Take a look at the topics of master (Mgr.), bachelor and PhD. thesis that we propose.
Come along for an informal inquire!
Self-consistent random matrix ensembles
Theory of random matrices (RMT) describes systems with effectively non-interacting particles in a random potential, such as nuclear matter or electrons in mesoscopic devices. In this project we would extend the random-matrix paradigm by including particle interactions at the mean-field level. Examples of mean-field theories are Hartree (for the electron-electron interaction), Hartree-Fock, Bogoliubov–de-Gennes (for the Bardeen-Cooper-Schrieffer interaction) and slave-boson mean-field (for the Kondo interaction). It is foreseen that entirely new features in the RMT emerge at the interacting level, such as new phases and critical points. The purpose of this project is to undergo a numerical exploration of this rather unknown area.
Theory of spin chains on metallic surfaces: emergence of the heavy-fermion behavior
When a magnetic moment is embedded in a metallic (free-electron) environment, spin-fluctuations give rise to a Kondo effect: excitations at low temperatures are free-fermion like and the magnetic moment is quenched. Similarly, a lattice of magnetic moments (plus the metallic environment) can lead to a heavy-fermion behavior, characterized by a new (heavy) electron band and suppression of magnetism.
In this project we want to study theoretically the evolution from the single-moment Kondo effect to a multiple-moment lattice (spin chains) and investigate the onset of heavy-fermion phenomenology as the chain length increases.
This study is inspired by a collaboration with an experimental group at the University of Zaragoza (David Serrate) (scanning-tunneling microscopy of atomic spin-chains on a metallic surface).
Current-induced forces in nanoscopic quantum conductors
Electronic transport in molecules and nanoscale conductors presents a research field with fascinating applications of Quantum Theory. In this project we would like to focus on the so called “wind force” that the electronic current exerts on the atomic backbone of the conductor (molecule). The aim is to understand these forces in molecular junctions and films. An interesting example is a graphene ribbon. Here it was shown that due to impurities, current density can be locally amplified by a factor 100 compared to the average current density. Interesting, so far unanswered questions are: what is the magnitude of these forces? When do they uptake? How to control/suppress them? This project will open a new research path in the field of Molecular Electronics.
Bachelor & PhD thesis
Conductance of molecular junctions via Friedel’s rule
The conductance of molecular junctions is of quantum nature. In certain cases, Friedel’s rule allows to calculate the conductance via charge transfer to the junction in equilibrium. The subject of this thesis is to analyze the charge density of molecular conductors and conclude upon the conductance.
Usually we have loads of ideas, don’t hesitate and contact us.