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Many-Body Effects in Optical Excitations of Transition Metal Dichalcogenides

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Many-Body Effects in Optical Excitations of Transition Metal Dichalcogenides Research Collection Doctoral Thesis Many-Body Effects in Optical Excitations of Transition Metal Dichalcogenides Author(s): Sidler, Meinrad Publication Date: 2018-02 Permanent Link: https://doi.org/10.3929/ethz-b-000290909 Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library DISS. ETH NO. 24988 Many-Body Effects in Optical Excitations of Transition Metal Dichalcogenides A thesis submitted to attain the degree of DOCTOR OF SCIENCES of ETH ZURICH (Dr. sc. ETH Zurich) presented by MEINRAD SIDLER MSc ETH Physics, ETH Zurich born on 21.06.1989 citizen of Grosswangen LU accepted on the recommendation of: Prof. Ata¸cImamo˘glu,examiner Prof. Bernhard Urbaszek, co-examiner 2018 c Summary This dissertation treats a quantum impurity problem in a semiconductor system. Quantum impurity problems describe the interaction between a single quantum object and a complex environment. They are ubiquitous in physical systems and represent a fundamental field of research in many-body physics. Prominent examples are the Anderson orthogonality catastrophe and the Kondo effect. In both cases, the impurity is much heavier than the constituents of the interacting environment. If the mass of the impurity is comparable to the surrounding particles, we have a mobile impurity. These systems are usually harder to solve, as evident in the case of lattice polarons, which were first proposed in 1933 by Lev Landau. A complex but accurate description was found years later in 1955 by Richard Feynman. In recent years, strong coupling between single, mobile quantum impurities and a fermionic bath was realized in cold atoms. The interaction results in the formation of new quasi- particles called Fermi polarons. In contrast to other mobile quantum impurities such as lattice polarons, Fermi polarons can be described with a simple and quantitatively accurate model, which renders them an especially attractive field of research of many-body physics. In this work, we report the observation of Fermi polarons in a solid state environ- ment, namely a new class of semiconductors called transition metal dichalcogenides (TMDs). TMDs consisting of the transition metal Tungsten or Molybdenum and the chalcogenide Sulphur or Selenium are semiconductors. In the monolayer limit, they feature a direct bandgap, a large Coulomb interaction and a large effective elec- tron and hole mass as compared to GaAs. In combination with the two-dimensional confinement, these result in a large binding energy of the exciton. As a consequence, the exciton remains a rigid particle even when it is surrounded by a two-dimensional electron system (2DES) with a large electron density. When the exciton is surrounded by a 2DES, a second resonance emerges in the optical spectrum. Previously, this resonance was attributed to the trion, a bound state of two electrons and a hole. In this dissertation, we demonstrate that this emerging red-shifted resonance has to be described as a Fermi polaron. Thanks to the large binding energy of excitons in TMDs, we can test the predictions of our model qualitatively and quantitatively for a large range of electron densities. For our experimental investigations, we employ cavity quantum electrodynamics in a zero-dimensional, tunable micro-cavity to investigate the optical spectrum of the TMD monolayer for different electron densities. The possibility to reduce the cavity length to a few wavelengths allows the formation of polaron-polariton modes. The strong light-matter coupling cannot be explained with the trion model, and provides solid evidence for the validity of the Fermi polaron model to describe optical resonances in a 2DES. e Zusammenfassung Diese Dissertation behandelt eine Form eines Quantenst¨orstellenproblemsin einem Halbleitersystem. Quantenst¨orstellenprobleme beschreiben eine Wechselwirkung zwischen einem einzelnen Quantenobjekt und einer komplexen Umgebung. Sie sind in vielf¨altigenphysikalischen System anzutreffen und stellen ein fundamentales Ge- biet der Vielteilchenphysik dar. Bekannte Vertreter sind beispielsweise die Anderson Orthogonalit¨atskatastrophe oder der Kondoeffekt. In beiden F¨allenist die St¨orstelle viel schwerer als die Bestandteile der wechselwirkenden Umgebung. Wenn die Masse der St¨orstellevergleichbar mit den umgebenden Teilchen ist, spricht man von einer mobilen St¨orstelle. Diese Systeme sind normalerweise schwieriger zu l¨osen,wie man am Beispiel der Gitterpolaronen sehen kann, die schon 1933 von Lev Lan- dau vorgeschlagen wurden, f¨urdie aber erst 1955 Richard Feynman eine komplexe, aber genaue, Beschreibung fand. In den letzten Jahren konnte die starke Koplung zwischen mobilen Quantenst¨orstelln und einem Fermisee in kalten Atomen realisiert werden. Die Wechselwirkung manifestiert sich in der Formation von neuen Qua- siteilchen namens Fermipolaronen. Im Gegensatz zu anderen mobilen St¨orstellen, wie zum Beispiel Gitterpolaronen, k¨onnenFermipolaronen mit einem einfachen und quantitativ pr¨azisenModel beschrieben werden, was sie besonders als attraktives Feld der Vielteilchenphysik auszeichnet. In dieser Arbeit, berichten wir die Beobachtung von Fermipolaronen in einem Festk¨orpersystem, n¨amlich in einer neuen Klasse von Halbleitern: Den Ubergangsmetalldichalkogeniden¨ (TMD). TMDs bestehend aus den Ubergangsmet-¨ allen Wolfram oder Molybd¨anund den Chalkogeniden Schwefel oder Selen sind Halbleiter. Als Monolage haben sie eine direkte Bandl¨ucke, eine starke Coulomb- Wechselwirkung und grosse effektive Elektronen- und Lochmasse. In der Kombina- tion mit der zweidimensionalen Geometrie f¨uhrenletztere zu einer grossen Exziton- bindungsenergie, welche bewirkt, dass das Exziton strukturell intakt ist, wenn es von einem dichten, zweidimensionalen Elektronensystem (2DES) umgeben ist. Wenn das Exziton sich in einem 2DES befindet, bildet sich eine zweite Resonanz im optischen Spektrum. Bisher wird diese Resonanz den Trionen, einem gebundenen Dreik¨orperzustand, zugeordnet. In dieser Dissertation argumentieren wir, dass jene optische Resonanz als Fermipolaron beschriben werden sollte. Dank der grossen Bindungsenergie der Exzitonen in TMDs, k¨onnenwir qualitative und quantitative Prognosen unseres Modells in einem grossen Bereich von Elektronendichten testen. F¨ur unsere experimentellen Untersuchungen benutzen wir Quantenelektrody- namik in einem null-dimensionalen optischen Resonator, um das optische Spek- trum der TMD Monolage f¨urverschiedene Elektronendichten zu untersuchen. Die M¨oglichkeit, die Resonatorl¨angeauf ein paar Wellenl¨angenzu reduzieren, erlaubt es uns, die Bildung von Polaron-Polaritonen zu zeigen. Diese starke Kopplung von Matterie und Licht kann vom Trionenmodell nicht erkl¨artwerden und liefert somit f stichhaltige Hinweise, dass das Fermipolaron eine gutes Modell von optischen Res- onanzen in einem 2DES darstellt. Contents g Contents Title b Summaryd Zusammenfassungf Contentsh List of symbols and abbreviations1 1 Introduction4 2 Transition metal dichalcogenides6 2.1 Crystal lattice...............................6 2.2 Tight binding model...........................7 2.3 Selection rules...............................7 2.4 Exciton..................................8 2.5 Exchange interaction...........................9 3 Theory of Fermi polarons 12 3.1 Quantum impurity problems....................... 12 3.2 Theoretical model............................. 13 3.2.1 Model Hamiltonian........................ 13 3.2.2 Chevy Ansatz........................... 13 3.2.3 Contact interaction........................ 14 3.2.4 Spectral function......................... 16 3.2.5 Quasiparticle weight....................... 17 3.2.6 Charge distribution........................ 18 3.2.7 Validity of our approximations.................. 20 3.3 Fermi polarons in TMDs......................... 20 3.3.1 Sample structure......................... 20 3.3.2 Capacitive model for the Fermi Energy............. 22 3.3.3 Spectroscopy of an exciton in a 2DES.............. 22 4 Fermi polaron polaritons 26 4.1 Cavity spectroscopy............................ 26 4.1.1 Fiber cavity............................ 26 4.1.2 Sample structure......................... 28 4.1.3 Cavity modes........................... 30 4.1.4 Resonant Transmission...................... 31 4.1.5 Photoluminescence........................ 33 h Contents 4.2 Strong light-matter coupling....................... 34 4.3 Fermi Polaron-Polaritons......................... 40 4.4 Theoretical modeling of Fermi polaron polaritons........... 42 5 Hole injection 46 6 Excitons, trions and polarons in magnetic fields 50 6.1 Introduction................................ 50 6.2 Exciton magnetic moment........................ 50 6.3 Measurement of the exciton magnetic moment............. 50 6.3.1 Sample and Setup......................... 50 6.3.2 Polarization-resolved photoluminescence and reflection spec- troscopy.............................. 52 6.4 Magnetic moment of localized trions.................. 56 6.5 Polarons in a magnetic field....................... 56 6.5.1 Correcting the phase shift in the reflection spectrum..... 60 6.6 Conclusion................................. 60 7 Single photon emitters in WSe2 64 7.1 Introduction................................ 64 7.2 Power dependence............................. 64 7.3 Spatial map................................ 66 7.4 Photon autocorrelation.......................... 69 7.5 Lifetime, spectral fluctuation
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