Final Report Summary - NANOHIGHTC (Search for novel mechanisms to increase the critical temperature of a superconductor) Most breakthroughs in superconductivity have been directly related to the discovery of materials (cuprates, iron pnictides, magnesium diboride...) with unexpectedly high critical temperatures. To a good extent these discoveries has been driven by intuition and trial and error. The enormous interest generated by these materials has not crystalized in a detailed theoretical understanding of the mechanisms leading to control and enhancement of superconductivity. The main aim of this project has been to overcome these limitations in order to understand better the superconducting state at and out of equilibrium. Overall the scientific outcome of the projects has been excellent: twenty two publications, most of them in leading journals such as Physical Review and Physical Review Letters, plus five preprints that will be published shortly. Part of this success has been related to the recruitment of two postdocs, Pedro Ribeiro and Hai-Qing Zhang, that have helped to attain, and even surpass, the original objectives of the projects. It has also been instrumental the multiple international collaborations that I have started during these years with a broad spectrum of leading researchers including Prof. Klaus Kern from Max Planck Institute in Stuttgart, Prof. Hong Liu in MIT, Dr. Paul Chesler in Harvard, Prof. Jorge Santos in Cambridge. The research results have had an impact in the community: I have been invited to more than ten international conferences and about fifteen seminars and short stays in leading research groups. Currently I am referee of a variety of leading research journals and funding agencies in Netherlands, Germany and UK. In the last years I have been the main organizer of the workshop: ’Control and enhancement of superconductivity in nano structures’, Lausanne, June 2012, by the Centre Europeen de Calcul Atomique et Moleculaire who brought together leading researchers in the field of superconductivity in nano/hetero structures. The past year I was the main organizer of a four weekProgramme “Mathematics and physics of the holographic principle”, Isaac Newton Institute Cambridge, September 2013, http://www.newton.ac.uk/programmes/HOL/ . Funding in both cases was awarded only after a highly competitive process that included anonymous peer review. I was also invited to be guest editor of a focus issue on superconductivity in nanoscale systems in the journal “Superconductor Science and Technology”, the leading research journal focused on superconductivity. All these facts points clearly to aleading position in all the fields I am actively working on. The only soft point has been that, though I was promoted to invited professor, I could not secure a permanent position in the host institution so I had to find a position somewhere else. The most relevant results of my research since the beginning of the project have been:2011-2012 See below the two main research areas addressed since the beginning of the project and main results obtained so far.I. Description and enhancement of superconductivity in nanoscale and low dimensional disordered superconductors.We have put forward a fully quantitative formalism to describe finite size effects in clean nanoscale superconductors in the limit in which mean field theory is applicable. This formalism has then been applied to study the potential enhancement of superconductivity by finite size effects in Iron-Pnictides thin films. We found that an increase of up to 30% in the critical temperature is feasiblefor sizes in which the mean field approach is correct. We have also developed a theoretical framework to describe deviations from mean field in nanoscale superconductors that included the combined effect of thermal and quantum fluctuations. In collaboration with experimentalists we successfully applied this theory to describe the evolution of superconductivity in Pb nanograins. We have also investigated the breaking of quasi-long range order in a strongly coupled, disordered, one dimensional superconductor by using DMRG techniques. Our main finding is that even in 1d superconductivity is robust to weak disorder. More importantly we identify a region of parametersclose to the superconductor-insulator transition in which disorder enhance quasi long order. Finally, we have studied analytically finite size effects in strongly coupled nanoscale superconductors by using holographic techniques. As a function of the coupling strength we identified the minimum size for superconductivity to exist. Moreover we showed analytically that in certain cases finite size effects can enhance the interaction that binds the electrons in a superconductor.II. Non equilibrium dynamics and the route of thermalization in strongly interacting, especially superconducting, systems.We have investigated the route to thermalization in strongly coupled superconductors by using holographic techniques. We have identified a region of parameters in which the system does not thermalize after a quench. The role of disorder in the far from equilibrium dynamics of a strongly interacting system after a quench was also by exact diagonalization techniques. Wefound that Anderson-Mott localization slows-down and eventually stops thermalization in a closed system initially at zero temperature. Moreover, for weaker disorder, we identified a novel route to thermalization characterized by power-law approach to thermal equilibrium.Finally we studied the time evolution of a strongly coupled superconductor in a disordered potential after it is released from an atomic trap. We found that the dynamics around the insulator transition is not universal. The time evolution is well described by a process of anomalous diffusion whose parameters depends strongly on the interaction strength and disorder. For instance the secondmoment of the distribution function that controls the expansion velocity increases dramatically with time as the interaction increases. However a weaker disorder is enough to stop the expansion.2012-2014The most relevant results of my research in the last two years have been: the proposal of a novel way to engineer arrays of nanograins which, in realistic conditions, increases the bulk critical temperature up to a few times with respect to the bulk non granular limit [9]. Shortly after it was posted in arXiv, the paper was portrayed in “Superconductor week”, the leading magazine for applied and industrialsuperconductivity. I have also proposed a novel mechanism to restore long range order (global superconductivity) in superconducting quantum nanowires by suppressing small quantum fluctuations and phase slips. This is a step to enhance global superconductivity in superconducting hetero- and nano- structures.Together with Marcos Rigol, a leading figure in the field, we have proposed a novel route to thermalization in strongly interacting quantum system characterized by slow power-law decay without a typical time scale to reach thermal equilibrium.By using AdS/CFT techniques I have teamed up with P. Chesler, (Harvard) and Hong Liu (MIT), a leading figure in the field, to describe a novel region, to study the time evolution of a superfluid after a temperature or quantum quench from the unbroken to the broken phase. We have discovered a novel region of out of equilibrium dynamic that changes the qualitatively the current picture of dynamical phase transitions based on the so called Kibble-Zurek scaling. Previously together Hai-Qing Zhang and Hua-Bi Zeng we have explored different methods to induce novel states of out of equilibrium superconductivity by using holographic dualities. Together Paul Matthews and Pedro Ribeiro we have studied the role of dissipation in topological superconductors as a novel way to detect Majorana fermions and also enhance superconductivity in low dimensions. In collaboration with Pedro Ribeiro we have described for the first time a full phase diagram of Josephson Junctions that includes dissipation, quasiparticle tunneling and charging effects. Refereed papers:[1-22] See Section A (list) belowPreprints:23. 'Enhancing bulk superconductivity by engineering granular materials' J. Mayoh, A. M. García-García, arXiv:1311.029524. 'Inhomogenous pairing and enhancement of superconductivity in large Sn nanograins' J. Mayoh, A. M. García-García, arXiv:1309.625525. 'Far-from-equilibrium coarsening, defect formation, and holography' P .M. Chesler, A. M. Garcia-Garcia, H. Liu, arXiv:1407.186226. 'Destruction of Long-range Order by Quenching the Hopping Range in One dimension' M. Tezuka, A. M. García-García, M. A. Cazalilla, arXiv:1403.1739
