Electron-phonon interaction within classical molecular dynamics

We present a model for nonadiabatic classical molecular dynamics simulations that captures with high accuracy the wave-vector $q$ dependence of the phonon lifetimes, in agreement with quantum mechanics calculations. It is based on a local view of the $e$-ph interaction where individual atom dynamics couples to electrons via a damping term that is obtained as the low-velocity limit of the stopping power of a moving ion in a host. The model is parameter free, as its components are derived from ab initio-type calculations, is readily extended to the case of alloys, and is adequate for large-scale molecular dynamics computer simulations. We also show how this model removes some oversimplifications of the traditional ionic damped dynamics commonly used to describe situations beyond the Born-Oppenheimer approximation.

Figure 1

Electronic density in Ni crystal with a single vacancy along the $\langle 100\rangle$ (red) and $\langle 110\rangle$ (blue) directions. The solid line is obtained with the ASA method, and dashed line is calculated using vasp. The symbol Vac shows the location of a vacancy in Ni crystal.

Figure 2

Damping term $\beta$ in the Langevin equations as a function of local electronic density calculated using TDDFT for Ni and Fe projectiles moving across a vacancy site in an fcc Ni crystal. Also plotted is the fitted quadratic function for $\beta \left(\rho \right)$ that was used in MD simulations.

Figure 3

The amplitude decay during the $e$-ph MD simulation of the phonon longitudinal modes in fcc Ni crystal along the $\langle 100\rangle$ direction with wave vectors $0.05,0.25$, and $0.50$ (in units of $2\pi /a)$. The simulation contains 32 000 atoms in a cubic supercell. The horizontal dotted line shows the result when the dissipative term in Eq. (1) is turned off (and energy is conserved as in a normal NVE simulation).

Figure 4

Inverse phonon lifetimes in a fcc Ni crystal along the $\langle 100\rangle ,\langle 110\rangle$, and $\langle 111\rangle$ directions. The polarization vectors investigated are shown in the legend. Results are shown for the model described in the text, for a perturbative QM calculation, and for the standard two-temperature model.

Figure 5

Inverse phonon lifetimes for a NiFe random solid solution in the fcc phase as a function of wave vector $q$ for three polarizations at various number concentrations (c Fe 0.00, 0.01, 0.10). These are obtained with our MD model from the decay of an initial phononlike excitation characterized by wave vector $q$ along principal directions in the Brillouin zone and polarization (longitudinal and two transversal). Values reported in the top panel correspond to the $e$-ph contribution alone, measured from the energy transferred to the electronic system; those in the lower panel correspond to the actual decay of the mode that contains the $e$-ph interaction plus the decay produced by the disorder.