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).

Also available via Google Scholar (external link, opens in a new window).

• M. Iannuzzi, J. Wilhelm, F. Stein, A. Bussy, H. Elgabarty, D. Golze, A.-S. Hehn, M. Graml, Š. Marek, B. S. Gökmen, C. Schran, H. Forbert, R. Z. Khaliullin, A. Kozhevnikov, M. Taillefumier, R. Meli, V. V. Rybkin, M. Brehm, R. Schade, O. Schütt, J. V. Pototschnig, H. Mirhosseini, A. Knüpfer, D. Marx, M. Krack, J. Hutter, and T. D. Kühne, The CP2K Program Package Made Simple, J. Phys. Chem. B 130, 1237 (2026).
• R. Pasquier, M. Graml, and J. Wilhelm, Gaussian Basis Sets for All-Electron Excited-State Calculations of Large Molecules, J. Chem. Theory Comput. 22, 540 (2025).
• M. Graml, K. Zollner, D. Hernangómez-Pérez, P. E. Faria Junior, and J. Wilhelm, Low-Scaling GW Algorithm Applied to Twisted Transition-Metal Dichalcogenide Heterobilayers, J. Chem. Theory Comput. 20, 2202 (2024).
• C. Roelcke, L. Z. Kastner, M. Graml, A. Biereder, J. Wilhelm, J. Repp, R. Huber, and Y. A. Gerasimenko, Ultrafast atomic-scale scanning tunnelling spectroscopy of a single vacancy in a monolayer crystal, Nat. Photonics 18, 595 (2024).
• M. Graml, M. Nitsch, A. Seith, F. Evers, and J. Wilhelm, Influence of chirp and carrier-envelope phase on noninteger high-harmonic generation, Phys. Rev. B 107, 054305 (2023).