Protected Pseudohelical Edge States in Z2-Trivial Proximitized Graphene

We investigate topological properties of models that describe graphene on realistic substrates which induce proximity spin-orbit coupling in graphene. A Z(2) phase diagram is calculated for the parameter space of (generally different) intrinsic spin-orbit coupling on the two graphene sublattices, in the presence of Rashba coupling. The most fascinating case is that of staggered intrinsic spin-orbit coupling which, despite being topologically trivial, Z(2) = 0, does exhibit edge states protected by time-reversal symmetry for zigzag ribbons as wide as micrometers. We call these states pseudohelical as their helicity is locked to the sublattice. The spin character and robustness of the pseudohelical modes is best exhibited on a finite flake, which shows that the edge states have zero g factor, carry a pure spin current in the cross section of the flake, and exhibit spin-flip reflectionless tunneling at the armchair edges

Theoretical investigation of the interplay of proximity-induced spin interactions and correlated phenomena in multilayer graphene systems

The interplay of proximity-induced spin interactions and correlated phenomena in multilayer graphene systems is a promising avenue for developing electronics and spintronics. Being able to manipulate and alter correlated states in these systems is of great importance in studying new physical phenomena. This thesis delves into the interplay of proximity-induced spin interactions and correlated phenomena in Bernal bilayer graphene (BBG) and rhombohedral trilayer graphene (RTG) systems in detail. We utilize ab initio-fitted effective models of BBG and RTG, which are encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic Cr2Ge2Te6 (exchange proximity effect) and include Coulomb interactions using the random-phase approximation to study potential correlated phases at different displacement field and doping. Our results show a wide range of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin-orbit proximity effects, such as the emergence of a spin-valley-coherent phase due to valley-Zeeman coupling

Ab initio studies of extrinsic spin-orbit coupling effects in graphene and quantum Monte Carlo simulations of phosphorene

The field of two-dimensional (2D) materials offers a rich playground to study new physics and concepts for device applications. Starting with the discovery of graphene, the field has seen intense research activity, with interest peaking also in terms of other 2D materials, for example the insulating transition metal dichalcogenides (TMDCs), or superconducting and magnetic materials. Technologically, most of them are very promising, but considerable amount of scientific research centers still around graphene, owing to its peculiar dispersion relation and recent advancements in device preparation quality. One goal of research is to assess graphene's qualification for spintronics applications. Spintronics (shorthand for spin-based electronics) aims to utilize the spin degree of freedom of electrons for new forms of information storage and logic devices, using effects from magnetization and spin-orbit coupling. Spin-orbit coupling is an important ingredient for spin-based phenomena and devices such as the spin Hall effect, for spin relaxation, spin transistors and many more. On the other hand, in graphene, spin-orbit coupling and nuclear-spin-electron-spin coupling is relatively weak. Therefore, along with its exceptional charge transport properties, it is expected to be a good material for the transportation of spin currents. Spin transport in graphene is limited by imperfections through external sources, e.g., by sample fabrication, underlying substrates, and atomic residuals, which may induce magnetism and spin-orbit coupling. The first part of the thesis is dedicated to quantify spin-orbit coupling introduced by copper atoms and the copper substrate. Copper atom adsorbates are studied by means of density functional theory (DFT) combined with effective tight-binding model Hamiltonians. Copper atoms, adsorbed at the top and bridge positions induce sizeable spin-orbit coupling on the order of 20 meV by the interaction of the copper p and d levels with the graphene low energy electronic structure. Another reason to study the effects of spin-orbit coupling in graphene is to actually control the spin degree of freedom. This can be achieved by proximitizing the material with other surfaces. The second part of the thesis studies the proximity effect of graphene placed on the Cu(111) surface by means of a DFT study. It is revealed that the Dirac electronic structure of graphene remains largely intact and that the contacting induces sizeable spin-orbit coupling and sublattice symmetry breaking. These effects are studied also with the help of a distance-dependent extraction of an effective graphene continuum Hamiltonian. Along with a strong distance dependence of the parameters, strong Rashba spin-orbit coupling on the order of millielectronvolts is found. Intrinsic spin-orbit couplings are enhanced as well, being larger by one or two orders of magnitudes compared to pristine graphene. Such increased values of special staggered intrinsic spin-orbit coupling, as in the case of graphene on TMDCs can possibly lead to topological effects. In the third part of the thesis we provide an explanation of the edge state physics associated with proximity induced spin-orbit coupling in graphene nanoribbons. The staggered case of intrinsic spin-orbit coupling, which is a realistic realization of proximity spin-orbit coupling in graphene, leads to two pairs of edge states per edge in zigzag ribbons, which at the same time is a Z2-trivial system. This clarifies the contradictory findings in literature of triviality/nontriviality. Even though it is a trivial system, protected pseudohelical edge states can be stabilized by finite size quantization. The protection against short-range scattering of these pseudohelical states is discussed. From a technological point of view, graphene is not always the best choice for some applications, such as field effect transistors, which require a band gap. This is where other family members come into play, such as black phosphorus. Black phosphorus is a very promising material, because it offers a way to tune its band gap by the number of layers it is composed of. The monolayer building block of black phosphorus is called phosphorene, which possesses a direct band gap. In order to understand the optical properties of the composed system, we need to understand the single layer first. Experimental and theoretical consensus on the fundamental gap of phosphorene is not found yet. Conventional theoretical methods to determine the band gap may fail or are harder to converge, when dealing with systems in which Coulomb interactions are strong as it is the case in open 2D systems. Not only is it important to gain a more quantitative understanding of simulations obtained with conventional ab initio calculations, but also to apply new methods to the class of 2D systems. This is why we employ quantum Monte Carlo (QMC) simulations to study the fundamental gap of phosphorene. We find a fundamental gap of about 2.4 eV along with an optical gap of 1.75 eV and an exciton binding energy of 0.65 eV