# Spin and valley waves in Dirac semimetals with population imbalance

## TL;DR

This paper predicts a new gapless collective mode called the intervalley wave in Dirac semimetals with population imbalance, which could influence energy transfer processes and is analogous to a spin wave in certain conditions.

## Contribution

It introduces the existence and properties of an intervalley wave mode in Dirac semimetals with population imbalance, expanding understanding of collective excitations in these materials.

## Key findings

- Intervalley wave mode is gapless and proportional to wave vector squared at low frequencies.
- The mode's dispersion is inversely related to electron-electron exchange energy.
- The mode can serve as an energy source for external fields inducing intervalley transitions.

## Abstract

We find an intervalley wave collective mode in two- and three-dimensional Dirac semimetals in the presence of a valley population imbalance. The dispersion relation of this mode is gapless, proportional to the square of the wave vector at small frequencies, and inversely proportional to the electron-electron exchange interaction energy. The valley wave serves as an energy gain source for the external field, that generates the intervalley transitions. The spin wave analog is discussed for the case of a semimetal with nonequilibrium spin orientation.