PHYSICAL REVIEW B 94, 035411 (2016) Current-induced phonon renormalization in molecular junctions Meilin Bai, 1, 2 Clotilde S. Cucinotta, 2 , * Zhuoling Jiang, 1 Hao Wang, 1 Yongfeng Wang, 1, 3 Ivan Rungger, 2, 4 Stefano Sanvito, 2 , * and Shimin Hou 1, 3 , * 1 Key Laboratory for the Physics and Chemistry of Nanodevices, Department of Electronics, Peking University, Beijing 100871, China 2 School of Physics, Advanced Materials and Bioengineering Research Centre (AMBER) and Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN) Institute, Trinity College, Dublin 2, Ireland 3 Beida Information Research (BIR), Tianjin 300457, China 4 Materials Division, National Physical Laboratory, Teddington, TW11 0LW, United Kingdom (Received 14 March 2016; revised manuscript received 17 June 2016; published 8 July 2016) We explain how the electrical current flow in a molecular junction can modify the vibrational spectrum of the molecule by renormalizing its normal modes of oscillations. This is demonstrated with first-principles self-consistent transport theory, where the current-induced forces are evaluated from the expectation value of the ionic momentum operator. We explore here the case of H 2 sandwiched between two Au electrodes and show that the current produces stiffening of the transverse translational and rotational modes and softening of the stretching modes along the current direction. Such behavior is understood in terms of charge redistribution, potential drop, and elasticity changes as a function of the current. DOI: 10.1103/PhysRevB.94.035411 I. INTRODUCTION Current-induced forces are at the origin of a rich variety of effects, including vibrations and rotations, as well as mass and energy flow at interfaces [1]. These forces, developing in the presence of a current, underpin electromigration, a phenomenon arising from the transfer of momentum from the conduction electrons to the ions. They can induce structural transformation in nanosystems and transfer energy to phonons, in addition of being the ultimate cause of Joule heating [2]. When the electron current density is large enough, current- induced forces can control redox reactions at electrode surfaces and affect the functionality and stability of nanodevices, molecular motors, and switches [3–8]. As a consequence, gain- ing insight into the microscopic mechanisms and achieving control of current-induced forces in nanojunctions will pave the way for key advances in interface chemistry, molecular electronics, and in memory and logic applications. Molecular electronic devices, consisting of a single or a few molecules bridging two electrodes, have been thoroughly studied [9,10]. In designing robust molecular devices, it is crucial to have information on the status of the molecule in current-carrying conditions, since the applied bias and the current-induced forces may affect the chemical bonds both at the molecule-electrode interfaces and within the molecule itself. Molecular vibrations are directly related to the molecule geometry and inter/intramolecular bonds. Hence, vibrational spectroscopy methods, such as inelastic electron tunneling, infrared, and Raman, have been widely employed to investigate the conduction mechanism and the stability of molecular devices [11–19]. There is also some experimental evidence that the current can modify the vibrational modes of the molecule in a junction [17–19]. For example, the vibrational frequencies of a single C 60 sandwiched between two Au electrodes appear to be systematically lowered by the applied bias voltage, indi- cating that the C-C bonds may be weakened by the current [19]. * Corresponding authors: cucinotc@tcd.ie; SANVITOS@tcd.ie; smhou@pku.edu.cn Although experiments may sometimes achieve atomic res- olution [20,21], most of them can only measure macroscopic averaged quantities, meaning that the details of the micro- scopic processes occurring in a nanojunction often remain a matter of conjecture. This implies that computer simulations, which have the power to resolve processes atom by atom, are essential to magnify our view on these phenomena. One way to investigate how a current density perturbs the phonons of a biased system was proposed by L¨ u et al. [8]. A semiclassical generalized Langevin equation obtained from path integrals was employed together with parameters obtained from density functional theory (DFT). This approach is based on a perturbative expansion of an electron effective action [22] over the electron-phonon interaction matrix. Using this approach, the impact of the different forces—random forces describing Joule heating, current-induced forces including nonconservative wind forces, dissipative frictional forces, and the effective Lorentz-type force due to the Berry phase of the nonequilibrium electrons—was compared for a graphene nanoconstriction carrying high current [23]. The authors observed a strongly nonlinear current-induced heating and a breakdown of the harmonic approximation when the Fermi level was tuned close to a resonance in the electronic structure of the nanoconstriction, caused by the presence of negatively damped phonons. Here, we take an alternative approach and describe current- induced forces within the Born-Oppenheimer approximation. Since we are dealing with a nonequilibrium state where the energy may not be conserved [1], we follow the derivation of Di Ventra [24] and compute current-induced forces in a general way from the expectation value of the ionic momentum operator [25]. Importantly, in the presence of a stationary current, charge redistribution occurs, causing atomic rearrangements and modifying the instantaneous Hamiltonian. As a consequence, the vibrational spectrum changes. We account for such phenomena by calculating the electron density with the nonequilibrium Green’s function formalism (NEGF) combined with DFT. The density is then used to self-consistently evaluate the effective nonequilibrium 2469-9950/2016/94(3)/035411(7) 035411-1 ©2016 American Physical Society