Name of the laboratory: Centre de Physique Théorique
Web page:
http://www.cpt.univ-mrs.fr/
Team: Nanophysics team (E6)
Thesis advisors: Thibaut Jonckheere and Jérôme Rech
Co-advisors : Benoît Grémaud and Thierry Martin
Email addresses:
thibaut.jonckheere@cpt.univ-mrs.fr,
jerome.rech@cpt.univ-mrs.fr,
benoit.gremaud@cpt.univ-mrs.fr,
thierry.martin@cpt.univ-mrs.fr
Laboratory address : Centre de Physique Théorique, Bat TPR2, 163 Av. de Luminy, Case 907, 13288 Marseille Cedex 09
Web page of the team: [
www.cpt.univ-mrs.fr]
PhD subject’s title: Quantum field theory approaches to electronic transport in the fractional Hall effect and other topological matter
Subject description:
The nanophysics team of CPT is looking for a motivated PhD thesis student to compute analytically and numerically transport quantities in nanostructures (integer and fractional quantum Hall bars, topological insulators, cold atoms…) which are either connected to leads or considered as isolated systems. The possibility for generating « exotic » excitations propagating along the edges of the system, with possibly fractional charge or fractional (anyonic) statistics offer new perspectives for quantum transport. In particular, even though there are numerous experiments studying various aspects of these topological materials, one is still looking for unambiguous observations of, among other things, anyonic statistics, Majorana fermions,... Similarly, from the theory point of view, there sometimes exist many different candidates for describing edge physics of the fractional quantum Hall effect (FQHE). Therefore, in all these situations, it is crucial to identify the proper “smoking guns” that will allow people a better/proper understanding of the experimental results. Studying quantum transport can precisely play this role: it is typically characterized by the charge, spin or heat currents, but also by more involved quantities giving additional information, namely current-current correlations in time, called «Noise », or even higher moments of the current operators. The aim of the thesis is therefore to explore quantum transport in realistic experimental situations of FQHE. The directions foreseen include (but are not limited to) multiple quantum point contact geometries, and exotic filling factors involving counter-propagating modes (e.g. 2/3).
In such unconventional states of matter, for out of equilibrium conditions when either a voltage bias or a temperature gradient is imposed via the leads connected to the sample, one resorts to specific methods, in particular the Keldysh Green’s function formalism of Quantum field theory. The CPT nanophysics team has a strong tradition of excellence in using these tools to study the current and noise.
Equilibrium properties of an isolated system are also interesting and thus also deserve attention in these unconventional states of matter. One can then study the thermal properties of quantum mechanical observables (density, charge, persistent currents…) or Josephson-like currents (in the presence of a phase difference between two such subsystems), which are typically tackled using equilibrium methods such as the Matsubara technique, or advanced numerical methods (see below).
Since such topological systems carry current via so-called edge states – which constitute one-dimensional systems – from the analytical point of view, one typically uses the Abelian bosonization technique along with the chiral Luttinger liquid model for continuum model Hamiltonians. From the numerical point of view, one uses advanced numerical methods such as exact diagonalization, quantum Monte Carlo Methods, and Density Matrix Renormalization Group for models on a lattice.
Concerning out of equilibrium situations, early theoretical works focused solely on a constant (DC) voltage and zero frequency noise. In the last decade, the nanophysics team of CPT has been also focusing on so-called « Electronic Quantum Optics » (EQO), where the injection of charge is achieved with time dependent voltages or single electron sources. One is then able to model the analog of quantum optics two particle interference experiments, such as Hambury-Brown and Twiss correlations or Hong-Ou-Mandel collisions at the location of a “beam splitter”. Contrary to photons, electrons bear a charge and thus interact strongly with their electromagnetic environment. Electrons are always accompanied by a Fermi sea, and they obey the fermionic statistics rather than the bosonic one. EQO has attracted a lot of experimental and theoretical interest in the last decade. As experiments need large statistical ensembles of data to monitor signals, they typically use periodic voltage pulses, in the spirit of so called “photo-assisted transport”: this is precisely mirrored in our theoretical approach as we use a combination of Keldysh and Floquet formalisms.
The team benefits from a strong network of collaborations, in particular with Heinrich Heine Universitat Dusseldorf (R. Egger and A. Zazunov), Universidad Autonoma Madrid (A. Levy-Yeyati), ISSP Tokyo University (T. Kato), Universita degli Studi di Genova (M. Sassetti), Hiroshima University (K. Imura), Laboratoire de Physique de l’Ecole Normale Supérieure Paris (G. Fève). Its research style is to use effective condensed matter theory models (rather than ab initio calculations) to compute quantities which are measurable by experimental groups. While this is not directly connected to the present thesis topic, the Nanophysics team is also active in modeling quantum transport in (conventional and topological) superconducting hybrid systems.
Candidates not having their own PhD funding will be subject to the PhD fellowship contest of the Ecole Doctorale 352 of Aix-Marseille Université in the spring 2021 (see [
ecole-doctorale-352.univ-amu.fr]).
Advisors short CV:
Thibaut Jonckheere, Chargé de Recherche CNRS, 46 years old (Undergrad and Masters degree from Ecole Normale Supérieure (ENS) Paris, PhD at Laboratoire Kastler Brossel; h-index 25).
Jérôme Rech, Chargé de Recherche CNRS, 40 years old (Undergrad and Masters degree from Ecole Normale Supérieure (ENS) Lyon, joint PhD at IPhT CEA Saclay and Rutgers University, USA; h-index 23).
Benoît Grémaud, DR2 CNRS, 51 years old (Undergrad and Masters degree from Ecole Normale Supérieure (ENS) Paris, PhD at Laboratoire Kastler Brossel; h-index 28).
Thierry Martin, Professeur Classe Exceptionnelle 2ème echelon, 58 years old (Undergrad EPFL Switzerland, Masters and PhD University of California Los Angeles, USA; h-index 40).
Selected publications which are relevant to the PhD topic:
Thierry Martin, Noise in mesoscopic physics, les Houches Session LXXXI, H. Bouchiat et. al. eds. (Elsevier 2005), arXiv:cond-mat/0501208
I. Safi, P. Devillard and T. Martin, Partition noise and Statistics in the fractional quantum Hall effect, Phys. Rev. Lett. 86, 4628 (2001).
A. Crépieux, R. Guyon, P. Devillard and T. Martin, Electron injection in a nanotube: noise correlations and entanglement, Phys. Rev. B 67, 205408 (2003).
A. Crépieux, P. Devillard and T. Martin, Photon-assisted shot noise in the quantum Hall effect, Phys. Rev. B 69, 205302 (2004).
A. Zazunov, M. Creux, E. Paladino, A. Crépieux, and T. Martin, Detection of Finite-Frequency Current Moments with a Dissipative Resonant Circuit, Phys. Rev. Lett. 99, 066601 (2007).
D. Chevallier, T. Jonckheere, E. Paladino, G. Falci, and T. Martin, Detection of finite-frequency photoassisted shot noise with a resonant circuit, Phys. Rev. B 81, 205411 (2010)
Y. Hamamoto, T. Jonckheere, T. Kato, and T. Martin, Dynamic response of a mesoscopic capacitor in the presence of strong electron interactions, Phys. Rev. B 81, 153305 (2010)
C. Wahl, J. Rech, T. Jonckheere, and T. Martin, Interactions and Charge Fractionalization in an Electronic Hong-Ou-Mandel Interferometer, Phys Rev. Lett. 112, 046802 (2014).
D. Ferraro, C. Wahl, J. Rech, T. Jonckheere and T. Martin, Electronic Hong-Ou-Mandel interferometry in two-dimensional topological insulators, Phys. Rev. B 89, 075407 (2014)
J. Rech, D. Ferraro, T. Jonckheere, L. Vannucci, M. Sassetti, and T. Martin, Minimal Excitations in the Fractional Quantum Hall Regime, Phys. Rev. Lett. 118, 076801 (2017)