Applying laser pulses with a driving frequency ω to solids, one observes ultrafast dynamics including high-harmonic generation with frequencies n*ω (n ∈ ℕ). We use our open-source software package CUED (external link, opens in a new window) [1] to investigate the high-harmonic emission spectrum emitted by the surface of the topological insulator Bi2Te3. Currently, we are further exploring the continuous shift of a high-harmonic order to arbitrary non-integer multiples of the driving frequency r*ω (r ∈ ℝ) beyond Ref. [2] by varying the shape of the driving pulse. We have developed an analytical formula for the shift of high-harmonics frequencies while changing the shape of the laser pulse. We have compared the analytical formula to numerical data finding quantitative agreement, thus validating the formula [3].

Using density-functional theory (DFT) and many-body perturbation theory within the GW approximation, electronic band structures and quasiparticle energies in molecules can be computed to model a wide range of materials, e.g. electronics, pharmaceuticals or cosmetics. The GW-Bethe-Salpeter equation (GW-BSE) approach further enables the accurate computation of optical properties corresponding to excitations of the system, e.g. providing a means to find potential candidates for novel photovoltaics and other electronics. We are currently working on an implementation of the BSE in the open-source package CP2K to take advantage of the available low-scaling GW methods [4,5].

[1] J. Wilhelm et al.:  Semiconductor Bloch-equations formalism: Derivation and application to high-harmonic generation from Dirac fermions, Phys. Rev. B 103, 125419 (2021). (external link, opens in a new window)

[2] C. P. Schmid et al.: Tunable non-integer high-harmonic generation in a topological insulator, Nature 593, 385-390 (2021). (external link, opens in a new window)

[3] M. Graml et al.: Theory of non-integer high-harmonic generation in a topological surface state, Physical Review B 107, 054305 (2023) (external link, opens in a new window)

[4] J. Wilhelm et al.: Toward GW calculations on thousands of atoms, J. Phys. Chem. Lett. 9, 306-312 (2018) (external link, opens in a new window).

[5] M. Graml et al.: Low-Scaling GW Algorithm Applied to Twisted Transition-Metal Dichalcogenide Heterobilayers, J. Chem. Theory Comput. 20, 2202–2208 (2024) (external link, opens in a new window).