Energy loss rate of an electron in three-dimensional tilting Dirac semimetals

Abstract

We have computed the energy loss rate (ELR) of an intruding electron in three-dimensional tilting Dirac semimetals in the light of the excitation process. In contrast to two-dimensional electron gas, ELRs contributed by single-particle excitation (${\mathrm{ELRs}}^{(\mathrm{SP})}$) show a nondecreasing tendency as the incidence velocity increases, and tend to replicate the behavior of the untilt intrinsic ${\mathrm{ELR}}^{(\mathrm{SP})}$, which is described by a cubic polynomial coupling with a logarithm velocity term. In comparison, ELRs contributed by the plasmon excitation (${\mathrm{ELRs}}^{(\mathrm{P})}$) first reach a maximum in the small velocity region followed by a slow discrepancy. As the contribution of plasmon excitation is restricted by the vanishing imaginary part of the dielectric function, the ${\mathrm{ELRs}}^{(\mathrm{P})}$ also manifest as an opposite counterpart to the corresponding ${\mathrm{ELRs}}^{(\mathrm{SP})}$ with different tilts. In addition, the threshold velocities in both ELRs are tilt and chemical potential dependent, and governed by the interplay of the Pauli exclusion constraints and the conservation law concealed in the energy loss function. Finally, we briefly discuss the inelastic mean scattering time. Our results may be verified by investigating the femtosecond electron dynamics in the time-resolved two-photon photoemission.