Dynamical LEED computation

We performed dynamical LEED simulations on the commensurate CDW phase of 1T-TaS2, varying the atomic displacements of sulfur and tantalum continuously from the undistorted structure towards the C-phase structure recently reconstructed [129]. We are aware that the C phase is a simple approximation for the description of the high-temperature incommensurate CDW phase. However, it exhibits the same crucial feature of opposing sulfur displacements that we believe is responsible for the different sensitivities of the main lattice peaks. Also, dynamic LEED calculations involve high computational effort, in particular for large unit cells necessary for incommensurate structures.

The obtained data contains PLD-amplitude- and energy-dependent scattering intensities for main lattice and CDW satellites spots. In the following, we focus on main lattice diffraction intensities.

In the electron energy range of 70-140 eV, the diffraction intensity is mainly determined by scattering from sulfur atoms, explaining the strong dependence from the PLD amplitude of sulfur atoms (Fig.3.11a).

Figure 3.11b shows PLD dependent intensities for an electron energy of 100 and 80 eV, each normalized to the intensity value for zero distortion (metal structure). The PLD amplitude range is adapted to the expected values realized in the incommensurate phase [42] which are assumed to be considerably smaller (∼ 30% of PLD amplitude of the commensurate low-temperature phase).

In this range for 100 eV, we can show that there are two groups of main lattice spots that respond differently upon PLD change, whereas for 80 eV, all intensities follow a common curve. Moreover,

the magnitude of the relative intensity changes approximately matches the observed ones in the experiment. The curves within a group of main lattice peaks {(1 0), (-1 1)} and {(-1 0), (0 1), (1 -1)} conincide since the simulation is performed at normal incidence.

Figure 3.11c shows energy-dependent intensity curves for two main lattice peaks contained

b

Main Lattice reflexes - 80 eV 0.95

1

Norm. Intensity

Main Lattice reflexes - 100 eV

( 1 0 )

Figure 3.11: Dynamical LEED simulations. (a) Normalized intensity of main lattice reflex (1 0) as a function of sulfur and tantalum displacement for an electron energy of 100 eV. Enhanced scattering off sulfur atoms results in a much stronger dependence on the sulfur atom displacements. (b) Normalized intensities of main lattice spots for an electron energy of 80 and 100 eV as a function of the fraction of the maximum commensurate PLD amplitude. The diffraction reflexes split up into two spot groups. Light and dark blue curves coincide, respectively, due to normal incidence of the electron beam. (c) LEED spectra (top) for both groups (light and dark blue) for vanishing (points) and finite (dash points) distortion. The percentage refers to the amplitude of the commensurate PLD in low-temperature phase. The intensity ratio (bottom) illustrates the energy-dependent sensitivity between reflex groups.

in one of the two groups (light and dark blue), each for zero PLD and 30% PLD amplitude of the commensurate low-temperature phase. The ratio of spectra for each spot with minimal and maximal amplitude (Fig.3.11c, bottom) displays a rich oscillatory behavior. Importantly, however, for energies of 80 eV and 100 eV, the spots exhibit a drastically different sensitivity to PLD changes, with a small and large difference for the separate spot groups, respectively. These predictions directly corroborate our experimental findings at the different electron beam energies.

In the following, a brief summary of the previous two chapters is given. After this,the current technological status of ultrafast LEED are discussed and possible future perspectives for more detailed work on CDW or CDW-related materials systems are pointed out.

4.1 Summary of Publications

Chapter 2 reports the design and fabrication of a micrometer-scale electron gun for the implemen-tation in ULEED experiments. The fabrication process consists of multiple steps, including the preparation of a suitable support for electrical contacts by means of photolithography, as well as the construction of the gun assembly, the nanometric tip emitter and the shielding using focused-ion-beam (FIB) etching. We achieve an effective gun diameter of 80 µm, allowing for a considerably shorter propagation distance to the sample in the diffraction experiment as compared to the previous minigun design.

Finite element simulations enable us to estimate the gun performance. A large number of particles, each having different initial conditions, are propagated to obtain the trajectories in the electric field determined by the gun geometry. At a distance of 400µm behind the ground aperture, the pulse duration is extracted from the differences in time of flight within the ensemble of particles for an energy range of 40-100 eV, yielding values of 1 ps or less for most electron energies.

Finally, the pulse duration and the momentum resolution are characterized experimentally. For the measurement of the pulse duration, the electron pulses traverse a time-dependent electric field that forms when an intense laser pulse hits a metal grid. From the transient change of the projected image, we obtain a pulse duration of 1.3± 0.2 ps. LEED images of 1T-TaS₂ demonstrate the achievable momentum resolution yielding a transfer width of 25 nm and a beam emittance of 200 nm rad.

In chapter 3, the microgun is employed to study the non-equilibrium lattice dynamics of the charge-density wave material 1T-TaS₂with 1 ps temporal resolution. In the nearly commensurate

and incommensurate CDW phase, we trace the time-dependent intensity of main and satellite reflexes as well as the diffuse background. The intensity redistribution within a diffraction pattern is governed by changes of the average PLD amplitude, CDW-related fluctuation modes and non-CDW phonons.

We use two approaches in order to separate the dynamics of the structural order parameter from the phonon population. We compare the different intensities of two inequivalent classes of main lattice reflections to the PLD, and exploit the direct sensitivity of the satellite reflexes to the PLD.

When we apply these methods to our data, we obtain the transient non-equilibrium signal of the average PLD amplitude that recovers over the course of about 60 ps.

The observations suggest a sequence of processes that include the laser-induced heating of the electronic system, efficient coupling to CDW-coupled modes, lattice equilibration, and cooling of the thermalized state. We assign the long thermalization time of the order parameter to the presence of a hot population of long-lived CDW-coupled excitations. For strong laser excitation, the broadening of superlattice satellite reflexes indicates the presence of dislocation-type CDW defects that additionally reduce the PLD in the defect core.