Correlated Electron-ion Dynamics Research Articles

Anharmonic coupling between electrons and TO phonons in the vicinity of a ferroelectric quantum critical point

We explore a novel coupling mechanism of electrons with the transverse optical (TO) phonon branch in a regime when the TO mode becomes highly anharmonic and drives the ferroelectric phase transition. We show that this anharmonicity, which leads to a collective motion of ions, is able to couple electronic and lattice displacement fields. An effective correlated electron-ion dynamics method is required to capture the effect of the onset of the local electric polarization due to this collective behavior close to the quantum critical point. We identify an intermediate temperature range where an emergent phonon drag may contribute substantially to thermoelectric conductivity in this regime. We find that, under optimal conditions, this extra contribution may be larger than values achieved so far in the benchmark material, PbTe. In the last part we make a case for the importance of our results in the generic problem of anharmonic electron-lattice dynamics.

Analog of Rabi oscillations in resonant electron-ion systems

Quantum coherence between electron and ion dynamics, observed in organic semiconductors by means of ultrafast spectroscopy, is the object of recent theoretical and computational studies. To simulate this kind of quantum coherent dynamics, we have introduced in a previous article [L. Stella, M. Meister, A. J. Fisher, and A. P. Horsfield, J. Chem. Phys. 127, 214104 (2007)] an improved computational scheme based on Correlated Electron-Ion Dynamics (CEID). In this article, we provide a generalization of that scheme to model several ionic degrees of freedom and many-body electronic states. To illustrate the capability of this extended CEID, we study a model system which displays the electron-ion analog of the Rabi oscillations. Finally, we discuss convergence and scaling properties of the extended CEID along with its applicability to more realistic problems.

Modelling non-adiabatic processes using correlated electron-ion dynamics

Here we survey the theory and applications of a family of methods (correlated electron-ion dynamics, or CEID) that can be applied to a diverse range of problems involving the non-adiabatic exchange of energy between electrons and nuclei. The simplest method, which is a paradigm for the others, is Ehrenfest Dynamics. This is applied to radiation damage in metals and the evolution of excited states in conjugated polymers. It is unable to reproduce the correct heating of nuclei by current carrying electrons, so we introduce a moment expansion that allows us to restore the spontaneous emission of phonons. Because of the widespread use of Non-Equilibrium Green's Functions for computing electric currents in nanoscale systems, we present a comparison of this formalism with that of CEID with open boundaries. When there is strong coupling between electrons and nuclei, the moment expansion does not converge. We thus conclude with a reworking of the CEID formalism that converges systematically and in a stable manner.

Stochastic quantum molecular dynamics

An approach to correlated dynamics of quantum nuclei and electrons both in dynamical interaction with external environments is presented. This stochastic quantum molecular dynamics rests on a theorem that establishes a one-to-one correspondence between the total ensemble-averaged current density of interacting nuclei and electrons and a given external vector potential. The theory allows for a first-principles description of phenomena previously inaccessible via standard quantum molecular dynamics such as electronic and nuclear relaxation in photochemistry, dissipative correlated electron-ion dynamics in intense laser fields, nuclear dephasing, etc. As a demonstration of the approach, we discuss the rotational relaxation of 4-(N,N-dimethylamino)benzonitrile in a uniform bath in the limit of classical nuclei.

Generalization of correlated electron-ion dynamics from nonequilibrium Green’s functions

We present a new formulation of the correlated electron-ion dynamics (CEID) by using equations of motion for nonequilibrium Green's functions, which generalizes CEID to a general nonequilibrium statistical ensemble that allows for a variable total number of electrons. We make a rigorous connection between CEID and diagrammatic perturbation theory, which furthermore allows the key approximations in CEID to be quantified in diagrammatic terms, and, in principle, improved. We compare analytically the limiting behavior of CEID and the self-consistent Born approximation (SCBA) for a general dynamical nonequilibrium state. This comparison shows that CEID and SCBA coincide in the weak electron-phonon coupling limit, while they differ in the large ionic mass limit where we can readily quantify their difference. In particular, we illustrate the relation between CEID and SCBA by perturbation theory at the fourth-order in the coupling strength.

Inelastic quantum transport in nanostructures: The self-consistent Born approximation and correlated electron-ion dynamics

A dynamical method for inelastic transport simulations in nanostructures is compared to a steady-state method based on nonequilibrium Green's functions. A simplified form of the dynamical method produces, in the steady state in the weak-coupling limit, effective self-energies analogous to those in the Born approximation due to electron-phonon coupling. The two methods are then compared numerically on a resonant system consisting of a linear trimer weakly embedded between metal electrodes. This system exhibits an enhanced heating at high biases and long phonon equilibration times. Despite the differences in their formulation, the static and dynamical methods capture local current-induced heating and inelastic corrections to the current with good agreement over a wide range of conditions, except in the limit of very high vibrational excitations where differences begin to emerge.

Correlated electron-ion dynamics in metallic systems

In this paper we briefly discuss the problem of simulating non-adiabatic processes in systems that are usefully modelled using molecular dynamics. In particular we address the problems associated with metals, and describe two methods that can be applied: the Ehrenfest approximation and correlated electron-ion dynamics (CEID). The Ehrenfest approximation is used to successfully describe the friction force experienced by an energetic particle passing through a crystal, but is unable to describe the heating of a wire by an electric current. CEID restores the proper heating.

Robust nonadiabatic molecular dynamics for metals and insulators

We present a new formulation of the correlated electron-ion dynamics (CEID) scheme, which systematically improves Ehrenfest dynamics by including quantum fluctuations around the mean-field atomic trajectories. We show that the method can simulate models of nonadiabatic electronic transitions and test it against exact integration of the time-dependent Schrodinger equation. Unlike previous formulations of CEID, the accuracy of this scheme depends on a single tunable parameter which sets the level of atomic fluctuations included. The convergence to the exact dynamics by increasing the tunable parameter is demonstrated for a model two level system. This algorithm provides a smooth description of the nonadiabatic electronic transitions which satisfies the kinematic constraints (energy and momentum conservation) and preserves quantum coherence. The applicability of this algorithm to more complex atomic systems is discussed.

Using the quantized mean-field method to model Joule heating in a short nano-conductor

The quantized mean-field method (QMF) is an extension of the traditional mean-field method for simulating quantum mechanical systems with electrons and ions. It adds the quantum nature of the ions to the simulations. Here we transform the QMF equations from wave function form to density operator form, study the connection between QMF and the recent correlated electron–ion dynamics (CEID) method, and show that QMF is a special case of CEID. Our simulations show that QMF fails to produce correct Joule heating in a nano-conductor. This is due to the mean-field approximation for the electrons. However, quantum properties of the ions, such as zero point energy, are conserved.

Correlated electron–ion dynamics: the excitation of atomic motion by energeticelectrons

Correlated electron–ion dynamics (CEID) is an extension of molecular dynamicsthat allows us to introduce in a correct manner the exchange of energy betweenelectrons and ions. The formalism is based on a systematic approximation: smallamplitude moment expansion. This formalism is extended here to include theexplicit quantum spread of the ions and a generalization of the Hartree–Fockapproximation for incoherent sums of Slater determinants. We demonstrate thatthe resultant dynamical equations reproduce analytically the selection rules forinelastic electron–phonon scattering from perturbation theory, which control themutually driven excitations of the two interacting subsystems. We then use CEIDto make direct numerical simulations of inelastic current–voltage spectroscopyin atomic wires, and to exhibit the crossover from ionic cooling to heating as afunction of the relative degree of excitation of the electronic and ionic subsystems.

Correlated electron–ion dynamics with open boundaries: formalism

We extend a new formalism, which allows correlated electron–ion dynamics tobe applied to the problem of open boundary conditions. We implement this atthe first moment level (allowing heating of ions by electrons) and observe theexpected cooling in the classical part of the ionic kinetic energy and current-inducedheating in the quantum contribution. The formalism for open boundaries should beeasily extended to higher moments of the correlated electron–ion fluctuations.