY, a program for phonon calculations.本研究介绍一款名为KPROJ的程序，可对超胞构建的材料展开电子与声子能带结构。该程序基于k投影法，将超胞的波函数投影至人工原胞布里渊区的k点上。通过对k投影波函数执行部分积分，该程序可获取有效的“局域”能带结构；例如，针对异质界面可得到带有层投影的展开能带结构，针对平板体系可得到真空区域内的加权能带结构。层k投影运算可通过结合快速傅里叶变换（FFT）与逆FFT算法的方案实现加速。目前，该程序已与多款基于平面波的第一性原理计算程序实现对接，例如VASP、Quantum Espresso及ABINIT。此外，它还适配基于数值原子基组的第一性原理模拟软件ABACUS，以及声子计算程序PHONOPY。