The crazy world of transport in complex materials

Complex systems are characterized by the presence and interplay of many different degrees of freedom. Understanding the mechanism behind a certain phenomenology is not an easy task. A great example is provided by the transport properties of iron-based superconductors in which the interplay between magnetic and orbital degrees of freedom give rise to an extremely rich phenomenology. I spent a huge part of my Ph.D program working on several aspects of this topic and still nowadays I am fascinated by new and surprising effects displayed by these superconductors. It is amazing to see how the experimental techniques become more and more refined and powerful every day and it is a challenge for us, theorists, be able to provide new ideas and theories that not only fit the experimental picture, but also suggest new experiments to test and validate such theories.

Our team recently investigated a new aspect of this topic: the anisotropic properties of iron-based superconductors in the nematic phase. As you may (or may not) know, in the context of Fe-based materials the nematic phase is a state in which the system exhibits strong anysotropic properties probed by e.g. measurements of lattice parameters, dc resistivity, optical conductivity, magnetic susceptibility and others. The debate about the origin of this phase has been extremely lively: who is the responsible of this transition? Phonos, spin or orbital degrees of freedom ? (go here if you want to know more about it).

The analysis of the anisotropy displayed by the resistivity in this phase could help us to understand more about the origin of the nematic state. To make the story short we can simplified the results presented so far in the literature as follows: within a spin-driven scenario we expect the anisotropy of the resistivity being dominated by the x/y anisotropy of the scattering rate (that measure the collision time of a carrier moving in the system ), within the orbital-driven scenario instead we expect the anisotropy of the resistivity as the result of the anisotropy on the Fermi velocity.

In our work published in Physical Review B (here!) we showed that the situation is much more complex since orbital and spin degrees of freedom are not independent! In the last years we widely discussed the spin-orbital interplay within our Orbital Selective Spin-Fluctuation Model for iron-based superconductors and in this last work we carefully analyzed the effect of anisotropic orbital-dependent spin fluctuations on both scattering rate and Fermi surface for different members of the Fe-based family.

If you want to know more, I suggest you to watch this 20 mins talk that my amazing PhD student Raquel Fernandez-Martin presented at the international conference SUPERFLUCTUATIONS 2020

A single model to explain Superconductivity & Nematicity in FeSe

Soon after the discovery of superconductivity in iron-based systems, it has been proposed that pairing could be unconventional, i.e., based on a non-phononic mechanism.^1,2 This proposal has been triggered, from one side, by the small estimated value of the electron-phonon coupling, and, from the other side, by the proximity in the temperature-doping phase diagram of a magnetic instability nearby the superconducting one. Within an itinerant-electron picture, pairing could be provided by repulsive spin fluctuations between hole and electron pockets, connected (“nested”) by the same wavevector characteristic of the spin modulations in the magnetic phase. Notice however that the explicit roles of the orbitals are completely neglected within the itinerant scenario. In fact, within the itinerant approach, the band nesting properties of a system should rule completely its phenomenology.  On the contrary, strong orbital selective features have been experimentally found both in the IBS nematic and superconducting phase.

To fill the gap B.Valenzuela and I derived in 2015 the effective low-energy theory for IBS projecting into the band basis the multi-orbital interacting Hamiltonian³. The projection of the orbital information at low-energy unveils a non trivial spin-orbital interplay that results in a strong orbital selectivity of the Spin Fluctuations: Spin Fluctuations peaked around the QX /QY vectors involve only the yz/xz orbitals, respectively. Over the years our Orbital Selective Spin Fluctuation (OSSF) model⁴ has proven to be extremely successful to describe the complex phenomenology of IBS, in particular, of the intriguing FeSe compound that presents an unusual nematic state without magnetism that evolves at low temperature into a superconducting state. Recent experiments observed a noteworthy anisotropy of the superconducting gaps^5,6 Its explanation is intimately related to the understanding of the nematic transition itself. In this paper, recently published on npj Quantum Material, we show that the spin-nematic scenario driven by Orbital-Selective Spin Fluctuations provides a simple scheme to understand both nematicity and superconductivity of FeSe. The pairing mediated by anisotropic spin modes is not only orbital selective but also nematic, leading to stronger pair scattering across the hole and X electron pocket. The delicate balance between orbital ordering and nematic pairing points also to a marked k_z dependence of the hole–gap anisotropy.

Nematic pairing from orbital-selective spin fluctuations in FeSe
npj Quantum Materials 3, 56 (2018)