Density-functional perturbation theory for one-dimensional systems: implementation and relevance for phonons and electron-phonon interactions*

We introduce a novel implementation of density-functional perturbation theory tailored for one-dimensional (1D) systems like chains, polymers, tubes, and wires. Our method incorporates a Coulomb cutoff to eliminate spurious interactions in 3D periodic-boundary conditions, restoring precise computations of total energies, forces, stress tensors, and crucially, phonons and electron-phonon interactions under 1D open-boundary conditions.

Validation on real materials (BN atomic chain, BN (4,4) armchair nanotube, GaAs nanowire) reveals previously debated softening of phonon dispersion curves [1] in the long-wavelength limit. Notably, for the first time to our knowledge, we extensively probe a non-monotonic Fröhlich electron-phonon coupling [2], holding significant implications for transport applications. We introduce an innovative analytical model to clarify the interactions between polar-optical phonons and electrons, providing a deeper understanding of observed phenomena.

This work not only unlocks accurate simulation capabilities for 1D systems but also sheds light on dimensional transitions, emphasizing opportunities to tailor material properties. Furthermore, it sets the stage for extensive exploration in various fields, including charge transport, optical coupling, and polaritronics.

 

[1] N. Rivano, N. Marzari, T. Sohier, npj Comput Mater 9, 194 (2023).

[2] N. Rivano, N. Marzari, T. Sohier (2023) -- arXiv preprint arXiv:2310.03907.