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Electronic and Magnetic Anisotropies in FeSe Family of Iron-Based Superconductors

Most parent compounds of iron-based superconductors (FeSCs) exhibit a tetragonal-to-orthorhombic lattice distortion below T s associated with an electronic nematic phase that breaks the four-fold (C 4 ) rotational symmetry of the underlying lattice, and then forms collinear antiferromagnetic (AF) order below T N (T N ≤ T s ). Optimal superconductivity emerges upon suppression of the nematic and AF phases. FeSe, which also exhibits a nematic phase transition below T s but becomes superconducting in the nematic phase without AF order, provides a unique platform to study the interplay amongst the nematic phase and superconductivity. In this review, we focus on the experiments done on uniaxial pressure detwinned single crystals of FeSe compared to other FeSCs and highlight the importance of understanding the electronic and magnetic anisotropy in elucidating the nature of unconventional superconductivity.

36 MATERIALS SCIENCE↗

Mossbauer study of FeSi2 and FeSe thin films

Structural studies of FeSi2 and FeSe thin films have been conducted via Mossbauer spectroscopy as continuation of earlier investigation of FeTe films. Results discuss structures of bulk and thin-film FeSi2 and bulk and thin-film FeSe.

Aggarwal, K.↗

Materials Data on FeSe by Materials Project

FeSe is Modderite-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Fe2+ is bonded to six equivalent Se2- atoms to form a mixture of distorted edge, face, and corner-sharing FeSe6 octahedra. The corner-sharing octahedral tilt angles are 51°. All Fe–Se bond lengths are 2.53 Å. Se2- is bonded in a 6-coordinate geometry to six equivalent Fe2+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on FeSe by Materials Project

FeSe is Tetraauricupride structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. Fe2+ is bonded in a body-centered cubic geometry to eight equivalent Se2- atoms. All Fe–Se bond lengths are 2.64 Å. Se2- is bonded in a body-centered cubic geometry to eight equivalent Fe2+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Tl(FeSe)2 by Materials Project

Tl(FeSe)2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Fe is bonded in a 4-coordinate geometry to four equivalent Se atoms. All Fe–Se bond lengths are 2.48 Å. Tl is bonded in a distorted body-centered cubic geometry to eight equivalent Se atoms. All Tl–Se bond lengths are 3.42 Å. Se is bonded in a 4-coordinate geometry to four equivalent Fe and four equivalent Tl atoms.

36 MATERIALS SCIENCE↗

Materials Data on FeSe by Materials Project

FeSe is Tetraauricupride structured and crystallizes in the tetragonal P4/nmm space group. The structure is three-dimensional. Fe2+ is bonded in a body-centered cubic geometry to eight equivalent Se2- atoms. There are four shorter (2.62 Å) and four longer (2.66 Å) Fe–Se bond lengths. Se2- is bonded in a body-centered cubic geometry to eight equivalent Fe2+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on FeSe by Materials Project

FeSe is Modderite structured and crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. Fe2+ is bonded to six equivalent Se2- atoms to form a mixture of edge, corner, and face-sharing FeSe6 octahedra. The corner-sharing octahedra tilt angles range from 47–59°. There are a spread of Fe–Se bond distances ranging from 2.42–2.60 Å. Se2- is bonded in a 6-coordinate geometry to six equivalent Fe2+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on K2(FeSe)5 by Materials Project

K2(FeSe)5 crystallizes in the tetragonal I4/m space group. The structure is three-dimensional. K is bonded in a distorted body-centered cubic geometry to eight Se atoms. There are a spread of K–Se bond distances ranging from 3.32–3.53 Å. There are two inequivalent Fe sites. In the first Fe site, Fe is bonded to four Se atoms to form a mixture of distorted corner and edge-sharing FeSe4 tetrahedra. There are a spread of Fe–Se bond distances ranging from 2.47–2.49 Å. In the second Fe site, Fe is bonded to four equivalent Se atoms to form a mixture of distorted corner and edge-sharing FeSe4 tetrahedra. All Fe–Se bond lengths are 2.46 Å. There are two inequivalent Se sites. In the first Se site, Se is bonded in a 7-coordinate geometry to three equivalent K and four Fe atoms. In the second Se site, Se is bonded in a 8-coordinate geometry to four equivalent K and four equivalent Fe atoms.

36 MATERIALS SCIENCE↗

Materials Data on FeSe by Materials Project

FeSe is Modderite-like structured and crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. Fe2+ is bonded to six equivalent Se2- atoms to form a mixture of distorted corner, edge, and face-sharing FeSe6 octahedra. The corner-sharing octahedra tilt angles range from 51–52°. There are a spread of Fe–Se bond distances ranging from 2.52–2.56 Å. Se2- is bonded in a 6-coordinate geometry to six equivalent Fe2+ atoms.

36 MATERIALS SCIENCE↗

Theory of Spin-Excitation Anisotropy in the Nematic Phase of FeSe Obtained From RIXS Measurements

Recent resonant inelastic x-ray scattering (RIXS) experiments have detected a significant high-energy spin-excitation anisotropy in the nematic phase of the enigmatic iron-based superconductor FeSe, whose origin remains controversial. We apply an itinerant model previously used to describe the spin-excitation anisotropy as measured by neutron scattering measurements, with magnetic fluctuations included within the RPA approximation. The calculated RIXS cross section exhibits overall agreement with the RIXS data, including the high energy spin-excitation anisotropy.

74 ATOMIC AND MOLECULAR PHYSICS↗

Lattice-shifted nematic quantum critical point in FeSe 1-x S x

We report the evolution of nematic fluctuations in FeSe 1-x S x single crystals as a function of Sulfur content x across the nematic quantum critical point (QCP) x c ~ 0.17 via Raman scattering. The Raman spectra in the B1g nematic channel consist of two components, but only the low energy one displays clear fingerprints of critical behavior and is attributed to itinerant carriers. Curie–Weiss analysis of the associated nematic susceptibility indicates a substantial effect of nemato-elastic coupling, which shifts the location of the nematic QCP. We argue that this lattice-induced shift likely explains the absence of any enhancement of the superconducting transition temperature at the QCP. The presence of two components in the nematic fluctuations spectrum is attributed to the dual aspect of electronic degrees of freedom in Hund’s metals, with both itinerant carriers and local moments contributing to the nematic susceptibility.

36 MATERIALS SCIENCE↗

Spontaneous orbital polarization in the nematic phase of FeSe

The origin of nematicity in FeSe remains a critical outstanding question towards understanding unconventional superconductivity in proximity to nematic order. To understand what drives the nematicity, it is essential to determine which electronic degree of freedom admits a spontaneous order parameter independent from the structural distortion. In this work, we use X-ray linear dichroism at the Fe K pre-edge to measure the anisotropy of the 3d orbital occupation as a function of in situ applied stress and temperature across the nematic transition. Along with using X-ray diffraction to precisely quantify the strain state, we reveal a lattice-independent, spontaneously ordered orbital polarization within the nematic phase, as well as an orbital polarizability that diverges as the transition is approached from above. These results provide strong evidence that spontaneous orbital polarization serves as the primary order parameter of the nematic phase.

36 MATERIALS SCIENCE↗

Atomic-scale frustrated Josephson coupling and multicondensate visualization in FeSe

In a Josephson junction involving multiband superconductors, competition between interband and interjunction Josephson couplings gives rise to frustration and spatial disjunction of superfluid densities among superconducting condensates. Such frustrated coupling manifests as the quantum interference of Josephson currents from different tunnelling channels and becomes tunable if channel transparency can be varied. To explore these unconventional effects in the prototypical s ± -wave superconductor FeSe, we use atomic-resolution scanned Josephson tunnelling microscopy for condensate-resolved imaging and junction tuning—capabilities unattainable in macroscopic Josephson devices with fixed characteristics. We quantitatively demonstrate frustrated Josephson tunnelling by examining two tunnelling inequalities. The relative transparency of two parallel tunnelling pathways is found tunable, revealing a tendency towards a 0–π transition with decreasing scanned Josephson tunnelling microscopy junction resistance. Here, the simultaneous visualization of both superconducting condensates reveals anticorrelated superfluid modulations, highlighting the role of interband scattering. Our study establishes scanned Josephson tunnelling microscopy as a powerful tool enabling new research frontiers of multicondensate superconductivity.

Scanning probe microscopy↗

Majorana zero modes in a heterogeneous structure of topological and trivial domains in FeSe 1−𝑥 ⁢Te 𝑥

Here, we propose that the existence of vortices in FeSe 1−𝑥 ⁢Te 𝑥 with and without Majorana zero modes (MZMs) can be explained by a heterogeneous mixture of strong topological and trivial superconducting domains, with only vortices in the former exhibiting MZMs. We identify the spectroscopic signatures of topological and trivial vortices and show that they are necessarily separated by a domain wall harboring Majorana edge modes. We demonstrate that when a vortex is moved from a trivial to a topological domain in real time, a domain wall Majorana edge mode is transferred to the vortex as an MZM.

Majorana bound states↗

Specific heat and gap structure of a nematic superconductor: Application to FeSe

We report the results of our in-depth analysis of spectroscopic and thermodynamic properties of a multiorbital metal, like FeSe, which first develops a nematic order and then undergoes a transition into a superconducting state, which coexists with nematicity. We analyze the angular dependence of the gap function and specific heat C v (T) of such a nematic superconductor. We specifically address three issues: (i) the angular dependence of the gap in light of the competition between the nematicity-induced s - d mixture and the orbital transmutation of low-energy excitations in the nematic state, (ii) the effect of nematicity on the magnitude of the jump of the specific heat C v (T) at T c and the temperature dependence of C v (T) below T c , and (iii) a potential transition at T c1 < T c from an s + d state to an s + e iη d state that breaks time-reversal symmetry. We consider two scenarios for a nematic order: scenario A, in which this order develops between d xz and d yz orbitals on hole and electron pockets, and scenario B, in which there is an additional component of the nematic order for d xy fermions on the two electron pockets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quasiparticle coherence in the nematic state of FeSe

We report electronic nematicity is a ubiquitous phenomenon in iron-based superconductors but its origin is still debated. Most models consider either spin or orbital degrees of freedom as the driving force but typically do not take electronic correlations into account. However, mass enhancements, coherent-incoherent crossovers, and the strong orbital differentiation can only be understood using correlations in a Hund's metal framework. Here, we study the influence of nematicity on the quasiparticle coherence in detwinned FeSe using angle-resolved photoemission spectroscopy (ARPES). We compare photoemission spectral weight from d xz and d yz orbitals in the coherent quasiparticle peak and in the incoherent Hubbard band and find an anisotropy between the two orbitals. We interpret our observation in terms of a more coherent d xz orbital compared to the d yz orbital inside the nematic phase. This result is in contrast to earlier predictions of an incoherent d xz orbital and highlights the importance of electronic correlations in the description of nematicity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Moessbauer study in thin films of FeSi2 and FeSe systems

Thin films of FeSi2 and FeSe were studied using Moessbauer spectroscopy information regarding dangling bond configuration and nature of crystal structure in thin films was derived. A significant influence of crystalline aluminum substrate on film structure was observed.

Escue, W. J.↗