Vibrational Instabilities in Charge Transport through Molecular Nanojunctions: The Role of Anharmonic Nuclear Potentials

Abstract

The current-induced vibrational dynamics is a key factor determining the stability of molecular nanojunctions. Beyond conventional Joule heating, a different mechanism caused by nonconservative current-induced forces has been predicted for models with multiple vibrational modes, leading to vibrational instabilities already at low bias voltages. So far, this mechanism has only been investigated in models with harmonic nuclear potentials. Consequently, a natural question is whether this effect can also be observed in more realistic models containing anharmonic nuclear potentials, and, if so, whether it has a measurable impact on observables such as the junction dissociation probability. In this work, we apply a mixed quantum-classical approach based on electronic friction and Langevin dynamics to various anharmonic two-mode systems. By performing Langevin simulations of the vibrational dynamics, we investigate the influence of anharmonicity on instabilities arising from nonconservative forces and the corresponding dissociation dynamics of the junction, as well as steady-state observables, such as the electronic current.

Figures (11)

• Figure 1: Potentials $U_{\mathrm{u},2}(x_2),~U^{(1)}_{\text{c}}(x_2),$ and $U^{(2)}_{\text{c}}(x_2)$ of the uncharged state and the charged states (1) and (2), as well as their harmonic approximations. The parameters are the same as in Set (1) in Tbl. \ref{['tab: paras_table']}, with $\omega_2=20~\mathrm{meV}$.
• Figure 2: Dissociation probability $P_{\mathrm{diss}}$ over time for different voltages and the two cases $\omega_1=\omega_{2}$ and $\omega_1\neq\omega_{2}$. For the case of $\omega_1\neq\omega_{2}$, we set $\omega_1=20~\mathrm{meV}$ and $\omega_2=22.5~\mathrm{meV}$. Other parameters are listed in Set (1) in Tbl. \ref{['tab: paras_table']}. The dissociation threshold is $x^{\mathrm{diss}}_2=10~\mathrm{\mathring{A}}$. The number of initial trajectories for each curve is $N_{\mathrm{traj}}=20000$. The standard deviation is marked by the shaded area around each curve.
• Figure 3: Total vibrational energy $\langle E\rangle =\langle E_1\rangle+\langle E_2\rangle$ over time for the anharmonic and harmonic system and the two respective cases $\omega_1=\omega_{2}$ and $\omega_1\neq\omega_{2}$. For the case of $\omega_1\neq\omega_{2}$, we set $\omega_1=20~\mathrm{meV}$ and $\omega_2=22.5~\mathrm{meV}$. Other parameters are the same as in parameter set (1) in Tbl. \ref{['tab: paras_table']}. The voltage is $\Phi=0.5 ~\mathrm{V}$.
• Figure 4: Kinetic energies $\langle E_{\mathrm{kin},1} \rangle$ and $\langle E_{\mathrm{kin},2} \rangle$ of the individual vibrational modes over time for the anharmonic system. At the time $t_{\mathrm{ss}}$, the system has reached a limit cycle and the average kinetic energy stops changing over time. Shown are the two cases $\omega_1=\omega_{2}$, and $\omega_1\neq\omega_{2}$. The trajectory has been initialized with the initial conditions $(x_1,x_2)=(0,0)$ and $(p_1,p_2)=(0,0)$. The parameters are the same as for Fig. \ref{['fig: dissociation_parameter_set_1']}, however the stochastic force is removed: $\mathbf{f}(t) = \boldsymbol{0}$. The voltage is $\Phi= 0.5~ \text{V}$.
• Figure 5: Trajectory in the $(x_1,x_2)$ plane after reaching a limit cycle in white for the anharmonic model and the case $\omega_1=\omega_{2}$. The random force has been removed, $\mathbf{f}(t) = \boldsymbol{0}$. The bias voltage is $\Phi=0.5~\mathrm{V}$. The background shows the curl of the force field.