Fe-based High-temperature Superconductors Research Articles

Rotation of the dislocation grid in multilayer FeSe films and visualization of electronic nematic domains via orbital-selective tunneling

Understanding the interplay of structural and electronic symmetry breaking in Fe-based high temperature superconductors remains of high interest. In this work we grow strain-patterned multilayer FeSe thin films in a range of thicknesses using molecular beam epitaxy. We study the formation of electronic nematic domains and spatially-varying strain using scanning tunneling microscopy and spectroscopy. We directly visualize the formation of edge dislocations that give rise to a two-dimensional edge dislocation network in the films. Interestingly, we observe a 45 degree in-plane rotation of the dislocation network as a function of film thickness, yielding antisymmetric strain along different directions. This results in different coupling ratios between electronic nematic domains and antisymmetric strain. Lastly, we are able to distinguish between different orthogonal nematic domains by revealing a small energy-dependent difference in differential conductance maps between the two regions. This could be explained by orbital-selective tip-sample tunneling. Our observations bring new insights into the dislocation network formation in epitaxial thin films and provide another nanoscale tool to explore electronic nematicity in Fe-based superconductors.

Spectroscopic evidence for the direct involvement of local moments in the pairing process of the heavy-fermion superconductor CeCoIn5

The microscopic mechanism for electron pairing in heavy-fermion superconductors remains a major challenge in quantum materials. Some form of magnetic mediation is widely accepted with spin fluctuations as a prime candidate. A novel mechanism, 'composite pairing' based on the cooperative two-channel Kondo effect directly involving the f-electron moments has also been proposed for some heavy fermion compounds including CeCoIn$_5$. The origin of the spin resonance peak observed in neutron scattering measurements on CeCoIn$_5$ is still controversial and the corresponding hump-dip structure in the tunneling conductance is missing. This is in contrast to the cuprate and Fe-based high-temperature superconductors, where both characteristic signatures are observed, indicating spin fluctuations are likely involved in the pairing process. Here, we report results from planar tunneling spectroscopy along three major crystallographic orientations of CeCoIn5 over wide ranges of temperature and magnetic field. The pairing gap opens at T$_p$ ~ 5 K, well above the bulk T$_c$ = 2.3 K, and its directional dependence is consistent with d$_{x^2-y^2}$ symmetry. With increasing magnetic field, this pairing gap is suppressed as expected but, intriguingly, a gaplike structure emerges smoothly, increasing linearly up to the highest field applied. This field-induced gaplike feature is only observed below T$_p$. The concomitant appearance of the pairing gap and the field-induced gaplike feature, along with its linear increase with field, indicates that the f-electron local moments are directly involved in the pairing process in CeCoIn$_5$.

Deep learning model for finding new superconductors

Exploration of new superconductors still relies on the experience and intuition of experts, and is largely a process of experimental trial and error. In one study, only 3% of the candidate materials showed superconductivity [Hosono et al., Sci. Technol. Adv. Mater. 16, (2015)]. Here, we report a deep learning model for finding new superconductors. We introduced the method named ``reading periodic table'' that represented the periodic table in a way that allows deep learning to learn to read the periodic table and to learn the law of elements for the purpose of discovering novel superconductors which are outside the training data. It is recognized that it is difficult for deep learning to predict something outside the training data. Although we used only the chemical composition of materials as information, we obtained an ${R}^{2}$ value of 0.92 for predicting ${T}_{\text{c}}$ for materials in a database of superconductors. We also introduced the method named ``garbage-in'' to create synthetic data of nonsuperconductors that do not exist. Nonsuperconductors are not reported, but the data must be required for deep learning to distinguish between superconductors and nonsuperconductors. We obtained three remarkable results. The deep learning can predict superconductivity for a material with a precision of 62%, which shows the usefulness of the model; it found the recently discovered superconductor ${\mathrm{CaBi}}_{2}$ and another one ${\mathrm{Hf}}_{0.5}{\mathrm{Nb}}_{0.2}{\mathrm{V}}_{2}{\mathrm{Zr}}_{0.3}$, neither of which is in the superconductor database; and it found Fe-based high-temperature superconductors (discovered in 2008) from the training data before 2008. These results open the way for the discovery of new high-temperature superconductor families. The candidate materials list, data, and method are openly available on the Internet.

A brief review on μSR studies of unconventional Fe- and Cr-based superconductors

Muon spin relaxation/rotation (muSR) is a vital technique for probing the superconducting gap structure, pairing symmetry and time reversal symmetry breaking, enabling an understanding of the mechanisms behind the unconventional superconductivity of cuprates and Fe-based high-temperature superconductors, which remain a puzzle. Very recently double layered Fe-based super-conductors having quasi-2D crystal structures and Cr-based superconductors with a quasi-1D structure have drawn considerable attention. Here we present a brief review of the characteristics of a few selected Fe- and Cr-based superconducting materials and highlight some of the major outstanding problems, with an emphasis on the superconducting pairing symmetries of these materials. We focus on muSR studies of the newly discovered superconductors ACa2Fe4As4F2(A = K, Rb, and Cs), ThFeAsN, and A2Cr3As3(A = K, Cs), which were used to determine the superconducting gap structures, the presence of spin fluctuations, and to search for time reversal symmetry breaking in the superconducting states. We also briefly discuss the results of muSR investigations of the superconductivity in hole and electron doped BaFe2As2.

Momentum distribution and non-Fermi-liquid behavior in low-doped two-orbital model: Finite-size cluster quantum Monte Carlo approach

The two-dimensional two-orbital Hubbard model is studied with the use of finite-size cluster worldline quantum Monte Carlo algorithm. This model is widely used for simulation of the band structure of FeAs clusters, which are structure elements of Fe-based high-temperature superconductors. The choice of a special basis set of hyper-sites allowed to take into account four-fermion operator terms and to overcome partly the sign problem. Spectral functions and the density of states for various parameters of the model are obtained in the undoped and low-doped regimes. The correlated distortion of the spectral density with the change of doping is observed, and the applicability of the "hard-band" approximation in the doped regime is demonstrated. Profiles of the momentum distribution are obtained for the first Brillouin zone; they have pronounced jump near the Fermi level, which decreases with the growth of the strength of the interaction. The invariance of the Fermi surface with respect to the strength of the interaction is testified. Nesting is found in the case of electron and hole doping. Fermi-liquid parameters of the model are derived. Z-factor grows sharply with the increasing the level of doping, and monotonously decreases with the growth of the strength of the interaction. Moreover, electron-hole doping asymmetry of the Z-factor is revealed. The non-Fermi liquid behaviour and the deviation from Luttinger theorem are observed.

Lattice distortion and stripelike antiferromagnetic order inCa10(Pt3As8)(Fe2As2)5

Ca10(Pt3As8)(Fe2As2)5 is the parent compound for a class of Fe-based high-temperature superconductors where superconductivity with transition temperatures up to 30 K can be introduced by partial element substitution. We present a combined high-resolution high-energy x-ray diffraction and elastic neutron scattering study on a Ca10(Pt3As8)(Fe2As2)5 single crystal. This study reveals the microscopic nature of two distinct and continuous phase transitions to be very similar to other Fe-based high-temperature superconductors: an orthorhombic distortion of the high-temperature tetragonal Fe-As lattice below T_S = 110(2) K followed by stripe-like antiferromagnetic ordering of the Fe moments below T_N = 96(2) K. These findings demonstrate that major features of the Fe-based high-temperature superconductors are very robust against variations in chemical constitution as well as structural imperfection of the layers separating the Fe-As layers from each other and confirms that the Fe-As layers primarily determine the physics in this class of material.

First-principles Wannier function analysis of the electronic structure of PdTe: weaker magnetism and superconductivity

We report a first-principles Wannier function study of the electronic structure of PdTe. Its electronic structure is found to be a broad three-dimensional Fermi surface with highly reduced correlation effects. In addition, the higher filling of the Pd d-shell, its stronger covalency resulting from the closer energy of the Pd d and Te p shells, and the larger crystal field effects of the Pd ion due to its near octahedral coordination, all serve to weaken significantly electronic correlations in the particle–hole (spin, charge, and orbital) channel. In comparison to the Fe chalcogenides, e.g. FeSe, we highlight the essential features (quasi-two-dimensionality, proximity to half-filling, weaker covalency, and higher orbital degeneracy) of Fe-based high-temperature superconductors.

What have we learned from high-pressure experiments on Cu-oxide and Fe-based superconductors?

High-pressure experiments have made many important contributions to the field of superconductivity, including studies on the Cu-oxide and Fe-based high-temperature superconductors (HTS). However, for detailed quantitative understanding, the nature of the high-pressure environment acting on the sample must be well defined, a requirement often not met. Since HTS are quasi-2D, all properties are anisotropic. As a result, only a combination of fully hydrostatic and uniaxial pressure experiments are capable of providing the detailed information required. Unfortunately, very few such experiments have been carried out. For both Cu-oxide and Fe-based HTS at optimal doping, Tc is found to be enhanced by either increasing the separation of the superconducting planes or decreasing their area. Future experiments will extend such hydrostatic/uniaxial studies over the entire doping range.

Phase diagram and electronic indication of high-temperature superconductivity at 65 K in single-layer FeSe films

Superconductivity in the cuprate superconductors and the Fe-based superconductors is realized by doping the parent compound with charge carriers, or by application of high pressure, to suppress the antiferromagnetic state. Such a rich phase diagram is important in understanding superconductivity mechanism and other physics in the Cu- and Fe-based high temperature superconductors. In this paper, we report a phase diagram in the single-layer FeSe films grown on SrTiO3 substrate by an annealing procedure to tune the charge carrier concentration over a wide range. A dramatic change of the band structure and Fermi surface is observed, with two distinct phases identified that are competing during the annealing process. Superconductivity with a record high transition temperature (Tc) at ~65 K is realized by optimizing the annealing process. The wide tunability of the system across different phases, and its high-Tc, make the single-layer FeSe film ideal not only to investigate the superconductivity physics and mechanism, but also to study novel quantum phenomena and for potential applications.

Possible nature of ground state of HTSC

A qualitative model describing the ground state and the mechanism of superconducting pairing in Cu- and Fe-based high-temperature superconductors (HTSCs) is suggested. In this model, doping by localized charges is supposed to be responsible for the closing of the gap between the occupied anionic band and unoccupied states of the cation band and for the formation of the electron-excitonic band of unusual nature.

Angle-resolved photoemission studies of the superconducting gap symmetry in Fe-based superconductors

The superconducting gap is the fundamental parameter that characterizes the superconducting state, and its symmetry is a direct consequence of the mechanism responsible for Cooper pairing. Here we discuss about angle-resolved photoemission spectroscopy measurements of the superconducting gap in the Fe-based high-temperature superconductors. We show that the superconducting gap is Fermi surface dependent and nodeless with small anisotropy, or more precisely, a function of the momentum location in the Brillouin zone. We show that while this observation seems inconsistent with weak coupling approaches for superconductivity in these materials, it is well supported by strong coupling models and global superconducting gaps. We also suggest that a smaller lifetime of the superconducting Cooper pairs induced by the momentum dependent interband scattering inherent to these materials could affect the residual density of states at low energies, which is critical for a proper evaluation of the superconducting gap.

How chemical pressure affects the fundamental properties of rare-earth pnictides: An ARPES view

Angle-resolved photoelectron spectroscopy, supplemented by theoretical calculations has been applied to study the electronic structure of heavy-fermion material CeFePO, a homologue to the Fe-based high-temperature superconductors, and CeFeAs${}_{0.7}$P${}_{0.3}$O, where the applied chemical pressure results in a ferromagnetic order of the 4$f$ moments. A comparative analysis reveals characteristic differences in the Fe-derived band structure for these materials, implying a rather different hybridization of valence electrons to the localized 4$f$ orbitals. In particular, our results suggest that the ferromagnetism of Ce moments in CeFeAs${}_{0.7}$P${}_{0.3}$O is mediated mainly by Fe 3${d}_{xz/yz}$ orbitals, while the Kondo screening in CeFePO is instead due to a strong interaction of Fe 3${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbitals.

Model for the Electron Structure of Cu- and Fe-Based High-Temperature Superconductors

A qualitative model describing the ground state and the mechanism of superconducting pairing in Cu- and Fe-based high-temperature superconductors (HTSCs) is suggested.

Iron based superconductors: Pnictides versus chalcogenides

We present a brief review of the present day situation with studies of high-temperature superconductivity in iron pnictides and chalcogenides. Recent discovery of superconductivity with Tc>30K in AxFe2−x/2Se2 (A=K, Cs, Tl, etc) represents the major new step in the development of new concepts in the physics of Fe-based high-temperature superconductors. We compare LDA and ARPES data on the band structure and Fermi surfaces of novel superconductors and those of the previously studied FeAs superconductors, especially isostructural 122-superconductors like BaFe2As2. It appears that electronic structure of new superconductors is rather different from that of FeAs 122-systems. In particular, no nesting properties of electron and hole-like Fermi surfaces is observed, casting doubts on most popular theoretical schemes of Cooper pairing for these systems. Doping of novel materials is extremely important as a number of topological transitions of Fermi surface near the Γ point in the Brillouin zone are observed for different doping levels. The discovery of Fe vacancies ordering and antiferromagnetic (AFM) ordering at pretty high temperatures (TN>500K), much exceeding superconducting Tc makes these systems unique antiferromagnetic superconductors with highest TN observed up to now. This poses very difficult problems for theoretical understanding of superconductivity. We discuss the role of both vacancies and AFM ordering in transformations of band structure and Fermi surfaces, as well as their importance for superconductivity. In particular, we show that system remains metallic with unfolded Fermi surfaces quite similar to that in paramagnetic state. Superconducting transition temperature Tc of new superconductors is discussed within the general picture of superconductivity in multiple band systems. It is demonstrated that both in FeAs-superconductors and in new FeSe-systems the value of Tc correlates with the value of the total density of states (DOSs) at the Fermi level.

One-Fe versus Two-Fe Brillouin Zone of Fe-Based Superconductors: Creation of the Electron Pockets by Translational Symmetry Breaking

We investigate the physical effects of translational symmetry breaking in Fe-based high-temperature superconductors due to alternating anion positions. In the representative parent compounds, including the newly discovered Fe-vacancy-ordered K(0.8)Fe(1.6)Se(2), an unusual change of orbital character is found across the one-Fe Brillouin zone upon unfolding the first-principles band structure and Fermi surfaces, suggesting that covering a larger one-Fe Brillouin zone is necessary in experiments. Most significantly, the electron pockets (critical to the magnetism and superconductivity) are found only created with broken symmetry, advocating strongly its full inclusion in future studies, particularly on the debated nodal structures of the superconducting order parameter.

Magnetic ordering in tetragonal FeS: Evidence for strong itinerant spin fluctuations

Mackinawite is a naturally-occurring layer type FeS mineral well-known to be important in biogeochemical cycles and, more recently, to the development of microbial fuel cells. Conflicting results have been published as to the magnetic properties of this mineral, with M\"ossbauer spectroscopy indicating no magnetic ordering and density functional theory predicting an antiferromagnetic ground state, similar to the Fe-based high-temperature superconductors with which it is isostructural and for which it is known that magnetism is suppressed by strong itinerant spin fluctuations. We investigated this latter possibility for mackinawite using photoemission spectroscopy (PES), near-edge X-ray absorption fine structure spectroscopy (XAS), and density functional theory (DFT) computations. Our Fe 3s core-level PES spectrum of mackinawite showed a clear exchange-energy splitting (2.9 eV) consistent with a 1 {\mu}B magnetic moment on the Fe ions, while the Fe L-edge XAS spectrum indicated rather delocalized Fe 3d electrons in mackinawite similar to those in Fe metal. DFT computations demonstrated that the ground state of mackinawite is single-stripe antiferromagnetic, with an Fe magnetic moment (2.7 {\mu}B) that is significantly larger than the experimental estimate and has a strong dependence on the S height and lattice parameters. All of these trends signal the existence of strong itinerant spin fluctuations.If strong spin fluctuations prove to be the mediators of electron pairing in these Fe-based superconductors, we conjecture that mackinawite may be one of the simplest Fe-based superconductors.

Intrinsic and structural isotope effects in iron-based superconductors

The currently available results of the isotope effect on the superconducting transition temperature T_c in Fe-based high-temperature superconductors (HTS) are highly controversial. The values of the Fe isotope effect (Fe-IE) exponent \alpha_Fe for various families of Fe-based HTS were found to be as well positive, as negative, or even be exceedingly larger than the BCS value \alpha_BCS=0.5. Here we demonstrate that the Fe isotope substitution causes small structural modifications which, in turn, affect T_c. Upon correcting the isotope effect exponent for these structural effects, an almost unique value of \alpha~0.35-0.4 is observed for at least three different families of Fe-based HTS.

Sign reversal of the order parameter near s ±-superconductor surface

The superconducting order parameter and LDOS spectra near an impenetrable surface are studied on the basis of self-consistent calculations for a two band superconductor with nodeless extended s-wave order parameter symmetry, as possibly realized in Fe-based high-temperature superconductors. It is found that for a wide range of parameters the spatial behavior of the order parameter at a surface is not reduced to a trivial suppression. If the interband scattering at a surface is of the order of the intraband one or dominates it, it can be energetically favorable to change the symmetry of the superconducting state near the surface from s ± to conventional s-wave. The range of existing of this surface conventional superconductivity is very sensitive to the relative values of interband and intraband pairing potentials. It is shown that the LDOS spectra near the surface can qualitatively differ upon calculating with and without taking into account the self-consistency of the order parameter.

Nematic Fermi Fluids in Condensed Matter Physics

Correlated electron fluids can exhibit a startling array of complex phases, among which one of the more surprising is the electron nematic, a translationally invariant metallic phase with a spontaneously generated spatial anisotropy. Classical nematics generally occur in liquids of rod-like molecules; given that electrons are point like, the initial theoretical motivation for contemplating electron nematics came from thinking of the electron fluid as a quantum melted electron crystal, rather than a strongly interacting descendent of a Fermi gas. Dramatic transport experiments in ultra-clean quantum Hall systems in 1999 and in Sr3Ru2O7in a strong magnetic field in 2007 established that such phases exist in nature. In this article, we briefly review the theoretical considerations governing nematic order, summarize the quantum Hall and Sr3Ru2O7experiments that unambiguously establish the existence of this phase, and survey some of the current evidence for such a phase in the cuprate and Fe-based high temperature superconductors.

Itinerant antiferromagnetism inBaCr2As2: Experimental characterization and electronic structure calculations

We report single-crystal synthesis, specific-heat and resistivity measurements and electronic structure calculations for ${\text{BaCr}}_{2}{\text{As}}_{2}$. This material is a metal with itinerant antiferromagnetism, similar to the parent phases of Fe-based high-temperature superconductors, but differs in magnetic order. Comparison of bare band-structure density of states and the low-temperature specific heat implies a mass renormalization of $\ensuremath{\sim}2$. ${\text{BaCr}}_{2}{\text{As}}_{2}$ shows stronger transition-metal--pnictogen covalency than the Fe compounds, and in this respect is more similar to ${\text{BaMn}}_{2}{\text{As}}_{2}$. This provides an explanation for the observation that Ni and Co doping is effective in the Fe-based superconductors, but Cr or Mn doping is not.