Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model

We study the collective states of interacting non-Abelian anyons that emerge in Kitaev's honeycomb lattice model. Vortex-vortex interactions are shown to lead to the lifting of the topological degeneracy and the energy is discovered to exhibit oscillations that are consistent with Majorana fermions being localized at vortex cores. We show how to construct states corresponding to the fusion channel degrees of freedom and obtain the energy gaps characterizing the stability of the topological low energy spectrum. To study the collective behavior of many vortices, we introduce an effective lattice model of Majorana fermions. We find necessary conditions for it to approximate the spectrum of the honeycomb lattice model and show that bi-partite interactions are responsible for the degeneracy lifting also in many vortex systems.Comment: 22 pages, 12 figures, published versio

Focus on topological quantum computation

Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances in the understanding of anyon properties inspired new quantum algorithms and helped in the characterization of topological phases of matter and their experimental realization. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This 'focus on' collection brings together several of the latest developments in the field and facilitates the synergy between different approaches

Combined treatment of refractory ascites with an alfapump (R) plus hernia repair in the same surgical session: A retrospective, multicentre, European pilot study in cirrhotic patients

International audienceIntroduction: The treatment of symptomatic hernia in cirrhotic patients with refractory ascites is critical but challenging. The objective of this study was to assess the feasibility and safety of the implantation of alfapump (R) combined with concomitant hernia repair in cirrhotic patients with refractory ascites. Methods: Using data from six European centres, we retrospectively compared patients treated with alfapump (R) system implantation and concomitant hernia repair [the combined treatment group (CT group, n = 12)] or with intermittent paracentesis hernia repair [the standard treatment group (ST group, n = 26)]. Some patients of the ST group had hernia repair in an elective setting (STel group) and others in emergency (STem group). The endpoints were requirement of peritoneal drainage, the rate of infectious complications, the in-hospital mortality, the length of stay, paracentesis-free survival. Results: Postoperatively, none of the patients in the CT group and 21 patients (80%) in the ST group underwent peritoneal drainage for the evacuation of ascites fluid (P < 0.0001). The overall incidence of infectious complications was not different between groups but there were fewer infections in the CT group than in the STem group (33% vs. 81%; P = 0.01). There was no difference for in-hospital mortality. The length of stay was shorter in the CT group (P = 0.03). Paracentesis-free survival was significantly better (P = 0.0003) in the CT group than in the ST group. Conclusion: Implantation of alfapump combined with concomitant hernia repair seems feasible and safe in cirrhotic patients; however, larger and randomized study are required. (C) 2020 Published by Elsevier Masson SAS

Tunneling transport in NSN Majorana junctions across the topological quantum phase transition

We theoretically consider transport properties of a normal metal (N)- superconducting semiconductor nanowire (S)-normal metal (N) structure (NSN) in the context of the possible existence of Majorana bound states in disordered semiconductor-superconductor hybrid systems in the presence of spin-orbit coupling and Zeeman splitting induced by an external magnetic field. We study in details the transport signatures of the topological quantum phase transition as well as the existence of the Majorana bound states in the electrical transport properties of the NSN structure. Our theory includes the realistic nonperturbative effects of disorder, which is detrimental to the topological phase (eventually suppressing the superconducting gap completely), and the effects of the tunneling barriers (or the transparency at the tunneling NS contacts), which affect (and suppress) the zero bias conductance peak associated with the zero energy Majorana bound states. We show that in the presence of generic disorder and barrier transparency the interpretation of the zero bias peak as being associated with the Majorana bound state is problematic since the nonlocal correlations between the two NS contacts at two ends may not manifest themselves in the tunneling conductance through the whole NSN structure. We establish that a simple modification of the standard transport measurements using conductance differences (rather than the conductance itself as in a single NS junction) as the measured quantity can allow direct observation of the nonlocal correlations inherent in the Majorana bound states and enables the mapping out of the topological phase diagram (even in the presence of considerable disorder) by precisely detecting the topological quantum phase transition point.Comment: 34 pages, 7 figures, 1 table. New version with minor modifications and more physical discussion