Topological and geometrical aspects of condensed matter systems

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Recent theoretical advances in condensed matter systems unveiled deep connections between observable features of quantum materials and sophisticated mathematics like topology and differential geometry. These distinct branches of science are united within field-theoretical approach to thermodynamic systems. In this project we will study models of van der Waals heterostructures comprising 2D materials with different properties. One example are RuCl3/graphene heterostructures. RuCl3 has been recently found to exhibit features of a quantum spin liquid, in particular its excitations behave as neither bosons nor fermions. They are anyons. Similar particles have attracted interest for potential use in quantum computation and there is a growing interest in finding phases of matter exhibiting such unusual and exotic properties for applications to quantum technology.The goal is to find novel ways to generate, detect and manipulate such exotic quasiparticles with conventional electronics. This is where the interaction with graphene comes into place, because graphene is the most studied 2D conductor. The hope is that we will be able to detect the unusual properties of quantum phases of strongly-correlated systems such as RuCl3 by measuring graphene electrons, when they interact with the excitations of the aforementioned systems. Thus, our project sits at the intersection between the fields of quantum material design, quantum technology and (because of the interactions between electrons with quantum magnetic phases) spintronics. The student will use quantum field theory and kinetic equation techniques to study the effect of the (graphene)electron-(RuCl3)spin interaction. They will derive equations of motions for the two quantities describing the exchange of energy/momentum between them. Equations will then be solved to find observables that can be related to experiments.