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

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.

💡 Research Summary

This paper investigates whether the non‑conservative current‑induced forces that can cause vibrational instabilities in molecular nanojunctions persist when realistic anharmonic nuclear potentials are taken into account. Previous theoretical work demonstrated that, in multi‑mode systems with purely harmonic vibrational potentials, the antisymmetric (Berry) component of the electronic friction tensor can generate a rotational flow in phase space when two vibrational frequencies are (near) degenerate. This flow continuously pumps energy into the nuclear motion, leading to an instability at relatively low bias voltages. However, real molecules are never perfectly harmonic; they possess at least modest anharmonicity, which could detune the frequencies or otherwise modify the electronic forces.

To address this, the authors employ a mixed quantum‑classical framework: electronic degrees of freedom are integrated out using nonequilibrium Green’s functions (NEGF) in the wide‑band limit, yielding three contributions to the nuclear equations of motion – an adiabatic mean force, a friction tensor, and a stochastic force obeying a fluctuation‑dissipation relation in equilibrium. The resulting Markovian Langevin equation is solved numerically with the ABOBA algorithm, allowing long‑time stochastic simulations of the nuclear dynamics. The model consists of a two‑level electronic subsystem coupled to two vibrational modes. Mode 1 is kept harmonic (½ m₁ω₁²x₁²) while mode 2 is treated either as a Morse potential or as a quartic (x₂⁴) anharmonic well. The electronic hopping depends linearly on x₁, and the on‑site energies depend linearly on x₂. The leads are modeled as featureless reservoirs with constant coupling Γ, and the bias voltage is applied symmetrically (μ_L = –μ_R = eΦ/2).

The study explores several parameter sets: (i) a fully harmonic reference where ω₁≈ω₂ (degenerate case), (ii) slightly anharmonic cases where the Morse depth or quartic coefficient introduces a few percent frequency shift, and (iii) strongly anharmonic cases with large detuning. For each case, the authors compute time‑averaged vibrational energies, monitor trajectories for rotational behavior, evaluate dissociation probabilities (defined by the coordinate exceeding a preset threshold), and calculate steady‑state electronic currents.

Key findings are:

1. In the purely harmonic, degenerate system, the antisymmetric Berry force drives a persistent clockwise (or counter‑clockwise) rotation in the (x₁,x₂) plane. The vibrational energy grows rapidly, and the dissociation probability becomes appreciable (≥10 %) even at bias voltages as low as 0.1 V. The current‑voltage characteristics show a modest increase due to the additional heating but are not dramatically altered.

2. Introducing a modest anharmonicity (≈5 % change in the effective frequency of mode 2) breaks the exact degeneracy. The rotational flow is strongly suppressed; the vibrational energy saturates at a value comparable to the equilibrium thermal energy, and the dissociation probability drops below 1 %. The I‑V curve remains essentially unchanged compared with the harmonic case, indicating that the current‑induced heating is dominated by Joule heating rather than the Berry force.

3. For strongly anharmonic potentials (deep Morse wells or large quartic coefficients), the antisymmetric component of the friction tensor becomes negligible. The system behaves as if only a conservative adiabatic force and a positive‑definite friction are present. Consequently, no instability is observed at any bias voltage studied, and the dissociation probability stays near zero. The steady‑state current is identical to that of the harmonic reference, confirming that the electronic transport is insensitive to the details of the nuclear potential in this regime.

These results demonstrate that the vibrational instability driven by non‑conservative electronic forces is extremely fragile: it requires both near‑degeneracy of the vibrational modes and an essentially harmonic nuclear landscape. Even slight anharmonicity, which is unavoidable in real molecules, is sufficient to quench the instability. This explains why experimental reports of low‑bias current‑induced rupture are scarce, despite theoretical predictions based on harmonic models.

The paper concludes that, for practical molecular electronics, anharmonicity can be viewed as a stabilizing factor rather than a source of additional failure. Future work should extend the analysis to more complex electronic structures (multiple orbitals, strong electron‑electron interactions), incorporate memory effects beyond the Markovian approximation, and explore temperature‑dependent anharmonicities to fully capture realistic device behavior.