The time evolution of two classes of systems is studied with real time molecular dynamics simulations. The first consists of a coupled electron-lattice system. For a periodic system, we present results for the time evolution of a one-dimensional system consisting of an electron, described by a tight-binding Hamiltonian, and a harmonic lattice, coupled by a deformation-type potential. We solve numerically the nonlinear system of equations of motion for this model in order to study the effects of varying the electronic effective mass for several initial conditions and coupling strengths. A large effective mass favors localized polaron formation for initially localized electrons. For initially extended electronic states, increasing the effective mass of an electron initially close to the bottom of the band makes localization more difficult, while for an initially highly excited electron, localized polaron formation is possible only when the electronic effective mass and the atomic masses of the lattice become of the same order. For a small parameter range, we find an impressive recurrence, a periodic and a complete exchange between the electronic and vibrational degrees of freedom of a small part of the initial electronic energy. The disordered case, described by a tight-binding model exhibiting metal-insulator transition (the diagonal matrix elements having a spatial variation incommensurate with the lattice), demonstrates the combined effects of disorder and electron-phonon interaction. The el-ph interaction has profound effects, especially on one-electron extended states just above the mobility edge, where the electronic states change from extended to localized. Polaron formation is facilitated close to the mobility edge and, in most cases, the localization length (lc) decreases upon increasing the disorder or el-ph coupling, as expected. However, for strongly localized states due to disorder or el-ph interaction, increase of el-ph coupling or disorder, respectively, results in an increase of lc. This increase is due to phonon assisted hopping. The second class of systems studied consists of carbon and hydrogen. We calculate phonon anharmonic effects in diamond and graphite using a tight-binding molecular dynamics scheme. Using one-phonon spectral intensities that have been calculated through the Fourier transform of the velocity-velocity correlation function, we study the temperature dependence of the phonon frequency shift and phonon linewidth. In the case of the zone-center optical mode of diamond where experimental data are available, our results are in good agreement with experiment. A tight-binding model for carbon-hydrogen interaction is developed and used in molecular dynamics simulations. The parameters are obtained by fitting to the electronic and vibrational properties of methane. The results obtained for hydrocarbon molecules are in good agreement with experimental data and first-principles results. Interstitial hydrogen in diamond is also studied with this model and the results are compared with available experimental and ab initio results. The case of hydrogenated amorphous carbon is considered as well.
The time evolution of two classes of systems is studied with real time molecular dynamics simulations. The first consists of a coupled electron-lattice system. For a periodic system, we present results for the time evolution of a one-dimensional system consisting of an electron, described by a tight-binding Hamiltonian, and a harmonic lattice, coupled by a deformation-type potential. We solve numerically the nonlinear system of equations of motion for this model in order to study the effects of varying the electronic effective mass for several initial conditions and coupling strengths. A large effective mass favors localized polaron formation for initially localized electrons. For initially extended electronic states, increasing the effective mass of an electron initially close to the bottom of the band makes localization more difficult, while for an initially highly excited electron, localized polaron formation is possible only when the electronic effective mass and the atomic masses of the lattice become of the same order. For a small parameter range, we find an impressive recurrence, a periodic and a complete exchange between the electronic and vibrational degrees of freedom of a small part of the initial electronic energy. The disordered case, described by a tight-binding model exhibiting metal-insulator transition (the diagonal matrix elements having a spatial variation incommensurate with the lattice), demonstrates the combined effects of disorder and electron-phonon interaction. The el-ph interaction has profound effects, especially on one-electron extended states just above the mobility edge, where the electronic states change from extended to localized. Polaron formation is facilitated close to the mobility edge and, in most cases, the localization length (lc) decreases upon increasing the disorder or el-ph coupling, as expected. However, for strongly localized states due to disorder or el-ph interaction, increase of el-ph coupling or disorder, respectively, results in an increase of lc. This increase is due to phonon assisted hopping. The second class of systems studied consists of carbon and hydrogen. We calculate phonon anharmonic effects in diamond and graphite using a tight-binding molecular dynamics scheme. Using one-phonon spectral intensities that have been calculated through the Fourier transform of the velocity-velocity correlation function, we study the temperature dependence of the phonon frequency shift and phonon linewidth. In the case of the zone-center optical mode of diamond where experimental data are available, our results are in good agreement with experiment. A tight-binding model for carbon-hydrogen interaction is developed and used in molecular dynamics simulations. The parameters are obtained by fitting to the electronic and vibrational properties of methane. The results obtained for hydrocarbon molecules are in good agreement with experimental data and first-principles results. Interstitial hydrogen in diamond is also studied with this model and the results are compared with available experimental and ab initio results. The case of hydrogenated amorphous carbon is considered as well.
We present results for the time evolution of a one-dimensional system consisting of an electron, described by a tight-binding Hamiltonian and a harmonic latttice, coupled by a deformation-type potential. We solve numerically the nonlinear system of equations of motion for this model in order to study the effects of varying the electronic effective mass for several initial conditions and coupling strengths. Different types of localized and extended states are formed with features that are absent from the traditional polaronic states and depend very strongly on the initial electronic configuration and effective mass in a very often unexpected manner. We find that, in general, an increase of the initial electronic energy decreases the ability of the system to form localized states. However, a large effective mass favors localized polaron formation for initially localized electrons, but this is not always the case for initially extended electronic states. In the latter case, increasing the effective mass of an electron initially close to the bottom of the band makes localization more difficult, while for an initially highly excited electron, localized polaron formation is possible only when the electronic effective mass and the atomic masses of the lattice become of the same order. Finally, for a small parameter range, we find an impressive recurrence, a periodic and a complete exchange between the electronic and vibrational degrees of freedom of a small part of the initial electronic energy.
We study the time dependence of a combined system of an electron described by a tight-binding model interacting with vibrational degrees of freedom in a one-dimensional lattice. The time evolution of our coupled model is described by a nonlinear system of differential-difference equations. Apart from localized solutions (polarons) and extended (Bloch-like) solutions, we found that for a small parameter range, there exists a periodic exchange of energy between the electronic and vibrational degrees of freedom: a small part of the electronic energy is transferred to the lattice and then completely back to the electron with an impressive regularity.
Optimizing various properties of materials have been under intensive focus for many decades. In recent years, the exposure of ultrafast techniques enhance the possibility of seizing this goal. As by employing these techniques, one can expose the system under strong short fields, and investigate the transient response of various low-lying excitations. Such studies will strengthen our understanding of interplays among various degrees of freedom in correlated materials, and thereby facilitate the chance to manipulate different properties of these systems. Of our particular attention is the electron-lattice dynamics, where modulating a particular vibrational mode of the crystal lattice, will lead to the emergence of new quasi stable'' lattice structures as well as novel transient phenomena. Aside from these experimental prospects, the above mentioned goals were also the subject of an extensive theoretical studies. In this thesis, we investigated the in and out of equilibrium dynamics of electronic systems which are interacting with lattice degrees of freedom. We employed the two-time Keldysh Green's function within the framework of the dynamical mean field theory to conduct our researches on this subject. In our first attempt, we studied the dynamical response of a one-electron system under a linear electron-lattice interaction. We explored the real-time formation of a bound quasiparticle, known as a polaron, under various parameter regimes of the model. We presented that when the carrier is suddenly coupled to the lattice degrees of freedom, the long-time response of the system in the strong coupling limit exhibits both bound, polaronic, and unbound, delocalized, states. We characterized the nature of such a mixed state using the adiabatic picture of the model. We also showed that the formed polaron is dressed by excited phononic states, in contrast to its equilibrium counterpart, where the ground-state phononic states are bounding the electron. We also addressed the response of a many-body electronic system, weakly coupled to a bosonic bath, under various time dependent excitations, which brings the system to a bad-metallic phase. We employed a model which treated the Coulomb repulsive interaction locally. We presented that the relaxation of this excited state varies by the strength of the electron-electron interaction. We demonstrated that, for both insulating and metallic regimes of the system, a slow relaxation dynamics can be observed close to the phase transition from the metallic to insulating regimes of the system. Our analysis revealed that in the metallic side, this slow evolution is rooted in the spin-related physics of the problem. However, in the insulating regimes of the model, our results showed that presence of a gap in the spectral density of the insulating system prohibits the relaxation of the excited particles. We also studied the associated timescale for the adiabatic dynamics near the Mott transition. Our results exhibited that there is a nonadiabatic window'' in the metallic side of the phase transition, in which the adiabatic timescale is extremely long. We pointed out that the presence of such a window is intertwined with the slow relaxation timescale of the spin-related dynamics close to the Mott transition. We also captured an induced metallic phase near metal-to-insulator transition out of equilibrium. We initiated this study using the slave-rotor impurity solver, which is been coupled to the self-energies obtained from the first-order Luttinger-Ward functional for the Phonon degrees of freedom. We presented the emergence of the larger spectral density at small frequencies both in metallic and insulating phases close to the phase transition, which is surrounded by pseudo gaps. We explored the physics of such spectral densities as well as their dependencies on the phononic parameters. We postulated that this response of the system is due to the evolution of the system, in a non-thermal mechanism, towards a temperature which is less than the initial temperature of the system, before coupling to the bath. We also pointed out that the associated very slow relaxation dynamics is the result of the formation of psuedo-gaps around the quasiparticle peak.
Electron-phonon interactions underpin a variety of phenomena, ranging from transport and superconductivity to polarons and ultrafast carrier dynamics. Despite being one of the most intensely studied subjects in condensed matter physics, research on electron-phonon physics mostly focused on linear, first-order couplings. Second- and higher-order nonlinear couplings are commonly ignored because their calculations are too demanding and we lack computational frameworks that can provide both diagonal and off-diagonal coupling matrix elements. In this work, we report a theory and computational method for computing nonlinear electron-phonon interactions of any order in real materials. Our approach combines the advantages of unit-cell calculations of electron wavefunctions and supercell calculations of phonon perturbations, is systematically improvable, can be used with either semilocal or nonlocal exchange-correlation functionals, and is amenable to Wannier-Fourier interpolation. As a first proof of concept, we illustrate this method by computing second-order electron-phonon coupling matrix elements in diamond, lithium fluoride, and graphite as representative nonpolar semiconductors, polar semiconductors, and metals, respectively. Furthermore, we generalize the ab initio polaron equations to second-order electron-phonon couplings, and we show that second-order couplings are essential to achieve quantitative accuracy in polaron formation energies and hopping barriers. The present methodology will find application in the study of all properties and phenomena that are currently being investigated within the linear electron-phonon coupling approximation, from phonon-mediated superconductivity to excited-states dynamics, both in harmonic and anharmonic systems.
We have studied strong correlation effects and localization in metallic systems. Strong correlation effects and localization occurred in metallic systems due to strong electron-electron interactions and strong electron phonon coupling. Strong electron-phonon interactions have been found in such materials as cuprates, fullerides and manganites. The interplay of electronelectron and electron-phonon interactions in these correlated systems leaded to coexistence of or competition between various phases such as super conductivity, charge-density-wave or spin-density wave phases or formation of novel non Fermi liquid phases, polarons, bipolarons and so on. We have considered Holstein-Hubbard model for our work. The Holstein-Hubbard model provides on over simplified description of both electron-electron and electron-phonon interactions, it retains to be the relevant ingredients of a system in which electrons experience simultaneously an instantaneous short range repulsion and a phononmediated retarded attraction. In spite of its formal simplicity, it is not exactly solvable even in one dimension. So quantum simulators of Fermi-Hubbard modes based on either fermionic atoms inoptical lattice or electrons in artificial quantum dot crystals have been used. In our work a classical analog simulator was theoretically proposed for the two site Holstein-Hubbard model based on light transport in engineered waveguide lattices, which is capable of reproducing the temporal dynamics of the quantum model in Fock space as spatial evolution in photonic lattice. We have found that in the strong correlation regime the periodic temporal dynamics exhibited by the Holstein-Hubbard Hamiltonian, related to the excitation Holstein polarons has been explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight binding lattice. Light transport in two dimensional photonic lattices simulated in Fock space the hopping dynamics of two correlated electrons on a one dimensional lattice and exploited to visualize such phenomena as correlated tunneling of bond electron-electron molecules and their coherent motion under the action of d.c. or a.c. fields. The obtained results were found in good agreement with previous results.
The formation of a polaron quasiparticle from a bare electron is studied in the framework of the Holstein model of electron-phonon coupling. Using Schrödinger's formalism, we calculate the time evolution of the distribution of the electron and phonon density, lattice deformation, and the electron-phonon (el-ph) correlation functions in real space. The quantum dynamical nature of the phonons is preserved. The polaron formation time is related to the dephasing time of the continuum of unbound phonon excited states in the spectral function, which depends on the phonon frequency and the el-ph coupling strength. As the el-ph coupling increases, qualitative changes in polaron formation occur when the one-phonon polaron bound state forms. In the adiabatic regime, we find that a potential barrier between the quasi-free and heavy polaron states exists in both 2D and 3D, which is crucial for polaron formation dynamics. We compare to recent experiments.