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Unconventional Superconductivity and Strong Electron Correlations: a Cooperative mechanism

Periodic Reporting for period 1 - SuperCoop (Unconventional Superconductivity and Strong Electron Correlations: a Cooperative mechanism)

Reporting period: 2019-09-01 to 2021-02-28

The understanding of optimal conditions giving rise to high temperature superconductivity is still a crucial challenge of condensed matter theory and the last obstacle for an effective design and exploitation of superconductors.
The discovery of iron-based superconductors was among the most significant breakthroughs in condensed-matter research since the discovery of superconductivity. I these unconventional materials superconductivity emerges from a (highly incoherent) “bad” metal, characterized by strong electronic correlations, as witnessed for example by the anomalous behavior of the resistivity. In that respect, to understand the bad metal and properly address the interplay between electronic correlations and superconductivity represents a challenge of crucial relevance in order to define the optimal conditions for superconductivity and contributing to efficiently design future superconductors. In the context of IBS, the role of electronic correlations in the bad metal phase has been widely investigated . Still the ultimate question, “Do correlations cooperate to the enhancement of the superconducting critical temperature?”, waits for an answer. With SuperCoop project we are moving a step forward along this direction.

SuperCoop introduces and develops a scenario in which the key ingredient for unconventional superconductivity comes from a novel cooperative interplay between electronic correlations and magnetic interactions. Within SuperCoop we are working to develop efficient methods to describe the incoherent metallic phase of iron-based materials from which superconductivity emerges and to analyze the role of correlations effects on the pairing mediated by magnetic degrees of freedom. The project articulated through three specific objectives: (1) Preliminary analysis of the interplay between correlations and superconductivity using a toy model; (2) Development of an efficient numerical approach to describe the incoherent metal phase of iron-based superconductors; (3) Self-consistent analysis of correlations effects for realistic five-orbital models.
In the first part of SuperCoop we worked on the first objective and completed the preliminary analysis on a simplified toy model for iron-based materials.
We studied how superconductivity is realized in a multiorbital correlated metal. The electron-electron repulsion manifest within a multiorbital system via different interacting channels, in particular the local Hubbard term that forces two electrons to occupy different lattice sites and the local Hund’s coupling that forces electrons on the same site to spread into the all available orbital levels maximizing locally the spin. We verify that the inteplay between unconventional superconductivity and electronic correlations changes depending on the nature of the those correlations.
Without assuming a precise origin of pairing we proved that a generic pairing can be enhanced by Hund's driven correlations if compared with standard strongly correlated systems (i.e. correlated systems dominated by Hubbard driven correlations). This follows from the dynamical properties of the Hund’s metal (enconded in the DMFT self-energy, see figure). In this system the spectra weight redistribution leads to the population of states in an energy window of order of the Hund’s coupling around the Fermi level. Such incoherent states participate the pairing together with the coherent quasiparticle part, thereby enhancing the superconducting tendency. The analysis performed using a finite cut-offenergy in the pairing interaction further confirms the involvement of the low-energy spectral weight in superconductivity and prove that the results we obtained are robust and they are going to to hold even once we account for a realistic superconducting coupling in the model.

We are currently working on a realistic modeling of the superconducting coupling mediated by spin-fluctuations using the conserving fluctuation exchange (FLEX) approximation to study self-consistently spin and charge susceptibility and the superconductivity within a realistic five-orbital model for iron-based superconductors.
In the last decade, extensive theoretical and experimental studies have highlighted the relevance of electronic correlations driven by local interactions in iron-based superconductors and there is nowadays a general consensus that the bad metallic behavior of the normal state can be described in terms of the Hund's metals physics. Nonetheless, more conventional theories based on the exchange of bosons (spin fluctuations are the most popular candidate) describe correctly a variety of phenomena pointing towards a more standard mechanism. Until now, the interplay between electronic correlations and unconventional superconductivity was poorly investigates.

Our analysis analyze the interplay between boson-mediated superconductivity and Hund’s like correlations, thus putting together two main topics of modern condensed matter physics. We demonstrated that Hund's driven correlations can enhance the tendency of the system towards superconductivity and explain that the key ingredient to obtain such a boost from Hund’s driven correlations comes from the dynamical propertied of the Hund’s metal. In that respect, the analysis performed during the first phase of the project represents a huge progress beyond the state of the art and put on a solid ground the original idea of SuperCoop that the key ingredient for unconventional superconductivity comes from a novel cooperative interplay between electronic correlations and boson mediated superconductivity.

The work we are currently performing includes considering a realistic modeling of iron-based electronic structure and deriving the superconducting coupling mediated by spin-fluctuation in the realistic multiorbital model. Once completed this work will give us quantitative information about the relationship between Hund’s correlations and spin-fluctuations and how they can cooperate to stabilize superconductivity to higher temperature. Such quantitative study will allows us to determine an optimal set of parameters and will serve as input for modeling and designing the new class of correlated superconductors.

Among the expected results we aim to achieve within the second phase of the project there is also the development of new computational tools that will represents an important methodological advance. Those tools, developed within this project to better characterized the bad metallic phase of iron-based superconductors, have the potential to be used for the analysis of correlations in a much broader context.

A final aspect we expect to be able to develop in the last year of the project is the dissemination and outreach plan outlined in the SuperCoop proposal. Since March 2020 we are in the mist of a global emergency caused by the Covid-19 pandemic. Among the various activities we were expected to participate, only a few took place before the outbreak of the emergency while all the others were canceled or (in the last month) moved virtually. We are currently revising our plan in order to be able to communicate/disseminate and organize outreach activity following the guide lines provided by the WHO and by Italian authorities.
Superconducting gap computed in the low vs high Hund's coupling JH regime.