Calculating electron-phonon coupling matrix: Theory introduction,code development and preliminary application

Electron-phonon coupling(EPC) in bulk materials is an important effect in multifarious physical and chemical phenomena. It is the key to explaining the mechanisms for superconductivity, electronic transport, etc. The EPC matrix describes the coupling of the electronic eigenstates of the studied system under the perturbation of phonons. Although the EPC matrix is closely relevant to many fundamental physicochemical properties, it remains a challenge to calculate the EPC matrix precisely due to the high computational cost. In recent years, Giustino et al. developed the EPW method on open-source ab-initio software Quantum Espresso, which uses Wannier functions(WFs) to calculate EPC matrix. However, due to the limitation of their implementation,it is not possible yet to calculate the EPC matrix under some important computational conditions, e.g., for DFT+U and HSE calculation. Given the importance of these computational conditions(e.g., for transition metal oxides), we have developed our own implementation of EPC matrix calculation based on the domestic ab-initio software PWmat. Our code allows the DFT+U and HSE correction, so we can get a more accurate EPC matrix in the related problems. In this article, we will first review the formulae and elucidate how to calculate the EPC matrix by constructing WFs. Then we will introduce our code along with its workflow on PWmat and present our test results of two classical semiconductor systems Al As and Si, showing consistency with EPW. Next, the EPC matrix of Li Co O_(2), a classical cathode material for lithium-ion batteries, is calculated using different exchange correlation(XC) functionals including LDA, PBE, DFT+U and HSE. A comparison is provided for the related EPC matrix. It shows there could be a significant difference for the EPC matrix elements due to the use of different XC functionals.Our implementation thus opens the way for fast calculation of EPC for the important class of materials, like the transition metal oxides.