Order In FeSe Research Articles

Spin-dependent high-order topological states and corner modes in a monolayer FeSe/GdClO heterostructure

We propose that a spin-dependent second-order topological insulator can be realized in monolayer FeSe/GdClO heterostructure, in which substrate GdClO helps to stabilize and enhance the antiferromagnetic order in FeSe. The second-order topological insulator is free from spin-orbit coupling and in-plane magnetic field. We also find that there exist two types of distinct corner modes residing in intersections of two ferromagnetic edges and two antiferromagnetic edges, respectively. The underlying physics for ferromagnetic corner mode follows a sublattice-chirality-kink picture. More interestingly, ferromagnetic corner mode shows spin-dependent property, which is also robust against spin-orbit coupling. Unexpectedly, antiferromagnetic corner mode can be taken as a typical emergent and hierarchical phenomenon from an array of ferromagnetic corner modes. Remarkably, antiferromagnetic corner modes violate general kink picture and can be understood as bound states of a one-dimensional Schrodinger equation under a connected potential well. Our findings not only provide a promising second-order topological insulator in electronic materials, but uncover some new properties of corner modes in high-order topological insulator.

Observation of an electronic order along [110] direction in FeSe

Multiple ordered states have been observed in unconventional superconductors. Here, we apply scanning tunneling microscopy to probe the intrinsic ordered states in FeSe, the structurally simplest iron-based superconductor. Besides the well-known nematic order along [100] direction, we observe a checkerboard charge order in the iron lattice, which we name a [110] electronic order in FeSe. The [110] electronic order is robust at 77 K, accompanied with the rather weak [100] nematic order. At 4.5 K, The [100] nematic order is enhanced, while the [110] electronic order forms domains with reduced correlation length. In addition, the collective [110] order is gaped around [−40, 40] meV at 4.5 K. The observation of this exotic electronic order may shed new light on the origin of the ordered states in FeSe.

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.

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.

Ultrafast nematic-orbital excitation in FeSe

The electronic nematic phase is an unconventional state of matter that spontaneously breaks the rotational symmetry of electrons. In iron-pnictides/chalcogenides and cuprates, the nematic ordering and fluctuations have been suggested to have as-yet-unconfirmed roles in superconductivity. However, most studies have been conducted in thermal equilibrium, where the dynamical property and excitation can be masked by the coupling with the lattice. Here we use femtosecond optical pulse to perturb the electronic nematic order in FeSe. Through time-, energy-, momentum- and orbital-resolved photo-emission spectroscopy, we detect the ultrafast dynamics of electronic nematicity. In the strong-excitation regime, through the observation of Fermi surface anisotropy, we find a quick disappearance of the nematicity followed by a heavily-damped oscillation. This short-life nematicity oscillation is seemingly related to the imbalance of Fe 3dxz and dyz orbitals. These phenomena show critical behavior as a function of pump fluence. Our real-time observations reveal the nature of the electronic nematic excitation instantly decoupled from the underlying lattice.

Frustrated spin order and stripe fluctuations in FeSe

The charge and spin dynamics of the structurally simplest iron-based superconductor, FeSe, may hold the key to understanding the physics of high temperature superconductors in general. Unlike the iron pnictides, FeSe lacks long range magnetic order in spite of a similar structural transition around 90 K. Here, we report results of Raman scattering experiments as a function of temperature and polarization and simulations based on exact diagonalization of a frustrated spin model. Both experiment and theory find a persistent low energy peak close to 500 cm−1 in B1g symmetry, which softens slightly around 100 K, that we assign to spin excitations. By comparing with results from neutron scattering, this study provides evidence for nearly frustrated stripe order in FeSe.

Universal understanding of nematicity and magnetism in Fe-pnictides and FeSe

By employing the mean field and variational Monte Carlo methods, we investigate the iron-based superconductors (FeSCs) based on a realistic five-orbital Hubbard model in which an off-site Coulomb interaction is explicitly included. Our results demonstrate that plays an important role in stabilizing the nematic state in both Fe-pnictides and FeSe. Below a critical , the model is shown to lie in the striped antiferromagnetic ground state, and an increasing of leads to an energy degeneracy between different magnetic configurations. This finding provides a natural explanation for the magnetism in Fe-pnictides with relatively small , and more importantly, unveils the microscopic mechanism behind the absence of magnetic order in FeSe with larger . Simultaneously, the common anisotropy of and orbital occupations in different magnetic configurations accounts for the similar orbital ordering observed in Fe-pnictides and FeSe. In addition, the unusual smallness of the Fermi surfaces in FeSe can be obtained when the renormalization effect of on the band structure is taken into account.

Quantum Spin Liquid Intertwining Nematic and Superconducting Order in Fese.

Despite its seemingly simple composition and structure, the pairing mechanism of FeSe remains an open problem due to several striking phenomena. Among them are nematic order without magnetic order, nodeless gap and unusual inelastic neutron spectra with a broad continuum, and gap anisotropy consistent with orbital selection of unknown origin. Here we propose a microscopic description of a nematic quantum spin liquid that reproduces key features of neutron spectra. We then study how the spin fluctuations of the local moments lead to pairing within a spin-fermion model. We find the resulting superconducting order parameter to be nodeless s±d wave within each domain. Further we show that orbital dependent Kondo-like coupling can readily capture observed gap anisotropy. Our prediction calls for inelastic neutron scattering in a detwinned sample.

Orbital Selectivity Enhanced by Nematic Order in FeSe.

Motivated by the recent low-temperature experiments on bulk FeSe, we study the electron correlation effects in a multiorbital model for this compound in the nematic phase using the U(1) slave-spin theory. We find that a finite nematic order helps to stabilize an orbital selective Mott phase. Moreover, we propose that when the d- and s-wave bond nematic orders are combined with the ferro-orbital order, there exists a surprisingly large orbital selectivity between the xz and yz orbitals even though the associated band splitting is relatively small. Our results explain the seemingly unusual observation of strong orbital selectivity in the nematic phase of FeSe, uncover new clues on the nature of the nematic order, and set the stage to elucidate the interplay between superconductivity and nematicity in iron-based superconductors.

Orbital order in FeSe: The case for vertex renormalization

We study the structure of the d-wave orbital order in FeSe in light of recent STM and ARPES data, which detect the shapes of hole and electron pockets in the nematic phase. The geometry of the pockets indicates that the sign of the orbital order $\Gamma = \langle d^{\dagger}_{xz} d_{xz}- d^{\dagger}_{yz} d_{yz}\rangle$ is different between hole and electron pockets $(\Gamma_h$ and $\Gamma_e$). We argue that this sign change cannot be reproduced if one solves for the orbital order within mean-field approximation, as the mean-field analysis yields either no orbital order, or order with the same sign of $\Gamma_e$ and $\Gamma_h$. We argue that another solution with the opposite signs of $\Gamma_e$ and $\Gamma_h$ emerges if we include the renormalizations of the vertices in $d-$wave orbital channel. We show that the ratio $|\Gamma_e/\Gamma_h|$ is of order one, independent on the strength of the interaction. We also compute the temperature variation of the energy of $d_{xz}$ and $d_{yz}$ orbitals at the center of electron pockets and compare the results with ARPES data.

Magnetic tricritical point and nematicity in FeSe under pressure

Magnetism induced by external pressure ($p$) was studied in a FeSe crystal sample by means of muon-spin rotation. The magnetic transition changes from second-order to first-order for pressures exceeding the critical value $p_{{\rm c}}\simeq2.4-2.5$ GPa. The magnetic ordering temperature ($T_{{\rm N}}$) and the value of the magnetic moment per Fe site ($m_{{\rm Fe}}$) increase continuously with increasing pressure, reaching $T_{{\rm N}}\simeq50$~K and $m_{{\rm Fe}}\simeq0.25$ $\mu_{{\rm B}}$ at $p\simeq2.6$ GPa, respectively. No pronounced features at both $T_{{\rm N}}(p)$ and $m_{{\rm Fe}}(p)$ are detected at $p\simeq p_{{\rm c}}$, thus suggesting that the stripe-type magnetic order in FeSe remains unchanged above and below the critical pressure $p_{{\rm c}}$. A phenomenological model for the $(p,T)$ phase diagram of FeSe reveals that these observations are consistent with a scenario where the nematic transitions of FeSe at low and high pressures are driven by different mechanisms.

Orbital mismatch boosting nematic instability in iron-based superconductors

We derive the effective action for the collective spin modes in iron-based superconductors. We show that, due to the orbital-selective nature of spin fluctuations, the magnetic and nematic instabilities are controlled by the degrees of orbital nesting between electron and hole pockets. Within a prototypical three-pockets model the hole-electron orbital mismatch is found to boost spin-nematic order. This explains the enhancement of the nematic order in FeSe as compared to 122 compounds, and its suppression under pressure, where the emergence of the second hole pocket compensates the orbital mismatch of the three-pockets configuration.

Evidence for short-range magnetic order in the nematic phase of FeSe from anisotropic in-plane magnetostriction and susceptibility measurements

The nature of the nematic state in FeSe remains one of the major unsolved mysteries in Fe- based superconductors. Both spin and orbital physics have been invoked to explain the origin of this phase. Here we present experimental evidence for frustrated, short-range magnetic order, as suggested by several recent theoretical works, in the nematic state of FeSe. We use a combination of magnetostriction, susceptibility and resistivity measurements to probe the in-plane anisotropies of the nematic state and its associated fluctuations. Despite the absence of long-range magnetic order in FeSe, we observe a sizable in-plane magnetic susceptibility anisotropy, which is responsible for the field-induced in-plane distortion inferred from magnetostriction measurements. Further we demonstrate that all three anisotropies in FeSe are very similar to those of BaFe2As2, which strongly suggests that the nematic phase in FeSe is also of magnetic origin.

Pressure-induced magnetic order in FeSe: A muon spin rotation study

The magnetic order induced by the pressure was studied in single crystalline FeSe by means of muon-spin rotation ($\mu$SR) technique. By following the evolution of the oscillatory part of the $\mu$SR signal as a function of angle between the initial muon-spin polarization and 101 axis of studied crystal it was found that the pressure induced magnetic order in FeSe corresponds either to the collinear (single-stripe) antiferromagnetic order as observed in parent compounds of various FeAs-based superconductors or to the Bi-Collinear order as obtained in FeTe system, but with the Fe spins turned by 45$^{\rm o}$. The value of the magnetic moment per Fe atom was estimated to be $\simeq 0.13-0.14$~$\mu_{\rm B}$ at $p\simeq 1.9$~GPa.

Spin excitations and the Fermi surface of superconducting FeS

High-temperature superconductivity occurs near antiferromagnetic instabilities and the nematic state. Debate remains on the origin of nematic order in FeSe and its relation with superconductivity. Here, we use transport, neutron scattering and Fermi surface measurements to demonstrate that hydrothermo grown superconducting FeS, an isostructure of FeSe, is a tetragonal paramagnet without nematic order and with a quasiparticle mass significantly reduced from that of FeSe. Only stripe-type spin excitations are observed up to 100 meV. No direct coupling between spin excitations and superconductivity in FeS is found, suggesting that FeS is less correlated and the nematic order in FeSe is due to competing checkerboard and stripe spin fluctuations.

Effect of disorder on the competition between nematic and superconducting order in FeSe

Crystalline FeSe is known to display strong nematic order below a weak tetragonal-orthorhombic structural transition around K, and a superconducting transition at . Recently, it was shown that electron irradiation, which creates pointlike potential scattering defects, has the surprising effect of enhancing Tc while suppressing Ts. Here we discuss a possible scenario for such an effect, which postulates a competition between superconductivity and nematic order. The transition to the nematic state is modeled by a mean field theory of a d-wave Pomeranchuk instability, together with a Cooper pairing interaction in both one- and multiband models. The effect of nonmagnetic impurities on both orders is treated on equal footing within the Born approximation. We find evidence that disorder can indeed enhance Tc while suppressing the competing nematic order, but only in a multiband situation. We discuss our results in the context of experimental data on FeSe crystals.

Strong cooperative coupling of pressure-induced magnetic order and nematicity in FeSe.

A hallmark of the iron-based superconductors is the strong coupling between magnetic, structural and electronic degrees of freedom. However, a universal picture of the normal state properties of these compounds has been confounded by recent investigations of FeSe where the nematic (structural) and magnetic transitions appear to be decoupled. Here, using synchrotron-based high-energy x-ray diffraction and time-domain Mössbauer spectroscopy, we show that nematicity and magnetism in FeSe under applied pressure are indeed strongly coupled. Distinct structural and magnetic transitions are observed for pressures between 1.0 and 1.7 GPa and merge into a single first-order transition for pressures ≳1.7 GPa, reminiscent of what has been found for the evolution of these transitions in the prototypical system Ba(Fe1−xCox)2As2. Our results are consistent with a spin-driven mechanism for nematic order in FeSe and provide an important step towards a universal description of the normal state properties of the iron-based superconductors.

The 45 K Onset Superconductivity and the Suppression of the Nematic Order in FeSe by Electrolyte Gating**Supported by the National Natural Science Foundation of China under Grant Nos 11174294, 11174291, 11374302, 11304319, U1332209, U1432251 and U1532153, the China Postdoctoral Science Foundation under Grant No 2015M582020, the Program of Users with Excellence, the Hefei Science Center of Chinese Academy of Sciences,

The electronic doping effect on both the superconductivity and the nematic order in the FeSe nanoflake are investigated by using the electric-double-layer transistor configuration. The superconductivity can be effectively controlled by electronic doping, and the onset superconducting transition temperature Tc reaches as high as 45 K at a gate voltage of Vg = 4 V. Meanwhile, the nematic phase is gradually suppressed with the increase of electronic doping (or Vg). The results provide an effective method with variable charge doping for investigation of the rich physics in the FeSe superconductor.

Momentum-dependent sign inversion of orbital order in superconducting FeSe

We investigate the electronic reconstruction across the tetragonal-orthorhombic structural transition in FeSe by employing polarization-dependent angle-resolved photoemission spectroscopy (ARPES) on detwinned single crystals. Across the structural transition, the electronic structures around the G and M points are modified from four-fold to two-fold symmetry due to the lifting of degeneracy in dxz/dyz orbitals. The dxz band shifts upward at the G point while it moves downward at the M point, suggesting that the electronic structure of orthorhombic FeSe is characterized by a momentum-dependent sign-changing orbital polarization. The elongated directions of the elliptical Fermi surfaces (FSs) at the G and M points are rotated by 90 degrees with respect to each other, which may be related to the absence of the antiferromagnetic order in FeSe.

Effect of magnetic frustration on nematicity and superconductivity in iron chalcogenides

Over the past few years Fe chalcogenides (FeSe/Te) have advanced to the forefront of Fe-based superconductors (FeBS) research. The most intriguing results thus far are for intercalated and monolayer FeSe, however experimental studies are still inconclusive. Yet, bulk FeSe itself remains an unusual case when compared with pnictogen-based FeBS, and may hold clues to understanding the more exotic FeSe-derivatives. The FeSe phase diagram is unlike the pnictides: the orthorhombic distortion, which is likely to be of a "spin-nematic" nature in numerous pnictides, is not accompanied by magnetic order in FeSe, and the superconducting transition temperature $T_{c}$ rises significantly with pressure before decreasing. In this paper we show that the magnetic interactions in chalcogenides, as opposed to pnictides, demonstrate unusual (and unanticipated) frustration, which suppresses magnetic, but not nematic order, favors ferro-orbital order in the nematic phase and can naturally explain the nonmonotonic pressure dependence of the superconducting critical temperature $T_{c}(P)$.