# Intervalley plasmons in crystals

## TL;DR

This paper develops a theory for shortwave intervalley plasmons in multivalley 2D materials, incorporating local-field effects, and analyzes their dispersion and interaction with external charges.

## Contribution

It introduces a comprehensive theory of intervalley plasmons in monolayer transition-metal dichalcogenides, including their dispersion and Coulomb interactions, which was previously less explored.

## Key findings

- Derived the energy dispersion of intervalley plasmons.
- Formulated the interaction between plasmons and external test charges.
- Provided a single-plasmon pole approximation for the Coulomb potential.

## Abstract

Collective charge excitations in solids have been the subject of intense research ever since the pioneering works of Bohm and Pines in the 1950s. Most of these studies focused on long-wavelength plasmons that involve charge excitations with a small crystal-momentum transfer, $q \ll G$, where $G$ is the wavenumber of a reciprocal lattice vector. Less emphasis was given to collective charge excitations that lead to shortwave plasmons in multivalley electronic systems (i.e., when $q \sim G$). We present a theory of intervalley plasmons, taking into account local-field effects in the dynamical dielectric function. Focusing on monolayer transition-metal dichalcogenides where each of the valleys is further spin-split, we derive the energy dispersion of these plasmons and their interaction with external charges. Emphasis in this work is given to sum rules from which we derive the interaction between intervalley plasmons and a test charge, as well as a compact single-plasmon pole expression for the dynamical Coulomb potential.