Iron-based Superconductor FeSe Research Articles

Picosecond Trajectory of Two-Dimensional Vortex Motion in FeSe_{0.5}Te_{0.5} Visualized by Terahertz Second Harmonic Generation.

We have investigated the vortex dynamics in a thin film of an iron-based superconductor FeSe_{0.5}Te_{0.5} by observing second-harmonic generation (SHG) in the terahertz frequency range. We visualized the picosecond trajectory of two-dimensional vortex motion in a pinning potential tilted by Meissner shielding current. The SHG perpendicular to the driving field is observed, corresponding to the nonreciprocal nonlinear Hall effect under the current-induced inversion symmetry breaking, whereas the linear Hall effect is negligible. The estimated vortex mass, as light as a bare electron, suggests that the vortex core moves independently from quasiparticles at such a high frequency and large velocity ≈300 km/s.

Orbital-Selective Mott Transition Effects and Nontrivial Topology of Iron Chalcogenide.

The iron-based superconductor FeSe_{1-x}Te_{x} has recently gained significant attention as a host of two distinct physical phenomena: (i)Majorana zero modes that can serve as potential topologically protected qubits, and (ii)a realization of the orbital-selective Mott transition. In this Letter, we connect these two phenomena and provide new insights into the interplay between strong electronic correlations and nontrivial topology in FeSe_{1-x}Te_{x}. Using linearized quasiparticle self-consistent GW plus dynamical mean-field theory, we show that the topologically protected Dirac surface state has substantial Fe(d_{xy}) character. The proximity to the orbital-selective Mott transition plays a dual role: it facilitates the appearance of the topological surface state by bringing the Dirac cone close to the chemical potential but destroys the Z_{2} topological superconductivity when the system is too close to the orbital-selective Mott phase. We derive a reduced effective Hamiltonian that describes the topological band. Its parameters capture all the chemical trends found in the first principles calculation. Our findings provide a framework for further study of the interplay between strong electronic correlations and nontrivial topology in other iron-based superconductors.

Pure nematic state in the iron-based superconductor FeSe

Pure nematic state in the iron-based superconductor FeSe

Anomalous Shiba states in topological iron-based superconductors

We demonstrate the formation of robust zero energy modes close to magnetic impurities in the iron-based superconductor FeSe$_{1-x}$Te$_x$. We find that the Zeeman field generated by the impurity favors a spin-triplet inter-orbital pairing as opposed to the spin-singlet intra-orbital pairing prevalent in the bulk. The preferred spin-triplet pairing preserves time-reversal symmetry and is topological, as robust, topologically-protected zero modes emerge at the boundary between regions with different pairing states. Moreover, the zero modes form Kramers doublets that are insensitive to the direction of the spin polarization or to the separation between impurities. We argue that our theoretical results are consistent with recent experimental measurements on FeSe$_{1-x}$Te$_x$.

Vortex lattice melting line in superconductors with paramagnetic pair breaking

Recent experiments on the iron-based superconductor FeSe in a high magnetic field have suggested the presence of both the fluctuation-induced vortex liquid regime and a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice. To get a general picture of the magnetic phase diagram in type II superconductors with strong superconducting (SC) fluctuation and strong paramagnetic pair breaking (PPB) such as FeSe, the vortex lattice melting curve ${H}_{m}(T)$ is theoretically investigated in situations where a FFLO state is expected to occur. In general, PPB tends to narrow the vortex liquid regime intervening between ${H}_{c2}(T)$ and ${H}_{m}(T)$. In particular, the vortex liquid regime is found to rapidly shrink upon entering; by cooling, the temperature range in which the FFLO state with a periodic modulation parallel to the magnetic field is stable in mean-field theory. Based on the present results, the high-field SC phase diagrams of FeSe in the parallel and perpendicular field configurations are discussed.

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.

New layered chalcogenides (Na0.5OH)Fe0.5Cu0.5X (X = Se, S): Synthesis, structure, magnetic and electrochemical properties

Two new layered chalcogenides (Na0.5OH)Fe0.5Cu0.5X (X = Se, S) have been successfully synthesized via a combination of solid-state reaction and hydrothermal ion-exchange method. They crystallize in a tetragonal space group P4/nmm and represent the very rare examples isostructural to the iron-based superconductor (Li1−xFexOH)FeSe, with (Na0.5OH) layers intercalated between adjacent Fe0.5Cu0.5X layers. Magnetization and electrical measurements suggest that the title compounds exhibit spin-glass and semiconducting properties rather than superconductivity. This is mainly attributed to the random distribution of Fe and Cu in the tetrahedral sites. Preliminary electrochemical test indicates that (Na0.5OH)Fe0.5Cu0.5S can be a good electrode material for lithium-ion batteries, especially when carbon nanotubes are incorporated (discharge capacity of 745 mAh g−1 at 0.2 A g−1, capacity retention of 49.1% after 50 cycles and rate capacity of 120 mAh g−1 at 5 A g−1). These results not only provide an efficient strategy to synthesize new intercalated chalcogenides but also demonstrate their potential applications in lithium-ion batteries.

Signatures of a Quantum Griffiths Phase Close to an Electronic Nematic Quantum Phase Transition.

In the vicinity of a quantum critical point, quenched disorder can lead to a quantum Griffiths phase, accompanied by an exotic power-law scaling with a continuously varying dynamical exponent that diverges in the zero-temperature limit. Here, we investigate a nematic quantum critical point in the iron-based superconductor FeSe_{0.89}S_{0.11} using applied hydrostatic pressure. We report an unusual crossing of the magnetoresistivity isotherms in the nonsuperconducting normal state that features a continuously varying dynamical exponent over a large temperature range. We interpret our results in terms of a quantum Griffiths phase caused by nematic islands that result from the local distribution of Se and S atoms. At low temperatures, the Griffiths phase is masked by the emergence of a Fermi liquid phase due to a strong nematoelastic coupling and a Lifshitz transition that changes the topology of the Fermi surface.

Interorbital nematicity and the origin of a single electron Fermi pocket in FeSe

The electronic structure of the enigmatic iron-based superconductor FeSe has puzzled researchers since spectroscopic probes failed to observe the expected electron pocket at the $Y$ point in the 1-Fe Brillouin zone. It has been speculated that this pocket, essential for an understanding of the superconducting state, is either absent or incoherent. Here, we perform a theoretical study of the preferred nematic order originating from nearest-neighbor Coulomb interactions in an electronic model relevant for FeSe. We find that at low temperatures the dominating nematic components are of interorbital ${d}_{xz}\text{\ensuremath{-}}{d}_{xy}$ and ${d}_{yz}\text{\ensuremath{-}}{d}_{xy}$ character, with spontaneously broken amplitudes for these two components. This interorbital nematic order naturally leads to distinct hybridization gaps at the $X$ and $Y$ points of the 1-Fe Brillouin zone, and may thereby produce highly anisotropic Fermi surfaces with only a single electron pocket at one of these momentum-space locations. The associated superconducting gap structure obtained with the generated low-energy electronic band structure from spin-fluctuation mediated pairing agrees well with that measured experimentally. Finally, from a comparison of the computed spin susceptibility to available neutron scattering data, we discuss the necessity of additional self-energy effects, and explore the role of orbital-dependent quasiparticle weights as a minimal means to include them.

Theoretical study on the magnetic properties of the superconductor FeSe

Identifying the form of superconducting order parameter is still a controversial problem for the iron-based superconductor FeSe. Based on anisotropic two-component Ginzburg–Landau theory, we study the temperature dependence of upper critical field and London penetration depth for FeSe. Without including the spin paramagnetic effect, all of our theoretical calculations fit the experimental data well in a broad temperature range. Our results thus show that FeSe is a two-gap s-wave superconductor. And the anisotropy of effective masses in the band with larger (or smaller) gap can be estimated as about 10 (or 2) respectively.

Spectroscopic Evidence for an Additional Symmetry Breaking in the Nematic State of FeSe Superconductor

The iron-based superconductor FeSe has attracted much recent attention because of its simple crystal structure, distinct electronic structure and rich physics exhibited by itself and its derivatives. Determination of its intrinsic electronic structure is crucial to understand its physical properties and superconductivity mechanism. Both theoretical and experimental studies so far have provided a picture that FeSe consists of one hole-like Fermi surface around the Brillouin zone center in its nematic state. Here we report direct observation of two hole-like Fermi surface sheets around the Brillouin zone center, and the splitting of the associated bands, in the nematic state of FeSe by taking high resolution laser-based angle-resolved photoemission measurements. These results indicate that, in addition to nematic order and spin-orbit coupling, there is an additional order in FeSe that breaks either inversion or time reversal symmetries. The new Fermi surface topology asks for reexamination of the existing theoretical and experimental understanding of FeSe and stimulates further efforts to identify the origin of the hidden order in its nematic state.

Superconducting and flux pinning properties of FeSe<i><sub>x</sub></i>Te<sub>1–</sub><i><sub>x</sub></i> topological superconductors

Iron-based superconductor FeSe<i><sub>x</sub></i>Te<sub>1–</sub><i><sub>x</sub></i> has attracted attention because of its high upper critical field, low anisotropy, and high critical current density. Also, it is predicted to have nontrivial topological properties, so that it is a candidate of realizing Majorana fermion, when the superconductivity is combined with topological features. However, its flux pinning behavior and mechanism in superconducting state with varying Se/Te ratio have not been systematically studied . We use self-flux method to grow single crystal samples of FeSe<i><sub>x</sub></i>Te<sub>1–</sub><i><sub>x</sub></i> with different <i>x</i> values (0.3, 0.4, 0.5 and 0.6). The structural and morphological properties of the monocrystalline samples are characterized by XRD and SEM. All samples show that they possess the expected crystalline structures and their lattice parameters vary with <i>x</i> value. The magnetic properties at low temperatures are also measured, showing that all samples have good superconductivity. Superconducting properties, such as critical current densities and flux pinning force densities, are extracted from the magnetic measurements and analyzed, and the flux pinning behavior is discussed. The best Se:Te ratio is determined to be nearly 0.4/0.6 based on the comparison among these properties of different samples. By utilizing the Dew-Hughes theory and analyzing the pinning force density peak, the flux pinning mechanism in the best samples (<i>x</i> = 0.4, 0.5) can be regarded as the mixture of normal point pinning and Δ<i>κ</i><italic/> volume pinning. This work provides important information for the further study of the topological and superconducting properties of FeSe<i><sub>x</sub></i>Te<sub>1–</sub><i><sub>x</sub></i>.

Bulk Superconductivity and Role of Fluctuations in the Iron-Based Superconductor FeSe at High Pressures.

The iron-based superconductor FeSe offers a unique possibility to study the interplay of superconductivity with purely nematic as well magnetic-nematic order by pressure (p) tuning. By measuring specific heat under p up to 2.36GPa, we study the multiple phases in FeSe using a thermodynamic probe. We conclude that superconductivity is bulk across the entire p range and competes with magnetism. In addition, whenever magnetism is present, fluctuations exist over a wide temperature range above both the bulk superconducting and the magnetic transitions. Whereas the magnetic fluctuations are likely temporal, the superconducting fluctuations may be either temporal or spatial. These observations highlight similarities between FeSe and underdoped cuprate superconductors.

Observation of orbital ordering and origin of the nematic order in FeSe

In iron-based superconductors the interactions driving the nematic order that breaks the lattice four-fold rotational symmetry in the iron plane may also facilitate the Cooper pairing, but experimental determination of these interactions is challenging because the temperatures of the nematic order and the order of other electronic phases appear to match each other or to be close to each other. Here we performed field-dependent 77Se-nuclear magnetic resonance (NMR) measurements on single crystals of iron-based superconductor FeSe, with magnetic field B0 up to 16 T. The 77Se-NMR spectra and Knight shift split when the direction of B0 is away from the direction perpendicular to the iron planes (i.e. B0 ∥ c) upon cooling in temperature, with a significant change in the distribution and magnitude of the internal magnetic field at the 77Se nucleus, but these do not happen when B0 is perpendicular to the iron planes, thus demonstrating that there is an orbital ordering. Moreover, stripe-type antiferromagnetism is absent, while giant antiferromagnetic spin fluctuations measured by the NMR spin-lattice relaxation gradually developed starting at ∼40 K, which is far below the nematic order temperature Tnem = 89 K. These results provide direct evidence of orbital-driven nematic order in FeSe.

Photoinduced possible superconducting state with long-lived disproportionate band filling in FeSe

Photoexcitation is a very powerful way to instantaneously drive a material into a novel quantum state without any fabrication, and variable ultrafast techniques have been developed to observe how electron, lattice, and spin degrees of freedom change. One of the most spectacular phenomena is photoinduced superconductivity, and it has been suggested in cuprates that the transition temperature Tc can be enhanced from the original Tc with significant lattice modulations. Here, we show a possibility for another photoinduced high-Tc superconducting state in the iron-based superconductor FeSe. The transient electronic state over the entire Brillouin zone is directly observed by time- and angle-resolved photoemission spectroscopy using extreme ultraviolet pulses obtained from high harmonic generation. Our results of dynamical behaviors from 50 fs to 800 ps consistently support the favourable superconducting state after photoexcitation well above Tc. This finding demonstrates that multiband iron-based superconductors emerge as an alternative candidate for photoinduced superconductors.

Room temperature local nematicity in FeSe superconductor

We report pair distribution function measurements of the iron-based superconductor FeSe above and below the structural transition temperature. Structural analysis reveals a local orthorhombic distortion with a correlation length of about 4 nm at temperatures where an average tetragonal symmetry is observed. The analysis further demonstrates that the local distortion is larger than the distortion at temperatures where the average observed symmetry is orthorhombic. Our results suggest that the low-temperature macroscopic nematic state in FeSe forms from an imperfect ordering of orbital-degeneracy-lifted nematic fluctuations which persist up to at least 300 K.

Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te).

Majorana quasiparticles in condensed matter are important for topological quantum computing1-3, but remain elusive. Vortex cores of topological superconductors may accommodate Majorana quasiparticles that appear as the Majorana bound state (MBS) at zero energy4,5. The iron-based superconductor Fe(Se,Te) possesses a superconducting topological surface state6-9 that was investigated by scanning tunnelling microscopy (STM) studies, which suggest such a zero-energy vortex bound state (ZVBS)10,11. Here we present ultrahigh energy-resolution spectroscopic imaging (SI)-STM to clarify the nature of the vortex bound states in Fe(Se,Te). We found the ZVBS at 0 ± 20 μeV, which constrained its MBS origin, and showed that some vortices host the ZVBS but others do not. We show that the fraction of vortices hosting the ZVBS decreases with increasing magnetic field and that local quenched disorders are not related to the ZVBS. Our observations elucidate the necessary conditions to realize the ZVBS, which paves the way towards controllable Majorana quasiparticles.

Unusual effects of Be doping in the iron-based superconductor FeSe

Recent superconducting transition temperatures (Tc) over 100 K for monolayer FeSe on SrTiO3 have renewed interest in the bulk parent compound. In KCl:AlCl3 flux-transport-grown crystals of FeSe0.94Be0.06, FeSe0.97Be0.03 and, for comparison, FeSe, this work reports doping of FeSe using Be—among the smallest of possible dopants, corresponding to an effective ‘chemical pressure’. According to lattice parameter measurements, 6% Be doping shrank the tetragonal FeSe lattice equivalent to a physical pressure of 0.75 GPa. Using this flux-transport method of sample preparation, 6% of Be was the maximum amount of dopant achievable. At this maximal composition of FeSe0.94Be0.06, the lattice unit cell shrinks by 2.4%, Tc—measured in the bulk via specific heat—increases by almost 10%, the Tc versus pressure behavior shifts its peak downwards by ~1 GPa, the high temperature structural transition around TS = 89 K increases by 1.9 K (in contrast to other dopants in FeSe which uniformly depress TS), and the low temperature specific heat γ increases by 10% compared to pure FeSe. Also, upon doping by 6% Be the residual resistivity ratio, ρ(300 K)/ρ(T → 0), increases by almost a factor of four, while ρ(300 K)/ρ() increases by 50%.

Pseudogap Behavior of the Nuclear Spin–Lattice Relaxation Rate in FeSe Probed by 77Se-NMR

We conducted $^{77}$Se-nuclear magnetic resonance studies of the iron-based superconductor FeSe in magnetic fields of 0.6 to 19 T to investigate the superconducting and normal-state properties. The nuclear spin-lattice relaxation rate divided by the temperature $(T_1T)^{-1}$ increases below the structural transition temperature $T_\mathrm{s}$ but starts to be suppressed below $T^*$, well above the superconducting transition temperature $T_\mathrm{c}(H)$, resulting in a broad maximum of $(T_1T)^{-1}$ at $T_\mathrm{p}(H)$. This is similar to the pseudogap behavior in optimally doped cuprate superconductors. Because $T^*$ and $T_\mathrm{p}(H)$ decrease in the same manner as $T_\mathrm{c}(H)$ with increasing $H$, the pseudogap behavior in FeSe is ascribed to superconducting fluctuations, which presumably originate from the theoretically predicted preformed pair above $T_\mathrm{c}(H)$.

The ab initio study of unconventional superconductivity in CeCoIn5 and FeSe

The electronic structure and shape of the Fermi surface are known to be of fundamental importance for the superconducting instability in real materials. We demonstrate that such an instability may be explored by static Cooper pair susceptibility renormalized by pairing interaction and present an efficient method of its evaluation using Wannier orbitals derived from ab initio calculation. As an example, this approach is used to search for an unconventional superconducting phase of the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) type in a heavy-fermion compound CeCoIn5 and an iron-based superconductor FeSe. The results suggest that the FFLO superconducting phase occurs at finite magnetic field in both materials.