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The defence will be in English.
Abstract: This thesis falls within the field of condensed matter physics and focuses more specifically on the electronic properties of non-crystalline solids.
A major objective of this field is to predict and model new phases of matter that are both robust and potentially promising for technological applications.
Over the past decades, numerous topological phases have been discovered, including the quantum Hall effect (both integer and fractional) as well as Weyl semimetals.
These phases exhibit remarkable electronic properties that can be harnessed in electronic devices.
In this thesis, we investigate whether such topological phases can emerge in non-crystalline systems, such as quasicrystals and amorphous materials.
We also examine the influence of electronic interactions in these disordered media.
To address these questions, we use a combination of analytical approaches and numerical simulations to characterize the electronic properties of these systems.
Our aim is to demonstrate that topological phases can indeed arise in non-crystalline solids and that electron–electron interactions can lead to other types of non-crystalline phases.
