Dome-shaped two-dimensional crystals: a playground for the study of the crystal mechanical and optoelectronic properties

Graphene -a single layer of carbon atoms tightly packed into a 2D honeycomb lattice- was first isolated in 2004 by A. K. Geim and K. S. Novoselov. The ground-breaking discovery that graphene can be isolated, previously thought to be impossible, opened the doors of Flatland to the condensed matter physics community. Since then, the family of 2D systems has grown rapidly, as many other crystals have been found to be characterised by a layered structure akin to graphite, with different layers bound together by weak van der Waals (vdW) forces. Among them, graphene features a semi-metallic nature and is characterised by exceptionally high carrier mobilities; hexagonal boron nitride (hBN) is an extremely good insulator and dielectric with a large bandgap; and the family of transition metal dichalcogenides (TMDs, such as MoS2 WS2, MoSe2, WSe2, MoTe2, WTe2, NbSe2, etc.) is richly varied, as it comprises superconducting materials with charge density waves and Weyl semimetal properties, as well as several semiconducting materials, with bandgaps ranging from the visible to the near infrared spectral region. In the single layer limit, semiconducting TMDs are characterised by extremely efficient light emission, which makes them ideal candidates for the realisation of innovative, flexible optoelectronic devices. Aside from the possibility of exploring the effects of lower dimensionality on the properties of atomically thin crystals, the existence of these crystals in stable form opens new avenues to materials engineering. Indeed, the inherent all-surface nature of these systems entails a higher sensitivity to external perturbations, which can in turn be exploited to modify the material properties. Among all possible external perturbations, the incredible mechanical flexibility and robustness of 2D crystals have offered the possibility to subject them to high mechanical deformations, engendering strains larger than 10 %. Such strains are able to induce major modifications in the electronic, optical, magnetic, transport and chemical properties of 2D materials, leading to the observation of a plethora of intriguing phenomena---ripe with new physics and novel opportunities. In the past decade, great attention has been thus devoted to the development of methods to mechanically deform 2D crystals and on the study of the effects of strain on these materials. This thesis will be focused on the development of an original strategy to induce strain fields in 2D crystals, and on the study of the effect of strain on the peculiar properties of the material. The thesis will be articulated as follows: The Prologue will briefly introduce the reader to the 2D world, especially highlighting the peculiar properties of 2D TMDs and hBN, thanks to which a flourishing interest in these materials has arisen. The final part of the Prologue will instead provide the reader with an overview of the field of strain engineering of 2D crystals. Chapter 1 will present the innovative method to induce strain in TMDs and hBN pioneered by the candidate and her group. It will be discussed how, by irradiating bulk flakes of these materials with low-energy hydrogen ions, it is possible to induce on the flake surface the formation of domes with thickness of one-to-few layers and filled with pressurised hydrogen. The basic properties of these structures will be discussed. This Chapter will also discuss the effects of hydrogen-ion irradiation of other crystals, where the formation of domes was not achieved but other interesting phenomenologies were observed. Chapter 2 will present a characterisation of the vibrational properties of the domes, highlighting their link with the strain distribution. This chapter will focus in particular on Raman studies of TMD domes and on Raman and infrared (IR) characterisations of hBN domes. The observed huge shifts and splittings of the vibrational modes will be correlated with the strain magnitude and character, which will be estimated by numerical calculations. Chapter 3 will focus on the possibility to engineer the domes. Lithography-based approaches will be used to achieve control over their size and position, and eventually over the strain magnitude. Chapter 4 will investigate from a fundamental point of view the morphology and mechanics of the system. In particular, an analytical method to describe the system will be presented. The model, coupled to morphological and mechanical experimental measurements, allows one to obtain precious information on the elastic properties of the membrane and on the adhesion energy between the monolayer and the bulk crystal. Chapter 5 will discuss how strain affects the optoelectronic properties of TMDs. In particular, this chapter will present steady-state and time-resolved photoluminescence (PL) studies aimed at highlighting the effect of strain on the free excitons. Such measurements highlight intriguing behaviours, such as strain-induced direct-to-indirect exciton crossovers, that deeply affect the emitted light intensity and decay time. Chapter 6 will present a characterisation of direct and indirect excitons when subjected to high magnetic fields. Indeed, magnetic fields induce a Zeeman effect in TMD MLs, which is promising for their utilisation for valleytronics. The effect of strain on the Zeeman effect has however not been investigated so far. The results presented in this chapter shed light on this, and highlight an unexpected behaviour, that unveils hybridisation phenomena between nearly resonant direct and indirect excitons. Chapter 7 will demonstrate the possibility to exploit strained 2D materials for quantum applications. In particular, this chapter will discuss the observation of single photon emitters at cryogenic temperatures in hBN-capped TMD domes. Chapter 8 will investigate a novel perspective: that of exploiting selective strain engineering in van der Waals heterostructures. Specifically, we will here focus on heterostructures made of a TMD dome and of an InSe unstrained layer, showing how strain is able to modify the electronic properties of the heterostructure.