# Broken adiabaticity induced by Lifshitz transition in MoS$_2$ and WS$_2$ single layers

## TL;DR

This paper reveals how Lifshitz transitions in doped single-layer MoS2 and WS2 cause breakdowns in adiabaticity, affecting phonon modes and electron-phonon interactions, with implications for Raman spectroscopy in 2D materials.

## Contribution

It demonstrates the link between Lifshitz transitions and adiabaticity breakdown in doped 2D transition metal dichalcogenides, highlighting the roles of electron-electron and electron-phonon interactions.

## Key findings

- Nonadiabatic coupling affects Raman-active phonon modes.
- Lifshitz transition triggers adiabaticity breakdown.
- Doping modifies phonon linewidths via electron-hole scattering.

## Abstract

The breakdown of the adiabatic Born-Oppenheimer approximation is striking dynamical phenomenon, however, it occurs only in a handful of layered materials. Here, I show that adiabaticity breaks down in doped single-layer transition metal dichalcogenides in a quite intriguing manner. Namely, significant nonadiabatic coupling, which acts on frequencies of the Raman-active modes, is prompted by a Lifshitz transition due to depopulation and population of multiple valence and conduction valleys, respectively. The outset of the latter event is shown to be dictated by the interplay of highly non-local electron-electron interaction and spin-orbit coupling. In addition, intense electron-hole pair scatterings due to electron-phonon coupling are inducing phonon linewidth modifications as a function of doping. Comprehending these intricate dynamical effects turns out to be a key for mastering characterization of electron doping in two-dimensional nano-devices by means of Raman spectroscopy.