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Study of some topological states of matter: from topological insulators to quantum magnetism

PHD proposal 2019

by Pierre Pujol - 7 December 2018

All the versions of this article: English , français

The proposed topic is for a PhD thesis to be done within the group "strongly correlated Fermions" of the Laboratory of Theoretical Physics at the Université Paul Sabatier.

The study of quantum frustrated magnetic systems is one of the areas where we find the more activity now in condensed matter physics. They are indeed the "laboratory" to see the emergence of exotic collective effects such as fractional excitations or topological degeneracy. They also serve as the first step in understanding the physics of complex systems such as those related to high-temperature superconductors.

The methods proposed by Haldane to define paths integrals for spin systems have already proven to be of great utility to study various non-trivial properties of magnetic systems at low temperature (for a review, see for example [1]). The path integral approach has proven to be a very powerful tool for studying topological states of matter (see for example [2]). There are still quite a lot of open questions, especially for frustrated systems in the presence of a magnetic field. The effect of Berry phases involved in the partition function, which have a very important role in the absence of a magnetic field, began to be studied in the presence of a non-zero field [3]. Moreover, recent studies have revealed particularly interesting phenomena when the magnetic degrees of freedom are coupled either to charge degrees of freedom or to a topological insulator [4] [5].

The aim of the project is to study frustrated systems in the presence of a magnetic field and build the field theory arising from them. This description should in principle allow to reveal in a rigorous way some properties that are the signature of a non-trivial physics. The predictions arising from our study should allow a better understanding of some experiments realized on novel materials under high magnetic fields. The research method is based on quantum field theory techniques and the path integral methods developed for spins systems.

The student is supposed to have some familiarity with the basics in solid state physics and condensed matter theory.


[1] D. Cabra et P. Pujol, Chapitre du livre "FIELD THEORETICAL METHODS IN QUANTUM MAGNETISM"

[2] Shintaro Takayoshi, Pierre Pujol, Akihiro Tanaka, Phys. Rev. B 94 235159 (2016).

[3] A. Tanaka, K. Totsuka et X. Hu, Phys. Rev. B 79 064412 (2009).

[4] Imam Makhfuzd et Pierre Pujol, Phys. Rev. B 92 144507 (2015) et Phys. Rev. Lett. 114 087204 (2015).

[5] H. D. Rosales, F. A. Albarracín, P Pujol, arXiv preprint arXiv:1810.00044