thesis for the degree of doctor of philosophy Microscopic Theory of Exciton Dynamics in Two-Dimensional Materials Samuel Brem Department of Physics Chalmers University of Technology G¨oteborg, Sweden 2020 Microscopic Theory of Exciton Dynamics in Two-Dimensional Materials Samuel Brem © Samuel Brem, 2020. ISBN 978-91-7905-391-8 Doktorsavhandlingar vid Chalmers tekniska h¨ogskola Ny serie nr 4858 ISSN 0346-718X Department of Physics Chalmers University of Technology SE-412 96 G¨oteborg Sweden Telephone + 46 (0)31-772 1000 Cover illustration: Artistic impression of momentum-indirect excitons composed of elec- trons and holes at different valleys of conduction and valence band. Created with the software Blender. Printed at Chalmers Reproservice G¨oteborg, Sweden 2020 ii Microscopic Theory of Exciton Dynamics in Two-Dimensional Materials Samuel Brem Department of Physics Chalmers University of Technology Abstract Transition Metal Dichalcogenides (TMDs) present a giant leap forward towards the realization of nanometer-sized quantum devices. As a direct consequence of their truly two-dimensional character, TMDs exhibit a strong Coulomb-interaction, leading to the formation of stable electron-hole pairs, so-called excitons. These quasi-particles have a large impact on optical properties as well as charge-transport characteristics in TMDs. Therefore, a microscopic understanding of excitonic de- grees of freedom and their interactions with other particles becomes crucial for a technological application of TMDs in a new class of optoelectronic and pho- tonic devices. Furthermore, deeper insights into the dynamics of different types of exciton states will open the possibility to explore new quantum effects of the matter-light interaction. The aim of this thesis is to investigate the many-particle processes governing the ultrafast dynamics of excitons in TMD mono- and bilayers. Based on the density matrix formalism we develop equations describing an interacting system of elec- trons, phonons and photons, and numerically simulate the time- and momentum- resolved dynamics of excitons in different TMDs. First, we provide a detailed picture of exciton-light and exciton-phonon interac- tions with special focus on the impact of momentum-dark exciton states. In partic- ular, we develop and apply quantitative models for the i) broadening of excitonic resonances in linear absorption spectra, ii) formation of side peaks in photolumi- nescence spectra resulting from phonon-assisted recombination of momentum-dark excitons and iii) dynamical simulations of the formation of bound excitons out of a free electron-hole gas. Then, we investigate how the exciton-light interaction is modified when two TMD monolayers are vertically stacked into homo- and hetero- bilayers. Here we focus on the modification of optical spectra in bilayer systems by controlling the stacking angle. In particular, we iv) show how the interlayer hybridization of momentum-dark excitons can be controlled through the stacking angle and v) investigate how the localization phase of moir´eexcitons can be tuned. Our theoretical models have allowed us to predict experimentally accessible exci- tonic characteristics, which have been demonstrated in several joint experiment- theory collaborations including linear absorption, photoluminescence and ultrafast pump-probe experiments. The gained microscopic insights into exciton optics, ex- citon dynamics and control of exciton phases is expected to contribute to the realization of TMD-based optoelectronic devices. Keywords: excitons, density matrix formalism, 2D materials, relaxation dynamics, exciton-phonon interaction, van der Waals materials iii iv List of publications This thesis consists of an introductory text and the following papers: 1. Exciton Relaxation Cascade in two-dimensional Transition Metal Dichalco- genides S Brem, M Selig, G Bergh¨auserand E Malic Scientific Reports 8: 8238 (2018) 2. Intrinsic Lifetime of Higher Excitonic States in Tungsten Diselenide Monolayers S Brem, J Zipfel, M Selig, A Raja, L Waldecker, J Ziegler, T Taniguchi, K Watanabe, A Chernikov, E Malic Nanoscale 11, 12381-12387 (2019) 3. Phonon-Assisted Photoluminescence from Indirect Excitons in Mono- layers of Transition-Metal Dichalcogenides S Brem, A Ekman, D Christiansen, F Katsch, M Selig, C Robert, X Marie, B Urbaszek, A Knorr, E Malic Nano Letters 20 (4), 2849{2856 (2020) 4. Hybridized Intervalley Moir´eExcitons and Flat Bands in Twisted WSe2 Bilayers S Brem, KQ Lin, R Gillen, JM Bauer, J Maultzsch, JM Lupton, E Malic Nanoscale 12, 11088-11094 (2020) 5. Tunable Phases of Moir´eExcitons in van der Waals Heterostructures S Brem, C Linder¨alv,P Erhart, E Malic Nano Letters (2020) https://dx.doi.org/10.1021/acs.nanolett.0c03019 My contribution to the appended papers As first-author, I developed the theoretical models, performed the numerical evaluation, analyzed the results and wrote the paper with the help of my main supervisor and other coauthors. v Publications not appended in this thesis: 6. Microscopic modeling of tunable graphene-based terahertz Landau- level lasers S Brem, F Wendler, E Malic Physical Review B 96 (4), 045427 (2017) 7. Symmetry-breaking supercollisions in Landau-quantized graphene F Wendler, M Mittendorff, JC K¨onig-Otto,S Brem, C Berger, WA de Heer, R B¨ottger,H Schneider, M Helm, S Winnerl, E Malic Physical Review Letters 119 (6), 067405 (2017) 8. Carrier Dynamics in Graphene: Ultrafast Many-Particle Phenomena E Malic, T Winzer, F Wendler, S Brem, R Jago, A Knorr, M Mittendorff, JC K¨onig-Otto,T Pl¨otzing,D Neumaier, H Schneider, M Helm, S Winnerl Annalen der Physik 529 (11), 1700038 (2017) 9. Dark excitons in transition metal dichalcogenides E Malic, M Selig, M Feierabend, S Brem, D Christiansen, F Wendler, A Knorr, G Bergh¨auser Physical Review Materials 2 (1), 014002 (2018) 10. Molecule signatures in photoluminescence spectra of transition metal dichalcogenides M Feierabend, G Bergh¨auser,M Selig, S Brem, T Shegai, S Eigler, E Malic Physical Review Materials 2 (1), 014004 (2018) 11. Dielectric engineering of electronic correlations in a van der Waals heterostructure P Steinleitner, P Merkl, A Graf, P Nagler, K Watanabe, T Taniguchi, J Zipfel, C Sch¨uller,T Korn, A Chernikov, S Brem, M Selig, G Bergha¨auser,E Malic, R Huber Nano Letters 18 (2), 1402-1409 (2018) 12. Electrically pumped graphene-based Landau-level laser S Brem, F Wendler, S Winnerl, E Malic Physical Review Materials 2 (3), 034002 (2018) 13. Impact of strain on the excitonic linewidth in transition metal dichalco- genides Z Khatibi, M Feierabend, M Selig, S Brem, C Linder¨alv,P Erhart, E Malic 2D Materials 6 (1), 015015 (2018) vi 14. Interlayer exciton dynamics in van der Waals heterostructures S Ovesen, S Brem, C Linder¨alv,M Kuisma, T Korn, P Erhart, M Selig, E Malic Communications Physics 2 (1), 23 (2019) 15. Dielectric disorder in two-dimensional materials A Raja, L Waldecker, J Zipfel, Y Cho, S Brem, J Ziegler, M Kulig, T Taniguchi, K Watanabe, E Malic, T Heinz, T Berkelbach, A Chernikov Nature Nanotechnology 14, 832{837 (2019) 16. Spatio-temporal dynamics in graphene R Jago, R Perea-Causin, S Brem, E Malic Nanoscale 11, 10017-10022 (2019) 17. Disorder-induced broadening of excitonic resonances in transition metal dichalcogenides M Dwedari, S Brem, M Feierabend, E Malic Physical Review Materials 3, 074004 (2019) 18. Ultrafast transition between exciton phases in van der Waals het- erostructures P Merkl, F Mooshammer, P Steinleitner, A Girnghuber, K-Q Lin, P Nagler, J Holler, C Sch¨uller,JM Lupton, T Korn, S Ovesen, S Brem, E Malic, R Huber Nature Materials 18, 691{696 (2019) 19. Exciton propagation and halo formation in two-dimensional materials R Perea-Causin, S Brem, R Rosati, R Jago, M Kulig, JD Ziegler, J Zipfel, A Chernikov, E Malic Nano Letters 19 (10), 7317-7323 (2019) 20. Exciton diffusion in monolayer semiconductors with suppressed dis- order J Zipfel, M Kulig, R Perea-Caus´ın,S Brem, JD Ziegler, R Rosati, T Taniguchi, K Watanabe, MM Glazov, E Malic, A Chernikov Physical Review B 101 (11), 115430 (2020) 21. Negative effective excitonic diffusion in monolayer transition metal dichalcogenides R Rosati, R Perea-Caus´ın,S Brem, E Malic Nanoscale 12, 356-363 (2020) 22. Suppression of intervalley exchange coupling in the presence of momentum- dark states in transition metal dichalcogenides M Selig, F Katsch, S Brem, GF Mkrtchian, E Malic, A Knorr Physical Review Research 2, 023322 (2020) 23. Optical fingerprint of bright and dark localized excitonic states in atomically thin 2D materials vii M Feierabend, S Brem, E Malic Physical Chemistry Chemical Physics 21 (47), 26077-26083 (2020) 24. Twist-tailoring Coulomb correlations in van der Waals homobilayers P Merkl, F Mooshammer, S Brem, A Girnghuber, KQ Lin, L Weigl, M Liebich, CK Yong, R Gillen, J Maultzsch, JM Lupton, E Malic, R Huber Nature Communications 11 (1), 1-7 (2020) 25. Microscopic modeling of pump{probe spectroscopy and population Inversion in transition metal dichalcogenides R Perea-Caus´ın,S Brem, E Malic Physica Status Solidi (b), 2000223 (2020) 26. Criteria for deterministic single-photon emission in two-dimensional atomic crystals JJP Thompson, S Brem, H Fang, J Frey, SP Dash, W Wieczorek, E Malic Physical Review Materials 4, 084006 (2020) 27. Brightening of spin-and momentum-dark excitons in transition metal dichalcogenides M Feierabend, S Brem, A Ekman, E Malic 2D Materials (2020) 28. Temporal evolution of low-temperature phonon sidebands in WSe2 monolayers R Rosati, S Brem, R Perea-Caus´ın,K Wagner, E Wietek, J Zipfel, M Selig, T Taniguchi, K Watanabe, A Knorr, A Chernikov, E Malic ACS Photonics (2020) 29. Strain-dependent exciton diffusion in transition metal dichalcogenides R Rosati, S Brem, R Perea-Caus´ın,R Schmidt, I Niehues, S Michaelis de Vas- concellos, R Bratschitsch, E Malic 2D Materials (2020) 30. Excitation-induced dephasing in 2D materials and van der Waals het- erostructures D Erkensten, S Brem, E Malic arXiv preprint 2006.08392 (2020) 31.