Research activities : Condensed Matter
PhD Thesis: Topological phases and Majorana fermions
This work was done both at Centre de Physique Théorique and at Laboratoire Pierre Aigrain (ENS) under the joint supervision of Karyn Le Hur and Christophe Mora.
The defence will be held in English Friday, September 8th at 02:00pm at Ecole Polytechnique in amphi Becquerel.
In this thesis, we study theoretically different aspects of topological systems. These models present resilient properties due to a non-trivial topology of their band structures, and in particular exotic edge excitations such as Majorana fermions. Entanglement markers have been fundamental to the study of these systems and of gapless systems in general, but are challenging to measure. Bipartite charge fluctuations were proposed as a weak measurement of entanglement entropy. We extend results on standard Luttinger Liquids to generic families of one- and two-dimensional non-interacting topological systems. A volume law arises, and is linked to the Quantum Fisher information, with non-analyticities at the phase transitions. Critical points are characterized by universal coefficients that reveal the topological aspect of the transitions.
In a second time, we include interactions and show that some of these signatures are preserved in interacting topological superconductors. Through analytical and numerical methods, we study two Coulomb-coupled topological superconducting wires. The interplay between unconventional superconductivity and strong interactions leads to exotic phases. We show the appearance of orbital currents spontaneously breaking the time-reversal symmetry, and of an unusual gapless phase that is the extension of two critical Majorana modes.
Finally, we focus on electronic transport mediated by Majorana fermions. We study a floating superconducting island carrying several such impurities, a potential building block for a quantum computer. The Majorana fermions affect the statistics of the charge carriers, which leads to very resilient fractionalized transport. We extend previous studies to the charge degenerate case and map it to the Multi-Channel Kondo model at large interaction, reinterpreted in terms of a particle moving in a high-dimensional, dissipative lattice.
Herviou L, Mora C, Le Hur K.
Phase diagram and entanglement of two interacting topological Kitaev chains.
Physical Review B 2016;93(16):165142.
Herviou L, Le Hur K, Mora C.
Many-terminal Majorana island: From topological to multichannel Kondo model.
Physical Review B 2016;94(23):235102.
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