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DFT2kp: effective kp models from ab-initio data

by João Victor V. Cassiano, Augusto L. Araújo, Paulo E. Faria Junior, Gerson J. Ferreira

Submission summary

Abstract

The $\bm{k}\cdot\bm{p}$ method, combined with group theory, is an efficient approach to obtain the low energy effective Hamiltonians of crystalline materials. Although the Hamiltonian coefficients are written as matrix elements of the generalized momentum operator $\bm{\pi}=\bm{p}+\bm{p}_{{\rm SOC}}$ (including spin-orbit coupling corrections), their numerical values must be determined from outside sources, such as experiments or \emph{ab initio} methods. Here, we develop a code to explicitly calculate the Kane (linear in crystal momentum) and Luttinger (quadratic in crystal momentum) parameters of $\bm{k}\cdot\bm{p}$ effective Hamiltonians directly from \emph{ab initio} wave-functions provided by Quantum ESPRESSO. Additionally, the code analyzes the symmetry transformations of the wave-functions to optimize the final Hamiltonian. This an optional step in the code, where it numerically finds the unitary transformation $U$ that rotates the basis towards an optimal symmetry-adapted representation informed by the user. Throughout the paper we present the methodology in detail, and illustrate the capabilities of the code applying it to a selection of relevant materials. Particularly, we show a ``hands on'' example on how to run the code for graphene (with and without spin-orbit coupling). The code is open source and available at \href{https://gitlab.com/dft2kp/dft2kp}{https://gitlab.com/dft2kp/dft2kp}.

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