Spin and valley waves in Dirac semimetals with population imbalance

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.
Comment: 4+ pages, 2 figures