A $k\cdot p$ effective Hamiltonian generator

TL;DR

This paper introduces 'kdotp-generator', a software tool that automates the creation of symmetry-allowed $k ext{ extperiodcentered}p$ Hamiltonians for magnetic materials, enhancing theoretical analysis capabilities.

Contribution

The paper presents an upgraded package that generates $k ext{ extperiodcentered}p$ Hamiltonians from arbitrary magnetic symmetries, covering extensive magnetic space groups and external field couplings.

Findings

Generated Hamiltonians for 1651 magnetic space groups.

Included third-order and linear external field couplings.

Facilitates future research in condensed matter physics.

Abstract

$k\cdot p$ effective Hamiltonian is important for theoretical analysis in condensed matter physics. Based on the 'kdotp-symmetry' package, we develop an upgraded package named 'kdotp-generator'. This generator takes in arbitrary magnetic symmetries with their representations and returns symmetry-allowed $k\cdot p$ Hamiltonians. Using this package, we calculate $k\cdot p$ Hamiltonians for irreducible corepresentations in 1651 magnetic space groups up to the third order, and their linear coupling to external fields including the electromagnetic field and the strain tensor. We hope that the package will facilitate related research in the future.