This work explores three different aspects of graphene, a single-layer of carbon atoms arranged in a hexagonal lattice, with regards to its usage in future electronic devices; for instance in the context of quantum information processing. For a long time graphene was believed to be thermodynamically unstable. The discovery of this strictly two-dimensional material completed the family of carbon based structures, which had already been subject of intensive research with focus on zero-dimensional fullerenes and one-dimensional carbon nanotubes. Within only a few years of its discovery, the field of graphene related research has grown into one of today’s most diverse and prolific areas in condensed matter physics, highlighted by the award of the 2010 Nobel Prize in Physics to A.K. Geim and K. Noveselov for “their groundbreaking experiments regarding the two-dimensional material graphene”. From the point of view of an experimental physicist interested in the electronic properties of a material system, the most intriguing characteristic of graphene is found in the Dirac-like nature of its charge carriers, a peculiar fact that distinguishes graphene from all other known standard semiconductors. The dynamics of charge carriers close to zero energy are described by a linear energy dispersion relation, as opposed to a parabolic one, which can be understood as a result of the underlying lattice symmetry causing them to behave like massless relativistic particles. This fundamentally different behavior can be expected to lead to the observation of completely new phenomena or the occurrence of deviations in well-known effects. Following a brief introduction of the material system in chapter 2, we present our work studying the effect of induced superconductivity in mesoscopic graphene Josephson junctions by proximity to superconducting contacts in chapter 3. We explore the use of Nb as the superconducting material driven by the lack of high critical temperature and high critical magnetic field superconductor technology in graphene devices at that time. Characterization of sputter-deposited Nb films yield a critical transition temperature of \(T_{C}\sim 8{\rm \,mK}\). A prerequisite for successful device operation is a high interface quality between graphene and the superconductor. In this context we identify the use of an Ti as interfacial layer and incorporate its use by default in our lithography process. Overall we are able to increase the interface transparency to values as high as \(85\%\). With the prospect of interesting effects in the ballistic regime we try to enhance the electronic quality of our Josephson junction devices by substrate engineering, yet with limited success. We achieve moderate charge carrier mobilities of up to \(7000{\rm \,cm^2/Vs}\) on a graphene/Boron-nitride heterostructure (fabrication details are covered in chapter 5) putting the junction in the diffusive regime (\(L_{device}<L_{\rm{mfp}}\)). We speculate that either inhomogeneities in the graphene channel or lithography residues are responsible for this observation. Furthermore we study the Josephson effect and Andreev reflection related physics in this device by low-temperature transport measurements. The junction carries a bipolar supercurrent which remains finite at the charge neutrality point. The genuine Josephson character is confirmed by the modulation of the supercurrent as a function of an out-of-plane magnetic field resembling that of a Fraunhofer-like pattern. This is further supported by the response of the junction to microwave radiation in the form of Shaprio steps. Surprisingly we find a strongly reduced superconducting energy gap of approximately \(\Delta = 400{\rm \,\mu eV}\) by quantitatively analyzing data of multiple Andreev reflections. We show this result to be consistent by careful analysis of the device parameters and comparison of these to a theoretical model. More experiments will be needed to determine the origin of this reduction and if the presence of the Ti interfacial layer plays an important role in that. With regards to possible usability of superconducting contacts in more complex hybrid structures we can conclude that our work establishes the necessary preconditions while still leaving room for improvements; especially in terms of device quality. In the second part of this work we are primarily interested in electrical transport properties of graphene nanodevices and their application in graphene-superconductor hybrid structures. The fact that graphene is mechanically stable down to a few tens of nanometers in width while exhibiting a finite conductance makes it an appealing choice as host for single-electron devices, also known as quantum dots. Our work on this topic is covered in chapter 4 where we first develop a high-resolution lithography process for the fabrication of single electron devices with critical feature sizes of roughly \(50{\rm \,nm}\). To this end we use a resist etch mask in combination with a reactive-ion etch process for device patterning. Carrier confinement in graphene is known to be hindered by the Klein tunneling phenomenon, a challenge that can be overcome by using all-graphene nano-constrictions to decouple the source and drain contacts from the central island. The traditionally used constriction design is comprised of long and narrow connections. We argue that a design with very short and narrow constrictions could be beneficial for the quantum dot performance as the length merely affects the overall conductance and requires extended side-gates to control their transmission. We confirm the functionality of two different devices in low-temperature measurements, which differ in the size of their central island with \(d=250{\rm \,nm}\) for device no. 1 and \(d=400{\rm \,nm}\) for device no. 2. Coulomb blockade measurements conducted at \(20{\rm \,mK}\) on both devices reveal clear sequences of Coulomb peaks with amplitudes of up to \(0.8\rm{\,e}^2/\rm{h}\), a value significantly larger than what is commonly reported for similar devices. We interpret this as an indication of rather homogeneous constrictions, resulting from the modified design. Coulomb diamond measurements display the behavior expected for a lithographically designed single quantum dot revealing no features related to the presence of an additional dot. Using the stability diagram we determine the addition energies of the two dots and find them to be in good agreement with values reported in the literature for devices of similar size. Using the normalized Coulomb peak spacing as a figure of merit for the device quality we find that device no. 1 quantitatively compares well with a similar device fabricated on a superior hexagonal boron-nitride substrate. This result underlines the importance of non-substrate related extrinsic disorder sources and emphasizes the cleanliness of our lithography process. Superconductor-graphene quantum dot hybrid structures employing Nb and Al electrodes were successfully fabricated from a lithography point of view, yet no evidence of any superconducting related effect was found in transport measurements. We assign the missing observation to interface issues that require careful analysis and likely a revision of the fabrication process. A property equally important in graphene Josephson Junctions and quantum dots is the electronic quality of the device, as has been addressed in the previous paragraphs. It turns out that the \(\rm{SiO}_{2}\;\) substrate and lithography residues constitute the two major sources of disorder in graphene. In chapter 5 we present an approach based on the original work of Dean et al. who utilize hexagonal-Boron nitride as a replacement substrate for \(\rm{SiO}_{2}\). This idea was then extended by Wang et al. who also used this material as a shield to protect the graphene surface from contaminations during the lithography process. These structures are commonly referred to as van der Waals heterostructures and are assembled by stacking individual crystals on top of each other. For this purpose we build a mechanical transfer system based on an optical microscope equipped with an additional micro-manipulator stage allowing precise alignment of two micrometer sized crystals with high precision. We demonstrate the functionality of this setup on the basis of successfully fabricated heterostructures. Furthermore a variation on the traditional method for single graphene/boron nitride structures is presented. Based on a reversed stacking order this method yields large areas of homogeneous graphene, however it comes with the drawback of limited yields. A common type of problem accompanying the fabrication of encapsulated graphene structures is the formation of contamination spots (also referred to as bubbles in the literature) at the interfaces between BN and graphene. We experience similar issues which we are unable to prevent and thus pose a limit to the maximum available device size. In the next step we develop a full lithography paradigm including high-resolution device patterning by electron beam lithography combined with reactive ion etching and two different ways to establish electrical contact to the encapsulated graphene flake. In this context we explore the use of three different types of etch masks and find a double layer of PMMA/HSQ best suited for our purposes. Our low power plasma etch process utilizes a combination of \(\rm{O}_{2}\;\) and \(\rm{CHF}_{3}\;\) and is optimized to show reproducible etch results. A widely used method for electrical contacts relies on one-dimensional edge contacts whose functionality crucially depends on the use of Cr as the interface layer. For compatibility reasons with superconducting materials, e.g. Nb, we develop a self-aligned contact process that instead of only Cr is also compatible with Ti. We achieve this by modifying the plasma etch parameters such that the etch process exhibits extremely low graphene etch rates while keeping a high etch rate for h-BN. This allows clearing of a narrow stripe of graphene at the edge of the structure by using a thick PMMA layer as etch mask as replacement of the PMMA/HSQ combination. The purpose of this PMMA mask is two-fold since it also serves as lift-off mask during metalization. The quality of the edge contacts fabricated with either method is excellent as determined from transport measurements at room and cryogenic temperatures. With typical contact resistances of a few hundred \({\rm \,}\Omega\mu{\rm m}\) and a record low of \(100{\rm \,}\Omega\mu{\rm m}\) the contacts can be considered to be state-of-the-art. The positive effect of encapsulation on the electronic quality is confirmed on a device exhibiting charge carrier mobilities exceeding \(10^5{\rm \,cm^2/Vs}\), one magnitude larger than what is commonly achieved on \(\rm{SiO}_{2}\). The investigation of induced superconductivity in graphene Josephson Junctions, quantum dots, and high mobility heterostructures underlines the versatility of this material system, while covering only a tiny fraction of its prospects. Combination of the acquired knowledge regarding the physical effects and the developed lithography processes lay the foundation towards the fabrication and study of novel graphene hybrid devices.

Nature shows us only the tail of the lion. But I have no doubt that the lion belongs with it even if he cannot reveal himself all at once. Albert Einstein In my dissertation, I addressed the question of whether the 3D topological insulator mercury telluride (3D TI HgTe) is a suitable material for spintronics applications. This question was addressed by investigating the SOTs generated by the 3D TI HgTe in an adjacent ferromagnet (Permalloy) by using the ferromagnetic resonance technique (SOT-FMR). In the first part of the dissertation, the reader was introduced to the mathematical description of the SOTs of a hybrid system consisting of a topological insulator (TI) and a ferromagnet (FM). Furthermore, the sample preparation and the measurement setup for the SOT-FMR measurements were discussed. Our SOT-FMR measurements showed that at low temperatures (T = 4.2 K) the out-of-plane component of the torque is dominant. At room temperature, both in-plane and out-of-plane components of the torque could be observed. From the symmetry of the mixing voltage (Figs. 3.14 and 3.15) we could conclude that the 3D TI HgTe may be efficient for the generation of spin torques in the permalloy [1]. The investigations reported here showed that the SOT efficiencies generated by the 3D TI HgTe are comparable with other existent topological insulators (see Fig. 3.17). We also discussed in detail the parasitic effects (such as thermovoltages) that can contribute to the correct interpretation of the spin torque efficiencies. Although the results reported here provide several indications that the 3D TI HgTe might be efficient in exerting spin-torques in adjacent ferromagnets [2], the reader was repeatedly made aware that parasitic effects might contaminate the correct writing and reading of the information in the ferromagnet. These effects should be taken into consideration when interpreting results in the published literature claiming high spin-orbit torque efficiencies [2–4]. The drawbacks of the SOT-FMR measurement method led to a further development of our measurement concept, in which the ferromagnet on top of the 3D TI HgTe was replaced by a spin-valve structure. In contrast with our measurements, in this measurement setup, the current flowing through the HgTe is known and changes in the spin-valve resistance can be read via the GMR effect. Moreover, the SOT-FMR experiments required the application of an in-plane magnetic field up to 300 mT to define the magnetization direction in the ferromagnet. Motivated by this fact, we investigated the influence of an in-plane magnetic field in the magnetoresistance of the 3D TI HgTe. The surprising results of these measurements are described in the second part of the dissertation. Although the TI studied here is non-magnetic, its transversal MR (Rxy) showed an oscillating behavior that depended on the angle between the in-plane magnetic field and the electrical current. This effect is a typical property of ferromagnetic materials and is called planar Hall effect (PHE) [5, 6]. Moreover, it was also shown that the PHE amplitude (Rxy) and the longitudinal resistance (Rxx) oscillate as a function of the in-plane magnetic field amplitude for a wide range of carrier densities of the topological insulator. The PHE was already described in another TI material (Bi2−xSbxTe3) [7]. The authors suggested as a possible mechanism the scattering of the electron off impurities that are polarized by an in-plane magnetic field. We critically discussed this and other theoretical proposed mechanisms existent in the literature [8, 9]. In this thesis, we attempted to explain the origin of the PHE in the 3D TI HgTe by anisotropies in the band structure of this material. The k.p calculations based on 6-orbitals were able to demonstrate that an interplay between Rashba, Dresselhaus, and in-plane magnetic field deforms the Fermi contours of the camel back band of the 3D TI HgTe, which could lead to anisotropies in its conductivity. However, the magnetic fields needed to experimentally observe this effect are as high as 40 T, i.e., one order of magnitude higher than reported in our experiments. Additionally, calculations of the DoS to assess if there is a difference in the states for Bin parallel and Bin perpendicular to the current were, so far, inconclusive. Moreover, the complicated dependence of Rashba in the p-conducting regime of HgTe [10] makes it not straightforward the inclusion of this term in the band structure calculations. Despite the extensive efforts to understand the origin of the galvanomagnetic effects in the 3D TI HgTe, we could not determine a clear mechanism for the origin of the PHE and the MR oscillations studied in this thesis. However, our work clarifies and excludes a few mechanisms reported in the literature as the origin of these effects in the 3D TI HgTe. The major challenge, which still needs to be overcome, is to find a model that simultaneously explains the PHE, the gate dependence, and the oscillations in the magnetoresistance of the 3D TI HgTe as a function of the in-plane magnetic field. To conclude, the author would like to express her hope to have brought the reader closer to the complexity of the questions addressed in this thesis and to have initiated them into the art of properly conducting electrical transport measurements on topological insulators with in-plane magnetic fields.

The study of magnetic phases in spintronic materials is crucial to both our fundamental understanding of magnetic interactions and for finding new effects for future applications. In this thesis, we study the basic electrical and magnetic transport properties of both epitaxially-grown MnSi thin films, a helimagnetic metal only starting to be developed within our group, and parabolic-doped ultra-thin (Ga,Mn)As layers for future studies and applications.