# On the role of the electron-phonon interaction in the temperature dependence of the gap of lead halide perovskites

## TL;DR

This paper investigates the temperature dependence of the optical gap in lead halide perovskites, revealing that thermal expansion significantly influences the gap shift, contrary to previous assumptions that emphasized electron-phonon interactions alone.

## Contribution

The study demonstrates that thermal expansion plays a dominant role in the temperature-dependent gap behavior of lead halide perovskites, challenging prior models that focused solely on electron-phonon effects.

## Key findings

- Thermal expansion accounts for about 60% of the gap shift in MAPbI3.
- Electron-phonon interaction explains roughly 40% of the temperature-induced gap change.
- Results are applicable across different phases and similar halide perovskites.

## Abstract

Lead halide perovskites are causing a change of paradigm in photovoltaics. Among other peculiarities, these perovskites exhibit an atypical temperature dependence of the fundamental optical gap: It decreases in energy with decreasing temperature. So far reports ascribe such a behavior to a particularly strong electron-phonon renormalization of the band gap, neglecting completely contributions from thermal expansion effects. However, high pressure experiments performed, for instance, on the archetypal perovskite MAPbI$_3$, where MA stands for methylammonium, yield a negative pressure coefficient for the gap of the tetragonal room-temperature phase, which speaks against the assumption of a negligible gap shift due to thermal expansion. On the basis of the high pressure results, we show here that for MAPbI$_3$ the temperature-induced gap renormalization due to electron-phonon interaction can only account for about 40\% of the total energy shift, thus implying thermal expansion to be the dominant term. Furthermore, this result possesses general validity, holding also for the tetragonal or cubic phase, stable at ambient conditions, of other halide perovskite counterparts.