DFT2kp: effective kp models from ab-initio data

TL;DR

This paper introduces an open-source code that derives effective k·p Hamiltonian parameters directly from ab initio wavefunctions, facilitating accurate modeling of crystalline materials' low-energy electronic properties.

Contribution

The authors develop a method and provide a code to compute k·p Hamiltonian parameters from ab initio data, including symmetry analysis and basis optimization, which was previously not straightforward.

Findings

Successfully applied to graphene with and without spin-orbit coupling.

Automates the extraction of Kane and Luttinger parameters from ab initio calculations.

Provides an open-source tool for the community to model low-energy electronic structures.

Abstract

The $\mathbf{k}\cdot\mathbf{p}$ 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 $\mathbf{\pi}=\mathbf{p}+\mathbf{p}_{{\rm SOC}}$ (including spin-orbit coupling corrections), their numerical values must be determined from outside sources, such as experiments or 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 $\mathbf{k}\cdot\mathbf{p}$ effective Hamiltonians directly from ab initio wavefunctions provided by Quantum ESPRESSO. Additionally, the code analyzes the symmetry transformations of the wavefunctions to optimize the final Hamiltonian. This is 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 of how to run the code for graphene (with and without spin-orbit coupling). The code is open source and available at https://gitlab.com/dft2kp/dft2kp.