Ultrafast coherent electron dynamics in solids

Due to recent developments in high-field laser systems, intense sub-cycle pulses can be generated on a routine basis in laser laboratories around the world. The electric fields originating from such few-femtosecond laser pulses can be on the same order of magnitude as the internal electric fields in bulk, crystalline solids. Due to the short duration of the pulses the laser fluence can remain below the damage threshold of the material. This paves the way for exploring strong-field effects in solids in a non-destructive regime experimentally, and hence motivates theoretical investigations in this field. This thesis is about numerical studies of strong-field effects in insulators and semiconductors. In particular, calculations are performed at a quantum mechanical level in order to examine the importance of quantum coherence in light-matter interactions in the strong-field regime. The dynamics of electrons in one-dimensional spatially periodic potentials excited by laser pulses was simulated. Upon introducing phenomenological decoherence into the dynamical equations, it was found that the optical responses calculated from geometric phases of mixed quantum system were in excellent agreement with conventional approaches for evaluating the optically induced current and polarization response. The excellent agreement even extended to highly non-linear, strong-field regimes, and motivated the development of a numerical method to simulate open quantum mechanical systems governed by spatially periodic Hamiltonians subject to perturbations with broken translation symmetry. Density functional theory was also employed to obtain wave functions from first principles for a number of materials, for which time-resolved optical responses were calculated. Field-induced intraband motion was found to modify the interband transitions significantly at high field strengths for transitions that would otherwise be resonant at low field strengths. For semiconducting materials like GaAs, where the transition elements are strongly peaked at the centre of the Brillouin zone, a step-like excitation mechanism was revealed at field strengths on the order of 0.5 V/Å. Similar ab initio methods were used to model the optical Faraday effect in the insulating, wide band gap material Al2O3 for few-cycle pulses. The magnitude of the effect was predicted using non-perturbative methods. Time-dependent calculations confirmed that a near-instantaneous response is to be expected.Es wurde die Dynamik von Elektronen in Festkörpern, die durch intensive, Subzykluslaserpulse erregt werden numerisch untersucht. Die Berechnungen wurden auf der quantenmechanischen Ebene und in verschiedenen, unabhängigen elektromagnetischen Eichungen ausgeführt. Zuerst wurde die Dynamik der Elektronen in eindimensionalen periodischen Potentialen berechnet um die Gültigket von neuen numerischen Verfahren zu bestätigen. Eines dieser Verfahren ermöglicht Simulationen von räumlich periodischen, gemischten Quantensystemen mit Hamilton-Operatoren mit gebrochener Translationssymmetrie. Durch Anwendung der Dichtefunktionaltheorie wurden Wellenfunktionen für Halbleiter und Insulatoren hergeleitet. Danach konnt der zeitliche Verlauf des optisch induzierten Strom nach ersten Prinzipien bestimmt werden. Die Bedeutung von intraband Bewegungen für Elektronen im halbleitenden Material GaAs wurde ebenfalls untersucht. Bei Erregung mit resonanten Pulsen konnte ein stufenförmiger Anregungsmechanismus beobachtet werden. Ähnliche Methoden wurden verwendet, um die Größe des optischen Faraday-Effektes in einem Insulator mit einer Bandlücke, grösser der Fotonenergie beider Pulse, zu bestimmen. Diese Berechnungen deuten darauf hin, dass ultraschnelle Kontrolle der optisch induzierten Chiralität möglich ist

Ultrafast coherent electron dynamics in solids

Due to recent developments in high-field laser systems, intense sub-cycle pulses can be generated on a routine basis in laser laboratories around the world. The electric fields originating from such few-femtosecond laser pulses can be on the same order of magnitude as the internal electric fields in bulk, crystalline solids. Due to the short duration of the pulses the laser fluence can remain below the damage threshold of the material. This paves the way for exploring strong-field effects in solids in a non-destructive regime experimentally, and hence motivates theoretical investigations in this field. This thesis is about numerical studies of strong-field effects in insulators and semiconductors. In particular, calculations are performed at a quantum mechanical level in order to examine the importance of quantum coherence in light-matter interactions in the strong-field regime. The dynamics of electrons in one-dimensional spatially periodic potentials excited by laser pulses was simulated. Upon introducing phenomenological decoherence into the dynamical equations, it was found that the optical responses calculated from geometric phases of mixed quantum system were in excellent agreement with conventional approaches for evaluating the optically induced current and polarization response. The excellent agreement even extended to highly non-linear, strong-field regimes, and motivated the development of a numerical method to simulate open quantum mechanical systems governed by spatially periodic Hamiltonians subject to perturbations with broken translation symmetry. Density functional theory was also employed to obtain wave functions from first principles for a number of materials, for which time-resolved optical responses were calculated. Field-induced intraband motion was found to modify the interband transitions significantly at high field strengths for transitions that would otherwise be resonant at low field strengths. For semiconducting materials like GaAs, where the transition elements are strongly peaked at the centre of the Brillouin zone, a step-like excitation mechanism was revealed at field strengths on the order of 0.5 V/Å. Similar ab initio methods were used to model the optical Faraday effect in the insulating, wide band gap material Al2O3 for few-cycle pulses. The magnitude of the effect was predicted using non-perturbative methods. Time-dependent calculations confirmed that a near-instantaneous response is to be expected.Es wurde die Dynamik von Elektronen in Festkörpern, die durch intensive, Subzykluslaserpulse erregt werden numerisch untersucht. Die Berechnungen wurden auf der quantenmechanischen Ebene und in verschiedenen, unabhängigen elektromagnetischen Eichungen ausgeführt. Zuerst wurde die Dynamik der Elektronen in eindimensionalen periodischen Potentialen berechnet um die Gültigket von neuen numerischen Verfahren zu bestätigen. Eines dieser Verfahren ermöglicht Simulationen von räumlich periodischen, gemischten Quantensystemen mit Hamilton-Operatoren mit gebrochener Translationssymmetrie. Durch Anwendung der Dichtefunktionaltheorie wurden Wellenfunktionen für Halbleiter und Insulatoren hergeleitet. Danach konnt der zeitliche Verlauf des optisch induzierten Strom nach ersten Prinzipien bestimmt werden. Die Bedeutung von intraband Bewegungen für Elektronen im halbleitenden Material GaAs wurde ebenfalls untersucht. Bei Erregung mit resonanten Pulsen konnte ein stufenförmiger Anregungsmechanismus beobachtet werden. Ähnliche Methoden wurden verwendet, um die Größe des optischen Faraday-Effektes in einem Insulator mit einer Bandlücke, grösser der Fotonenergie beider Pulse, zu bestimmen. Diese Berechnungen deuten darauf hin, dass ultraschnelle Kontrolle der optisch induzierten Chiralität möglich ist

DFT insight into the oxygen reduction reaction (ORR) on the Pt₃Co(111) surface

Proton exchange membrane fuel cells (PEMFC) are identified as future energy conversion devices, for application in portable and transportation devices. The preferred catalyst for the PEMFC is a Pt-catalyst. However, due to the slow oxygen reduction reaction (ORR) kinetics, high Pt loadings have to be used. The high Pt loadings lead to high costs of the PEMFC. Pt-Co alloys have been identified as catalysts having higher ORR activity higher than of a Pt-catalyst. Therefore, in the present study, the Density Functional Theory (DFT) technique is used to gain fundamental insight into the ORR on the Pt₃Co(111) surface. The calculations have been performed using the plane wave based code, the Vienna ab-initio Simulation Package (VASP). DFT spin-polarized calculations, utilizing the GGA-PW91 functional, have been used to study the adsorption of the ORR intermediates, viz. O₂, O, OOH, OH, H₂O and HOOH on the Pt₃Co(111) surface. The results obtained on the Pt₃Co(111) surface are compared to the results obtained on the Pt(111) surface. The adsorption strength of the ORR intermediates has been shown to be affected by the presence of Co to varying extents on the Pt₃Co(111) surface relative to adsorption on the Pt(111) surface. The most strongly stabilised ORR intermediate on the Pt₃Co(111) surface relative to adsorption on the Pt(111) surface is O: on the Pt₃Co(111) surface O is 0.45 eV more strongly adsorbed than on the Pt(111) surface. The least affected ORR intermediate is H₂O: H₂O adsorption on the Pt₃Co(111) surface is 0.20 eV more stable than on the Pt(111) surface. The energetically favorable, i.e. most strongly bound adsorption configurations for all the ORR intermediates involves a configuration in which the ORR intermediate is bonded to a surface Co atom. Therefore, the surface Co atom stabilizes the adsorption of the ORR intermediates, relative to adsorption on the Pt(111) surface. Coadsorbed configurations have been used to study the formation and dissociation of the ORR intermediates. From the coadsorption studies, it is shown that there is an energy cost associated with moving the adsorbates from their lowest energy sites, while separately adsorbed, to the higher energy coadsorbed state, prior to reaction. Hence, adsorbate-adsorbate interactions are expected to destabilize the coadsorbed state at the coverages considered in the present study. The Climbing Image Nudged Elastic Band (CI-NEB) method has been used to locate the transition states and to calculate the activation energies of the different elementary reaction steps. The calculated dissociation reaction activation energies for the Pt₃Co(111) surface are found to be lower than the dissociation activation energies calculated on the Pt(111) surface. The most lowered dissociation activation energy is for the dissociation of O₂: on the Pt₃Co(111) surface the activation energy is 0.08 eV, whilst on the Pt(111) surface the activation energy is 0.59 eV. For the hydrogenation reaction steps, only the hydrogenation of O to form OH occurs with a lower activation energy of 0.86 eV on the Pt₃Co(111) surface, compared to 0.95 eV on the Pt(111) surface. For other hydrogenation reaction steps, the activation energies on the Pt₃Co(111) surface are higher than those on the Pt(111) surface. Based on the calculated activation energies of the elementary ORR reaction steps, the dissociative and the O-assisted H₂O dissociation mechanisms are identified as the mechanisms most likely to be dominant on the Pt₃Co(111) surface, due to having lower activation energies relative to the associative mechanisms. For both mechanisms, the reaction step with the highest activation energy is the step involving O, i.e. O hydrogenation to form OH for the dissociative mechanism, and the O* + H₂O* --> 2OH* reaction for the O-assisted H₂O dissociation mechanism. Thus, the reaction step involving the reaction of the strongly adsorbed O species, is identified as the potential rate limiting step of the ORR. Both the dissociative and the O-assisted H₂O dissociation mechanisms are expected to be in competition on the Pt₃Co(111) surface, since the potential rate limiting step for both mechanisms have similar activation energies. Hence, the preferred mechanism will depend on the relative abundances of the H species and H₂O on the Pt₃Co(111) surface. A microkinetic analysis would be need needed to fully account for concentration and entropic contributions to the rate of reaction for the different ORR elementary reaction steps