First-Principles Electron-Phonon Interactions and Polarons in the Parent Cuprate La$_2$CuO$_4$

TL;DR

This study uses first-principles calculations to analyze electron-phonon interactions and polaron formation in La$_2$CuO$_4$, revealing strong coupling and spectral features consistent with experimental observations, thus clarifying the microscopic origin of these effects.

Contribution

First-principles Hubbard-corrected DFT calculations quantitatively characterize electron-phonon interactions and polaron effects in the parent cuprate La$_2$CuO$_4$, identifying specific phonon modes involved.

Findings

Identification of two classes of LO phonons with strong e-ph coupling.

Observation of broad quasiparticle peaks with small spectral weight and phonon sidebands.

Prediction of a 40-meV peak in e-ph coupling distribution matching experimental spectra.

Abstract

Understanding electronic interactions in high-temperature superconductors is an outstanding challenge. In the widely studied cuprate materials, experimental evidence points to strong electron-phonon ($e$-ph) coupling and broad photoemission spectra. Yet, the microscopic origin of this behavior is not fully understood. Here we study $e$-ph interactions and polarons in a prototypical parent (undoped) cuprate, La$_2$CuO$_4$ (LCO), by means of first-principles calculations. Leveraging parameter-free Hubbard-corrected density functional theory, we obtain a ground state with band gap and Cu magnetic moment in nearly exact agreement with experiments. This enables a quantitative characterization of $e$-ph interactions. Our calculations reveal two classes of longitudinal optical (LO) phonons with strong $e$-ph coupling to hole states. These modes consist of Cu-O plane bond-stretching and bond-bending as well as vibrations of apical O atoms. The hole spectral functions, obtained with a cumulant method that can capture strong $e$-ph coupling, exhibit broad quasiparticle peaks with a small spectral weight ($Z\approx0.25$) and pronounced LO-phonon sidebands characteristic of polaron effects. Our calculations predict features observed in photoemission spectra, including a 40-meV peak in the $e$-ph coupling distribution function not explained by existing models. These results show that the universal strong $e$-ph coupling found experimentally in lanthanum cuprates is an intrinsic feature of the parent compound, and elucidates its microscopic origin.