PhD subjects

In this  PhD project we intend to study  the phase diagram of cuprate superconductors using techniques coming from strong coupling theory. We will focus on  a recent idea for the mysterious pseudo-gap phase of  these materials, where a finite momentum  particle-particle pair  (also called Pair Density Wave) « fractionalizes » into a modulated particle-hole pair and a uniform particle-particle pair. This phenomenon of fractionalisation opens a gap in the Fermi  surface which can be connected with the pseudo-gap of cuprates. We will test this idea to experiments and produce predictions.  Meanwhile,  on a different topic we project a study of the potential superconductivity in ABC  graphite, with a focus on its topological properties.  This will be done in collaboration with Cristina Bena from IPhT. The  potential candidate will learn different techniques during her/ his PhD, with in particular writing and solving numerically strong coupling equations, diagrammatic techniques, impurity solvers. Last but not least, a strong interaction with experimentalists, with discussion of ideas and concepts  will be expected.

This subject is in the field of condensed matter theory, and concerns the physics of electrons in solids. In recent work (Phys. Rev. B 100, 081106(R) (2019)) we have provided a new and exact formalism to describe the formation of end, edge or surface states through the evolution of impurity-induced states. We have proposed a general procedure that consists of finding the impurity states via the T-matrix formalism and showing that they evolve into boundary modes when the impurity potential goes to infinity. We have applied this technique to obtain Majorana states in 1D and 2D systems, as well as topological insulator edge states, graphene edge states, graphite surface states and Fermi-arc surface states for Weyl insulators.



Here we propose to generalize this technique to other systems for which this technique would provide significant advantages: for example we plan to study the edge states of multilayer graphene with different stackings (ABA, ABC or twisted), in the normal and superconducting regimes, in particular exploring the possibility to form topological edge states. We also intend to use this technique to study Shiba chains, i.e. chains of magnetic or non-magnetic impurities located on the surface of a superconducting substrate, in the search for the formation of topological Majorana states.



The candidates should have good knowledge of advanced quantum mechanics, quantum field theory, solid state and many body physics.