Master Theses
 Matthijs Vernooij (August 2021)
The topological Hall effect: A study of a 2D Rashba ferromagnet
Skyrmions are specific patterns in the magnetisation direction of a ferromagnet. They are the subject of a lot of active research and a lot of ideas for their applications exist. Many of these applications require an efficient mechanism to measure the number of skyrmions. The topological Hall effect, which means that the Hall resistance is proportional to the number of skyrmions, is a candidate for this mechanism. In this thesis we theoretically calculate the resistivity for a 2D Rashba ferromagnet. We show that the Hall resistance is indeed proportional to the number of skyrmions, proving that the topological Hall effect is present in this model. This improves existing descriptions of the topological Hall effect by incorporating spinorbit coupling via the Rashba effect, which had not been studied before.
 Yann in 't Veld (October 2020)
Plasmonic superconductivity in layered materials (pdf, 4,7 MB)
Plasmons in twodimensional materials have a gapless squarerootlike dispersion which can be eﬀiciently tuned by external dielectric screening or charge doping. At the same time, plasmons can couple strongly to electrons, which renders them particularly interesting for superconducting properties in layered materials. In this thesis we use an extended version of density functional theory for superconductors (SCDFT) to account for both the full dynamic Coulomb interaction and phonon contributions in two dimensions. We find that interplaying phonons strongly enhance the superconducting critical temperature, especially at small interaction strengths. The interplay between phonons and plasmons shows both suppression and enhancement depending on the doping level. These results are promising in the view of exciton mediated superconductivity in sandwich structures and in various layered materials like transition metal dichalcogenides and twisted bilayer graphene. In all of these materials plasmonic contributions have so far been neglected.
 Tom Westerhout (August 2020)
Did we forget a phase? VUMPS study of tVV ′ model in one dimension
Recent advances in experiments with cold atoms confined to wire geometries using strong optical lattices allow for a realization of tunable strongly interacting bosonic and fermionic models. In such experiments probably the most distinguishing feature of 1D fermionic systems can be observed, namely, the Luttinger liquid behavior. tVV' model is a very popular model hosting a Luttinger liquid phase, and even though it has been studied extensively, there remains some controversy. Around 2000, it was suggested that the Luttinger liquid phase breaks for large V = 2V', but more recent studies did not confirm this statement. Here, using VUMPS, a modern tensornetwork algorithm which works directly in the thermodynamic limit, we thoroughly analyze the tVV' model and resolve the contradiction.
 Matteo Vandelli (October 2018)
ThreeParticle Response Functions in Condensed Matter Physics: Application to Optical Second Harmonic Generation and Chiral ThreeSpin Interaction (pdf, 2,9 MB)
Starting from the expression for the partition function of a quantum electronic system, threeparticle correlation functions are derived and analyzed the in the framework of a quantum field theory in condensed matter physics. Corresponding threepoint diagrams are calculated in the Matsubara scheme using the formalism of Green’s functions at finite temperatures. Afterwards, obtained results are applied to the following physical problems of interest. The first problem is related to optical properties of twodimensional Diraclike systems and consists of the calculation of the optical second harmonic response from these materials. The latter is presented in systems with the broken inversion symmetry and can be revealed, for example, in the Graphene model with the nonzero mass term. This situation is relevant, for instance, when the Graphene is disposed on top of an insulating substrate with the honeycomb lattice structure. Here, all components of the second harmonic response function have been calculated for the model of Graphene on the hexagonal boron nitride substrate, and their relation to the crystal symmetry of the obtained system has been investigated. The second problem concerns the study of the threespin interaction that appears in the system of localized spins coupled to itinerant electrons. Here, the general expression for the threeparticle correction to the energy of the system is explicitly calculated in the framework of the sd model. As the result, the relevant threespin interaction term that enters an effective spin model has been derived. It has been found that the chiral term corresponding to the triple product of spins emerges in the presence of a magnetic flux. Other terms that arise in the presence of strong electronspin interaction or spinorbit coupling have also been investigated. Furthermore, a continuous limit of the spin model in the presence of the chiral threespin interaction (micromagnetic model) has been developed, starting a preliminary study of the stability of topological spin textures that can appear in the system due to the novel twistedexchange interaction derived in this work.
 Claudius Müller (June 2018)
Extensive Magnetic Oscillation Study of Nodal Line Dirac Semimetals
In recent years topological semimetals (TSMs) have attracted much attention as they offer the possibilities to explore the low energy analogues of phenomena and particles predicted in high energy physics.
In this project the TSMs under investigation are the Dirac nodal line semimetals ZrSiS and HfSiS. The goal is to thoroughly study both materials experimentally and theoretically by means of magnetic quantum oscillations and DFT calculations. The magnetic quantum oscillation studies were performed by measuring the Shubnikov  de Haas (SdH) effect and the de Haas  van Alphen (dHvA) effect by means of magnetotransport and capacitive magnetotometry experiments up to 35T at the High Field Magnet Laboratory (HFML). For both materials a complex oscillatory behaviour of the SdH and dHvA oscillations is observed and compared to the bandsturcture obtained by DFT calculations. By Fourier analyzing the experimental data it becomes evident that the complex oscillatory behaviour is due to magnetic breakdown (MB) occuring in these two materials. Also, for ZrSiS a discrepancy between the frequency spectrum of the SdH and dHvA studies is observed.
 Giacomo Sesti (October 2017)
TimeEvolution of Magnetic Vector Fields through DisorderAveraged Green Functions in Layered Antiferromagnets (pdf, 1,3 MB)
 Davide Tisi (September 2017)
Temperature dependence of phonons in graphene comparison of different theoretical models
Graphene is a 2D allotrope of carbon with intriguing and highly nontrivial mechanical properties.
In my master project I developed a code to compute, numerically, the phonons of graphene and a coefficient called bending rigidity which is a measure of the energy needed to bend the graphene layer. It has been demonstrated that, near the Γ point, the two inplane acoustic modes of graphene exhibit a linear dispersion, while the outofplane acoustic mode has a quadratic dispersion. From this quadratic dispersion we can compute directly the bending rigidity. Since it has been shown that the usual quasiharmonic approximation does not work for graphene due to the large anharmonicity, the phonons will be obtained from the peaks of the power spectral density. This will be computed as the temporal Fourier Transform of the kspace velocity autocorrelation function (kVACS). To calculate kVACS, we need the positions and the velocities of all particles from a molecular dynamics simulation, using an existing code. This code uses an empirical potential, called longrange Carbon BondOrder Potential, to estimate the interactions between the carbon atoms. Previous numerical studies suggested that the temperature dependence of the bending rigidity changes, using a different torsion term in the potential of the molecular dynamics code. Therefore, I have implemented in the molecular dynamics code a new torsion term, and calculated the phonon spectrum with both models of the torsion.  Matteo Stifano (May 2017)
Skyrmion Manipulation of Ultrathin Films by Modification of Exchange Interactions
Skyrmions have shown to be promising candidates for the development of a ultradense, lowpower and lowcost storage technology. Achieving full control of such magnetic structures is of key importance for such a development. In this thesis, we perform a numerical analysis to investigate the stability of Néeltype skyrmions in ultrathin magnetic films and we discuss how a sudden modification of the antisymmetric exchange interaction can induce a switch from a skyrmion to a ferromagnetic state and, with the same mechanism, how to dynamically change the skyrmion chirality.
 Rob Ouwersloot (December 2016)
The effect of grain boundaries on the elastic properties of graphene and nanotubes
The currently most promising methods to produce graphene in large amounts tend to create graphene with relatively small grain sizes. Small grains mean many grains and many grain boundaries. While pristine graphene has been studied and characterized extensively both theoretically and experimentally, little is known about the properties of graphene with grain boundaries. To improve the understanding of the effect of grain boundaries on the elastic properties of graphene, we have done simulations on several model systems containing specific grain boundaries. Earlier work found the lowest energy structures of [0001]tilt grain boundary structures with varying misorientation angles. Here we take three of those structures as a starting point and go on to characterize several of their elastic properties, both for graphene with grain boundaries and for carbon nanotubes with grain boundaries.

On the interpretation of the quantum wave function (pdf, 1 MB)
Han van der Pluijm (August 2016)
Since the birth of quantum mechanics the theory has proven to generate reliable experimental predictions. But the status of the wave function is still at question: is it a real property of nature or is it the knowledge one has of nature? If we consider this question in an ontological model then the wave function would be called Ψontic and Ψepistemic respectively. Here an ontological model is a model that assumes there exist ontic states with fixed properties. In this thesis the PussyBarrettRudolph nogo theorem is introduced which is an argument in favour of the Ψontic view of quantum states. Furthermore, Spekkens' toy theory, an example of a Ψepistemic model is discussed. With this toy model it is possible to reproduce part of the phenomenology that is typical for quantum theory and therefore it motivates the Ψepistemic view of the wave function. Finally, a restricted description of the MachZehnder interferometer is given in terms of Spekkens' toy theory.
 Robert Sokolewicz (May 2016)
Nonlocal Josephson Effect induced by Entangled Bogoliubovde Gennes Quasiparticles (pdf, 3,2 MB)
Superpositions of electrons and holes that are called Bogoliubovde Gennes quasiparticles can emerge as bound states at normal metal/superconductor interfaces. In the presence of sufficiently strong magnetic fields such quasiparticles can propagate along unidirectional quantum Hall edge channels. By connecting two normal metals a beam splitter can be formed which allows for two BdG quasiparticles to interfere and entangle with eachother. By correlating the outgoing currents a behaviour is observed which is the nonlocal analogue of the Josephson effect [1]. The calculated correlation functions can be used to show the violation of the BellCSH inequality, indicating a nonclassical correlation, caused by the entanglement between two BdG quasiparticles.
[1] C. W. J. Beenakker, Phys. Rev. Lett. 112, 70604 (2014)
 Remco Hens (August 2015)
Simulations and modeling of thermal and mechanical deformations of graphene (pdf, 8,5 MB)
In this thesis we study two topics related to graphene. The first topic is about the dimer in an asymmetric periodic potential. We introduce it as a simple model to study the friction of graphene flakes on a graphite substrate. The second topic is about the mechanical deformation properties of graphene. We examine the differences between 1D (longstrips) and 2D graphene.
 Nicole Orval (July 2015)
Dynamics of domain wall kinks in external magnetic field
In this thesis we study a spin lattice where a domain wall may behave as a soliton. The domain wall then consists of two straight parts with a kink in the middle. We look at the dynamics of domain wall kinks in the presence of an external magnetic field. We are interested in the nontrivial relation between the speed of the kinks and the momentum which is applied by an external magnetic field.
 Annelot Schuring (August 2014)
Moiré patterns in graphene on hexagonal substrates
We present a theoretical/computational study of moir´e patterns in graphene on hexagonal substrates, in particular graphene on graphene and graphene on hexagonal boron nitride (hBN). We first consider rotated graphene on graphene systems. By varying the angle of rotation between the two layers, one can create beautiful super periodicity: moir´e patterns. One period of this hexagonal pattern is called a moiron. Our ambition is to answer this main question: How does minimization of the energy affect the moir´e patterns?
 Erik van Loon (October 2013)
Collective Excitations in Strongly Correlated Systems  Charge conservation in the dual boson approach (pdf, 3,5 MB)
This thesis contains the first step towards implentation and application of the dual boson approach. Quantum field theory methods are used to study the susceptibility of the (extended) Hubbard model. This model describes the electrons in a strongly correlated material. Depending on the choice of parameters, such a system can be metallic, insulating or even undergo a chargeordering transition. This thesis shows how the charge susceptibility changes in these phases.The further developments in this project can be found here.
 Maria Patelkou (August 2013)
Pushing and Sliding allotropes of Carbon (two files due to pdf size)
first pages (1 to 77)
last pages (70 to 107) (pdf, 13 MB)The focus of this master thesis lies on sliding friction and wear. What is the effect of pushing solid surfaces together and moving them with respect to each other? How can the effect be analyzed? We suggest a molecular dynamics simulation of pushing and sliding different allotropes of carbon bulk structures using the longrange order carbon bond order potential (LCBOP) and analyze the formation and the structure of the interface.  Lennert van Tilburg (May 2013)
Formation and vibrations of large carbon systems in the interstellar medium (pdf, 8 MB)
Since the identification of carbon systems like C60 and C70 in the interstellar medium by IR spectroscopy, a number of formation pathways where proposed to explain their existence. In the topdown production pathway, large flat Polycyclic Aromatic Hydrocarbons (PAH) are converted into closed carbon systems by photodissociation under intense UV radiation. In the intermediate states, pentagons and defects provide the curvature that will eventually lead to a closed system. We have studied this pathway by analysing the induced curvature and calculated the phonon spectra of the carbon systems.
 Linde van Heeringen (December 2012)
The band structure of SrTiO3/LaAlO3 heterostructures
 Guus Slotman (December 2012)
Structure, stablility and defects of single layer hBN (pdf, 16 MB)
The topic of this thesis is a single sheet of hexagonal boron nitride, in short: hBN. It is part of one of the hot topics in solid state physics: the study of twodimensional crystals. In this thesis, we study the structural stability, thermal expansion and defect formation in hBN by means of Molecular Dynamics (MD).
Part of this thesis has been publised in GJ Slotman, A. Fasolino, Structure, stability and defects of single layer hBN in comparison to graphene. J Phys Condens Matter. 2013 Jan 30;25(4):045009
 Inka Locht (August 2012)
The effect of temperature on the phonon dispersion relation in grahene (pdf, 2,5 MB)
The research in this Master thesis is about the influence of anharmonic effects on the out of plane acoustical mode in graphene. The harmonic approximation fails to describe this mode correctly since it gives results that are to soft compared to experiments. The phonon spectrum was calculted with the empirical potential LCBOP. We calculated a number of thermodynamic quantities in the quasiharmonic approximation and adapted the SCAILDmethod to calculate the temperature dependence of the phonons dispersion and of the bending rigidity. We conclude that the latter is due to coupling in the whole phonon spectrum. Calculation of this dependence was not yet possible, since we have found that the SCAILDmethod is not directly applicable for twodimensional materials. We discuss possible strategies to adapt the method to this situation.
 Jonas Sweep (April 2012)
The sd exchange model (pdf ,1593 kB) (pdf, 1,6 MB)
The metalinsulator transition within the sd exchange model is studied by the Dynamical Mean Field Theory and Dual Fermion approaches. The latter takes into account nonlocal correlation effects which are shown to be essential. In particular, the critical values of the sd exchange coupling constant for these two methods turn out to be different by a factor of more than two (for the case of square lattice and spin 1/2 electrons). The calculations were performed using a ContinuousTime Quantum Monte Carlo method. The difference of the quantum spin1/2 case and the classicalspin case is discussed. For the quantum case the sign of sd exchange coupling constant is relevant which demonstrates the importance of the Kondo effect.
 Joost van den Ende (October 2011)
Friction at the atomic scale, sliding velocity studied with the FrenkelKontorova model (pdf (pdf, 9,7 MB)
Friction is an important force, which affects both daily life and industrial processes. The origins of friction at the micro or nanoscale are not yet understood. At the nanoscale, the structure of the interface of the contacting surfaces (commensurate or incommensurate) is important. The FrenkelKontorova model, which describes the motion of a chain onto a periodic substrate, is suitable to understand the role of commensurability on friction. The periodic force due to the substrate can excite resonantly the phonons of the sliding chain and thereby dissipate mechanical energy into heat. We have studied this dissipation as a function of sliding velocity for different temperatures. We have found that resonant excitations remain important up to high temperatures for incommensurate interfaces and that the relation between friction and temperature is opposite for (in)commensurate interfaces. These effects could be studied with real systems, like solid xenon sliding on a silver substrate.
Part of this master thesis has been published in J. A. van den Ende, A. S. de Wijn, A. Fasolino, Effect of temperature and velocity on superlubricit. J. Phys.: Condens. Matter 24 (2012) 445009. A synopsis is given in Superlubricity in slow motion.
 Merel van Wijk (August 2011)
Catalysis by Au_{2}^{}: An ab initio thermodynamics study
This work is a computational study towards the atomistic understanding of a catalytic process. The reaction studied is the oxidation of carbon monoxide, catalyzed by gold dimer anions. A systematic approach fully from first principles is used to predict the structure of the catalyst and possible reaction intermediates.
 Koen Reijnders (August 2011)
Semiclassical theory of chiral tunneling in graphene
This thesis presents a systematic study of tunneling effects in graphene in graphene np and npn junctions. Using a variety of semiclassical methods, we derive very precise analytical formulae for the transmission and reflection coefficients for the case of angular scattering off a onedimensional potential barrier. These formulae turn out to be in good agreement with numerical calculations.
This master thesis has been awarded the``Universitaire studieprijs 2012'' of the Radboud university Nijmegen (see movie).
 Leendertjan Karssemeijer (August 2010)
Thermal expansion of carbon structures
In this thesis we will perform computer simulations based on a stateoftheart description of carbon interactions in order to reveal more about the temperature dependence of the structure of these systems. Emphasis will lie on the thermal expansion of graphitic crystals and in particular of carbon nanotubes.
Part of this thesis has been published in L.J. Karssemeijer, A Fasolino, Phonons of graphene and graphitic materials derived from the empirical potential LCBOPII. Surface Science 605 (17), 16111615
 Jaap Kroes (May 2010)
Graphene nanoribbons and edge reconstructions (pdf, 2,4 MB)
We have studied the edges of graphene nanoribbons using the LCBOPII potential [29] in molecular dynamics and Monte Carlo simulations. By analyzing molecular dynamics simulations we identified a reaction coordinate for the reconstruction of the zigzagedge to zz57. Based on this reaction coordinate we have calculated, by umbrella sampling in Monte Carlo simulations, the free energy profile for the transformation.
Part of this thesis has been published in J.M. H. Kroes, M.A. Akhukov, J.H. Los, N. Pineau, and A. Fasolino, Mechanism and freeenergy barrier of the type57 reconstruction of the zigzag edge of graphene. Phys. Rev. B 83, 165411 (2011)
 Titus van Erp (1999)
Frenkel Kontorova model on quasiperiodic substrate potentials (pdf, 1,8 MB)
Part of this thesis has been published in T. S. van Erp, A. Fasolino, O. Radulescu, and T. Janssen Pinning and phonon localization in FrenkelKontorova models on quasiperiodic substrates. Phys. Rev. B 60, 6522