- Sahel Katawazi (July 2023)
Quantum Synchronization and Entanglement calculations with the Lindblad equation (pdf, 794 kB)
Synchronization is a phenomenon where two or more oscillators, which start off without the same frequency, eventually oscillate with the same frequency. Such a phenomenon has also been discovered in a quantum scenario. In this thesis we will describe how a simple system of two quantum interacting spins coupled to a magnon bath may evolve in an external time dependent magnetic field. We derive the corresponding Lindblad equation and analyze quantum spin synchronization and the evolution of quantum spin entanglement. Such calculations might have some interesting consequences for spintronics and quantum computing.
- Sander Leisink (2021-2022)
Statistical physics of phase glasses (XY rotor models)
Thesis not available
- Pim Coenders (2021-2022)
Mapping the phase diagram of the quantum Heisenberg model with 4-spin exchange (pdf, 1,6 MB)
We numerically investigate a quantum Heisenberg model with ferromagnetic 2-spin exchange and a 4-spin plaquette interaction on a square lattice and compare it to the corresponding Ising model. We use the finite temperature Lanczos method (FTLM) algorithm to approximate the lowest eigenvalues and eigenvectors and use these to calculate observables. We construct the phase diagrams for different values of the anisotropy parameter, which serves the purpose of interpolating between the quantum Heisenberg model and the Ising model. We then proceed to investigate the phases and phase transitions. We also show the spin-spin correlation in the different phases. We find that this system is very rich and non-trivial, and that the quantum Heisenberg model exhibits interesting phases not encountered in the Ising model, like a 1st order phase transition from a ferromagnet to an antiferromagnet at zero and low temperature.
- Samber Bastiaansen (February 2022)
Plasmonic Excitations in Twisted bilayer Graphene (pdf, 5,9 MB)
The electronic fluid in metals and semi-conductors shows a reasonable resemblance to a gas in the ionized state, which is often referred to as a plasma. The optical properties of the plasma are of ever increasing interest, due to the applicability in opto-electronics and other real-world devices. An essential property is the natural oscillation spectrum of the plasma, which is often quantised by the means of the quasi-particles called plasmons.
This work presents an extensive study on the plasmonic structure of both monolayer and (twisted) AA-stacked bilayer graphene. The real-space lattices are modelled as finite hexagonal supercells, and are reviewed within a tight-binding approximation. The Coulomb interactions are modelled according to an Ohno-interpolation, which is fitted to ab-initio data provided by earlier publications. With the application of a real-space RPA-algorithm, the full dielectric and polarisability matrices are calculated. These matrices are then used to review both the plasmonic excitations in real- and momentum space, by the means of real-space and Fourier-space electronic loss spectra, and real-space plasmonic eigenmodes.
- Casper Pijnenburg (December 2021)
Poisson solver for layered materials in inhomogeneous dielectric environments
In this thesis an algorithm is proposed to numerically solve the Poisson equation in inhomogeneous environments and approximate the boundary conditions. The Poisson equation is expressed as a system of linear equations using the finite difference method and this system of linear equations is solved using the biconjugate gradient method. The solver is tested for convergence against known exact solutions of the Poisson equation and methods to approximate the boundary conditions are discussed. A brute force way is to use logarithmically spaced grids with a large extent but this is slow and not numerically stable. A new method that approximates the boundary conditions is proposed called the nested grid method. This new method is faster and more numerically stable and converged for all systems tested.
- Rens Theunissen (November 2021)
Computing the Hopf index for a magnetic lattice
This thesis describes a minimalistic formulation for the calculation of the Hopf index for a three dimensional magnetic lattice. This formulation is achieved by approximating the lattice as a divergenceless field and calculating the necessary derivatives using the finite difference method. This calculation is only accurate but the research shown in this thesis serves as a good starting point for further development of the calculation.
- Adrián Sousa-Poza (August 2021)
Plasmonic Excitations in Mono-Layer Graphene (pdf, 7,4 MB)
Graphene, which is a single-layer carbon nanosheet, has shattered the world of science in the past 20 years with its incredible physical properties. Due to graphene's single-atom thin honeycomb-like structure some interesting characteristics arise, like a very strong bond between neighbouring atoms and a high electron mobility within this two-dimensional lattice. This thesis deals with the collective electron oscillations in graphene, the so-called plasmons or plasmonic excitations, and their dependence on different environments. This has been done based on first principle cRPA calculations, in order to derive a continuous model for the screened Coulomb interaction in real-space for free-standing graphene. This model has been adjusted to graphene embedded in hexagonal Boron-Nitride (h-BN) to account for environmental screening effects such that it properly corresponds to the ab initio data provided for h-BN. Using the same model, it is possible to change parameters for the dielectric environment to see how the plasmonic excitations evolve. Combining this Coulomb interaction model with a simple tight-binding Hamiltonian, it is possible to determine the dielectric function and with it the plasmonic excitations including their dependence on the environment.
- Wietze Huisman (July 2021)
In this Bachelor Thesis, we give a minimalistic description of magnetism in
monolayer CrI3. This description is constructed from two seperate exchange interactions. We combine the antiferromagnetic Kugel-Khomski direct exchange,
with the ferromagnetic Goodenough-Kanamori indirect exchange. In contrast
to the individual models, the full model exhibits a magnetic phase transition.
The near additive interplay between both exchange mechanisms allows for an
insightful qualitative description of the magnetic properties.
- Jesse Vos (June 2021)
- Robin Smeets (June 2021)
- Femke Verheijen (June 2021)
In this project the scattering rates, which is equal to the inverse lifetime, of acoustic phonons was determined in graphene at 0 K. A Hamiltonian was found within a continuum elasticity description, describing the propagation of phonons and the interaction between them at large wavelength in graphene. By determining the transition probability of a phonon decay process, the rate of this phonon decay could be determined by using Fermi’s Golden Rule. With this decay rate, it could be determined if the phonon is well defined. It was found that for both longitudinal and transversal acoustic phonons decaying in two flexural acoustic phonons, the scattering rate is proportional to the initial momentum of the phonon and that both phonons are well defined at 0K, by considering only this decay process.
- Anne Riewald (July 2020)
During this project, a theoretical model to visualize plasmonic dispersions in a 2D heterostructure was created using the WFCE approach to handle the Coulomb screening. With this, the effect of varying 2D layer height and metallic, interband, and anisotropic screening on plamonic exciations was studied. It was found that increasing the screening in any of the screening channels dampens the plasmonic excitation. Increasing the 2D layer height has the same effect. Lastly, it was found that the screening resulting from anisotropic substrate layers, can results in an anisotropic plasmonic excitation in an isotropic 2D metal.
- Mohammad Hashem Jabr (December 2019)
In this project we computed the antiferromagnetic resonance frequency of a honeycomb lattice and studied the effect of electric currents on this frequency. We have done this by studying the Heisenberg model on a honeycomb lattice where neighboring spins are coupled through a negative exchange interaction. The effect of current can be included by an s-d energy term. By writing the energy of the system containing both localized spins and conducting spins, we can derive the equations of motion, called landau-lifshitz equations. By linearizing these equations one obtains the resonance frequency. The electric current gives rise to spin-orbit torques that enter the equations of motion, and thus affect the resonance frequency.
- Mark Beijer (August 2018)
Perovskites are crystals with chemical formula ABX_3 and are normally not conductive. However, at the boundary of two perovskites, in my case, SrTiO_3 and LaAlO_3 there is a conductive layer. To investigate this phenomena I calculated the spin textures of SrTiO_3 at the boundary.
- Lele Fang (July 2018)
- Yann in t Veld (July 2018)
- Tom Westerhout (August 2017)
- Jacqueline Zeitler (August 2017)
- Maxime Gidding (August 2017)
- Luuk Coopmans (July 2016)
Monte Carlo simulations have verified the scaling behaviour of several elastic moduli of graphene which was predicted by the theory of membranes. However, the temperature dependence of the bending rigidity found in this type of calculations is not fully explained. Since the bending rigidity also determines the dispersion of out-of-plane acoustic modes, we calculated the phonon modes of graphene directly and compared them to the results of the theory of membranes. We used a new method based on Molecular Dynamics Simulations and Fourier Analysis to obtain the phonon modes of graphene at several different temperatures and extracted the temperature dependence of the bending rigidity. We can conclude that the bending rigidity increases with temperature, which confirms the results found by Monte Carlo simulations.
- Nick Brummans (June 2015)
- Marijn Man (June 2015)
- Nicole Orval (February 2014)
- Timo de Ruijsscher (Summer 2012)
- Marco Stevens (Spring 2012)
- Edo van Veen (August 2012)
- Jan-Pieter Boersma (June 2011)
- Frank Buijnsters (August 2010)
- Linde van Heeringen (July 2010)
De onverwachte structuur van aluminium nanokristallen: Een moleculaire dynamica simulatie (pdf, 1,1 MB)In deze studie is de structuur van aluminiumclusters Al108 en Al1372 onderzocht met behulp van moleculaire dynamica. Er is gebruik gemaakt van een gefitte veel-lichamen potentiaal. Met behulp van verwarmen tot de vloeistoffase en koelen is voor A108 een amorfe structuur gevonden met een beduidend lagere energie dan een fcc-structuur (ΔE = 0.05 eV). Voor Al1372 verschillen beide structuren nagenoeg niet qua energie. Dit leidt tot het vermoeden dat clusters met een diameter grofweg kleiner dan 2.8 nm een stabiele amorfe structuur zullen hebben, terwijl grotere clusters de fcc-structuur behouden.
- Inka Locht (November 2009)
- Koen Reijnders (August 2008)
- Jamil Hetzel (August 2008)