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Unconventional Superconductivity and Strong Electron Correlations: a Cooperative mechanism

Periodic Reporting for period 2 - SuperCoop (Unconventional Superconductivity and Strong Electron Correlations: a Cooperative mechanism)

Reporting period: 2021-03-01 to 2022-02-28

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: preliminary analysis of the interplay between correlations and superconductivity using a toy model; development of an efficient numerical approach to describe the incoherent metal phase of iron-based superconductors; self-consistent analysis of correlations effects for realistic five-orbital models.
In the first part of SuperCoop we 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 Hubbard term that forces two electrons to occupy different lattice sites and the 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 interplay 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. This follows from the dynamical properties of the Hund’s metal. Hund’d driven correlations produce a spectral weight redistribution on 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.

In the second part of the action we worked on a realistic modeling of the superconducting coupling mediated by spin-fluctuations and developed a code to compute the pairing vertex using the conserving fluctuation exchange approximation. Motivated by an increasing evidence that the combination of forward scattering phonons and spin fluctuations could produce an enhancement of the superconducting critical temperature in FeSe monolayer, we also included the possible contribution to pairing coming from electron-phonon coupling. The code has an interface to use as input ab initio derived models. We are currently performing calculation on realistic five-orbital model for iron-based superconductors.

The description of the incoherent metallic state from which superconductivity emerges has been addressed by formulating a quantum theory of the collective excitations on top of the Gutzwiller mean-field approximation. The generalization of this method for a multiorbital system is currently in progress.

The duration of this action almost completely overlapped with the global emergency caused by the Covid-19 pandemic. This caused major problems and delays to almost any aspect of the action. Even if within a different timeline we were able to complete all the main activities planned. However, the very final step of combining the dynamical description of the incoherent metal with the pairing vertex obtained by spin/charge fluctuations (plus potential electron-phonon contribution) is not fully reach yet and it will be addressed in the following months.
Extensive theoretical and experimental studies have highlighted the relevance of electronic correlations driven by local interactions in iron-based superconductors. 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. The analysis performed during the action 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.

We developed advanced computational tools to explore this idea within a more realistic microscopic description of iron-based superconductors and we are currently performing the analysis of the pairing mediated by spin-fluctuation in the realistic multiorbital model. Once completed this work will give us quantitative information about how correlations and spin-fluctuations 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.

Beyond the scientific impact of this action, it is worthy considering the technological advance achieved. Within the action we developed a new set of computational tools to analyze different open questions concerning of physics of correlated superconductors. Those tools represent an important methodological advance and has the potential to be used by the scientific community in a much broader context.

The pandemic forced us to revise the plan for exploitation and dissemination of our results, however we managed to find suitable alternatives. (e.g. outdoor events, remote participation to conferences etc etc). Overall, the participation in numerous outreach events and several conferences guaranteed an effective dissemination of the results obtained so far.
Superconducting gap computed in the low vs high Hund's coupling JH regime.