Monolayer FeSe Research Articles

The crystal structure and physical properties of multiple components FeSe-based superconductors

The sample preparation, crystallographic structure, phase separation and superconductivity of FeSe-based superconductors are discussed here. First of all, we will introduce the ternary high tempeature superconductor K0.8Fe2− y Se2 with superconducting transition tempeature ( T c) at 31 K, which creates the record T c of FeSe-based superconductor under ambient pressure at that time. The single crystals can be grown through the self-flux method at high temperature. The crystal structure at high temperature shows the body-center tetragonal lattice with space group I4/mmm, while the superstructure developes at low tempeature with I4/m symmetry. The Fermi surface measured by angle resolution photoemission spectrum shows that K0.8Fe2− y Se2 has no any hole pockets at Fermi level, which is strikingly different from that of FeAs-based superconducors. This topology of Fermi surface implies that the superconducting mechanism of K0.8Fe2− y Se2 also should be distinguished from that of FeAs-based superconductors. The lack of interaction between electron and hole pockets would induce a possible d -wave superconducting gap. However, the mulitiple superstructure types, such as 5 × 5 , 2 × 2 , 2×2, etc, have been identified by transimission electron microscopy and neutron diffraction measurements, which reveal that K0.8Fe2− y Se2 is a phase-separated compound. Secondly, we develop the low tempeature liquid-NH3 method for synthesizing the pure FeSe-based superconducting compounds without phase separation. It is demonstrated that many alkali-metals, alkali-earth metals and rare-earth metals, such as Li, Na, Ca, Sr, Ba, Eu, and Yb, can be intercalated between FeSe layers and induce superconductivity with T c of 30–46 K, which can further enhance the record T c. In the K x (NH3) y Fe2Se2, two superconducting phases are discovered with different concentration of K ( x ≈0.3 and 0.6). The NH3 molecures play an important role in stabilizing the structures, moreover, the discrete superconducting phases implies that metal-intercalated FeSe superconductors are distinct from other FeAs-based superconductors. It is proposed that the main cause comes from their structures only being stable at particular doping levels and fine-tuning the concentrations of alkali metals may further enhance T c in the FeSe-based superconductors. Thirdly, we discuss the novel FeSe-based superconductors prepared by other metastable methods like the hydrothermal and solvent-thermal methods. The superconducting LiOHFeSe and Na x (En) y Fe2Se2 superconductors with T c over 40 K have been successfully synthesized, in which the former one shows the anti-ferromagentism at 8 K and the latter one exhibits structural tranistion at 350 K. The emergent properties from these novel high tempeature superconductors make the FeSe-based family becomes the hottest field in the community of superconductivity. In addition, the newly discovered monolayer FeSe on SrTiO3 further enhance the T c up to 65–70 K, which is close to the boiling point of liquid nitrogen. Finally, it is remarked that the structural flexibilty and weak bonds between FeSe layers are the most important advantages for exploring new superconductor with higher T c. We believe that more FeSe-based superconductors could be discovered once the new metastable methods are explored.

Dipolar phonons and electronic screening in monolayer FeSe on SrTiO3

Monolayer films of FeSe grown on SrTiO$_3$ substrates exhibit significantly higher superconducting transition temperatures than those of bulk FeSe. Interaction of electrons in the FeSe layer with dipolar SrTiO$_3$ phonons has been suggested as the cause of the enhanced transition temperature. In this paper we systematically study the coupling of SrTiO$_3$ longitudinal optical phonons to the FeSe electron, including also electron-electron Coulomb interactions at the random phase approximation level. We find that the electron-phonon interaction between FeSe and SrTiO$_3$ substrate is almost entirely screened by the electronic fluctuations in the FeSe monolayer, so that the net electron-phonon interaction is very weak and unlikely to lead to superconductivity.

How Correlated is the FeSe/SrTiO_{3} System?

Recent observation of ∼10 times higher critical temperature in a FeSe monolayer compared with its bulk phase has drawn a great deal of attention because the electronic structure in the monolayer phase appears to be different than bulk FeSe. Using a combination of density functional theory and dynamical mean field theory, we find electronic correlations have important effects on the predicted atomic-scale geometry and the electronic structure of the monolayer FeSe on SrTiO_{3}. The electronic correlations are dominantly controlled by the Se-Fe-Se angle either in the bulk phase or the monolayer phase. But the angle sensitivity increases and the orbital differentiation decreases in the monolayer phase compared to the bulk phase. The correlations are more dependent on Hund's J than Hubbard U. The observed orbital selective incoherence to coherence crossover with temperature confirms the Hund's metallic nature of the monolayer FeSe. We also find electron doping by oxygen vacancies in SrTiO_{3} increases the correlation strength, especially in the d_{xy} orbital by reducing the Se-Fe-Se angle.

Possible spin excitation structure in monolayer FeSe grown on SrTiO3

Based on recent high-resolution angle-resolved photoemission spectroscopy measurement in monolayer FeSe grown on SrTiO$_{3}$, we constructed a tight-binding model and proposed a superconducting (SC) pairing function which can well fit the observed band structure and SC gap anisotropy. Then we investigated the spin excitation spectra in order to determine the possible sign structure of the SC order parameter. We found that a resonance-like spin excitation may occur if the SC order parameter changes sign along the Fermi surfaces. However, this resonance is located at different locations in momentum space compared to other FeSe-based superconductors, suggesting that the Fermi surface shape and pairing symmetry in monolayer FeSe grown on SrTiO$_{3}$ may be different from other FeSe-based superconductors.

Comparative Review on Thin Film Growth of Iron-Based Superconductors

Since the discovery of the novel iron-based superconductors, both theoretical and experimental studies have been performed intensively. Because iron-based superconductors have a smaller anisotropy than high-Tc cuprates and a high superconducting transition temperature, there have been a lot of researchers working on the film fabrication of iron-based superconductors and their application. Accordingly, many novel features have been reported in the films of iron-based superconductors, for example, the fabrication of the epitaxial film with a higher Tc than bulk samples, the extraction of the metastable phase which cannot be obtained by the conventional solid state reaction, and so on. In this paper, we review the progress of research on thin film fabrications of iron-based superconductors, especially the four categories: LnFeAs(O,F) (Ln = Lanthanide), AEFe2As2 (AE = Alkaline-earth metal), FeCh (Ch = Chalcogen), and FeSe monolayer. Furthermore, we focus on two important topics in thin films of iron-based superconductors; one is the substrate material for thin film growth on the iron-based superconductors, and the other is the whole phase diagram in FeSe1-xTex which can be obtained only by using film-fabrication technique.

Electronic properties of superconducting FeS

We report first-principles density-functional theory results on the electronic and magnetic properties of the recently discovered superconducting FeS, which reveals important differences with the other members of the iron-chalcogenides (FeSe and FeTe). The band structure of FeS is characterized by two hole bands at the Fermi energy with a fully occupied ${d}_{xy}$ band at $\mathrm{\ensuremath{\Gamma}}$. A stripe-antiferromagnetic phase with a small magnetic moment is the most stable magnetic solution, but different magnetic phases have comparable energies indicating a tight competition. Including local interactions treated within dynamical mean-field theory, we find significant correlation effects with orbital-dependent strength and character, even if all the fingerprints of correlations are slightly weaker than in FeSe. The study of the effect of pressure reveals significant changes in the electronic structure of the material and of the correlation effects. These results point toward further studies on the possible superconducting phase stabilized by pressure effects or two dimensionality, in analogy with pressurized and monolayer FeSe.

Orbital selective pairing and gap structures of iron-based superconductors

We discuss the influence on spin-fluctuation pairing theory of orbital selective strong correlation effects in Fe-based superconductors, particularly Fe chalcogenide systems. We propose that a key ingredient for an improved itinerant pairing theory is orbital selectivity, i.e., incorporating the reduced coherence of quasiparticles occupying specific orbital states. This modifies the usual spin-fluctuation via suppression of pair scattering processes involving those less coherent states and results in orbital selective Cooper pairing of electrons in the remaining states. We show that this paradigm yields remarkably good agreement with the experimentally observed anisotropic gap structures in both bulk and monolayer FeSe, as well as LiFeAs, indicating that orbital selective Cooper pairing plays a key role in the more strongly correlated iron-based superconductors.

Filling-Enforced Magnetic Dirac Semimetals in Two Dimensions.

Filling-enforced Dirac semimetals, or those required at specific fillings by the combination of crystalline and time-reversal symmetries, have been proposed in numerous materials. However, Dirac points in these materials are not generally robust against breaking or modifying time-reversal symmetry. We present a new class of two-dimensional Dirac semimetal protected by the combination of crystal symmetries and a special, antiferromagnetic time-reversal symmetry. Systems in this class of magnetic layer groups, while having broken time-reversal symmetry, still respect the operation of time-reversal followed by a half-lattice translation. In contrast to 2D time-reversal-symmetric Dirac semimetal phases, this magnetic Dirac phase is capable of hosting just a single isolated Dirac point at the Fermi level, one that can be stabilized solely by symmorphic crystal symmetries. We find that this Dirac point represents a new quantum critical point, existing at the boundary between Chern insulating, antiferromagnetic topological crystalline insulating, and trivial insulating phases, and we discuss its relationship with condensed matter fermion doubling theorems. We present density functional theoretic calculations which demonstrate the presence of these 2D magnetic Dirac points in FeSe monolayers and discuss the implications for engineering quantum phase transitions in these materials.

Strong Landau-quantization effects in high-magnetic-field superconductivity of a two-dimensional multiple-band metal near the Lifshitz transition

We investigate the onset of superconductivity in magnetic field for a clean two-dimensional multiple-band superconductor in the vicinity of the Lifshitz transition when one of the bands is very shallow. Due to small number of carriers in this band, the quasiclassical Werthamer-Helfand approximation breaks down and Landau quantization has to be taken into account. We found that the transition temperature TC2(H) has giant oscillations and is resonantly enhanced at the magnetic fields corresponding to full occupancy of the Landau levels in the shallow band. This enhancement is especially pronounced for the lowest Landau level. As a consequence, the reentrant superconducting regions in the temperature-field phase diagram emerge at low temperatures near the magnetic fields at which the chemical potential matches the Landau levels. The specific behavior depends on the relative strength of the intraband and interband pairing interactions and the reentrance is most pronounced in the purely interband coupling scenario. The reentrant behavior is suppressed by the Zeeman spin splitting in the shallow band, the separated regions disappear already for very small spin-splitting factors. On the other hand, the reentrance is restored in the resonance cases when the spin-splitting energy exactly matches the separation between the Landau levels. The predicted behavior may realize in the gate-tuned FeSe monolayer.

Enhanced superconductivity accompanying a Lifshitz transition in electron-doped FeSe monolayer

The origin of enhanced superconductivity over 50 K in the recently discovered FeSe monolayer films grown on SrTiO3 (STO), as compared to 8 K in bulk FeSe, is intensely debated. As with the ferrochalcogenides AxFe2−ySe2 and potassium-doped FeSe, which also have a relatively high-superconducting critical temperature (Tc), the Fermi surface (FS) of the FeSe/STO monolayer films is free of hole-like FS, suggesting that a Lifshitz transition by which these hole FSs vanish may help increasing Tc. However, the fundamental reasons explaining this increase of Tc remain unclear. Here we report a 15 K jump of Tc accompanying a second Lifshitz transition characterized by the emergence of an electron pocket at the Brillouin zone centre, which is triggered by high-electron doping following in situ deposition of potassium on FeSe/STO monolayer films. Our results suggest that the pairing interactions are orbital dependent in generating enhanced superconductivity in FeSe.

Monolayer FeSe on SrTiO3

Epitaxial engineering of solid state heterointerfaces is a leading avenue to realizing enhanced or novel electronic states of matter. As a recent example, bulk FeSe is an unconventional superconductor with a modest transition temperature (Tc) of 9 K. However, when a single atomic layer of FeSe is grown on SrTiO3, its Tc can skyrocket by an order of magnitude to 65 K or 109 K. Since this discovery in 2012, efforts to reproduce, understand, and extend these findings continue to draw both excitement and scrutiny. In this review, we first present a critical survey of experimental measurements performed using a wide range of techniques. We then turn to the open question of microscopic mechanisms of superconductivity. We examine contrasting indications for both phononic (conventional) and magnetic/orbital (unconventional) means of electron pairing, as well as speculations about whether they could work cooperatively to boost Tc in a monolayer of FeSe.

On the origin of the shallow and “replica” bands in FeSe monolayer superconductors

We compare electronic structures of single FeSe layer films on SrTiO$_3$ substrate (FeSe/STO) and K$_x$Fe$_{2-y}$Se$_{2}$ superconductors obtained from extensive LDA and LDA+DMFT calculations with the results of ARPES experiments. It is demonstrated that correlation effects on Fe-3d states are sufficient in principle to explain the formation of the shallow electron -- like bands at the M(X)-point. However, in FeSe/STO these effects alone are apparently insufficient for the simultaneous elimination of the hole -- like Fermi surface around the $\Gamma$-point which is not observed in ARPES experiments. Detailed comparison of ARPES detected and calculated quasiparticle bands shows reasonable agreement between theory and experiment. Analysis of the bands with respect to their origin and orbital composition shows, that for FeSe/STO system the experimentally observed "replica" quasiparticle band at the M-point (usually attributed to forward scattering interactions with optical phonons in SrTiO$_3$ substrate) can be reasonably understood just as the LDA calculated Fe-3d$_{xy}$ band, renormalized by electronic correlations. The only manifestation of the substrate reduces to lifting the degeneracy between Fe-3d$_{xz}$ and Fe-3d$_{yz}$ bands in the vicinity of M-point. For the case of K$_x$Fe$_{2-y}$Se$_{2}$ most bands observed in ARPES can also be understood as correlation renormalized Fe-3d LDA calculated bands, with overall semi -- quantitative agreement with LDA+DMFT calculations.

Coexistence of Replica Bands and Superconductivity in FeSe Monolayer Films.

To elucidate the mechanisms behind the enhanced T_{c} in monolayer (1ML) FeSe on SrTiO_{3} (STO), we grew highly strained 1ML FeSe on the rectangular (100) face of rutile TiO_{2}, and observed the coexistence of replica bands and superconductivity with a T_{c} of 63K. From the similar T_{c} between this system and 1ML FeSe on STO (001), we conclude that strain and dielectric constant are likely unimportant to the enhanced T_{c} in these systems. A systematic comparison of 1ML FeSe on TiO_{2} with other systems in the FeSe family shows that while charge transfer alone can enhance T_{c}, it is only with the addition of interfacial electron-phonon coupling that T_{c} can be increased to the level seen in 1ML FeSe on STO.

The electron–phonon interaction with forward scattering peak is dominant in high Tc superconductors of FeSe films on (TiO2)

The theory of the electron–phonon interaction (EPI) with strong forward scattering peak (FSP) in an extreme delta-peak limit (Kulić and Zeyher 1994 Phys. Rev. B 49 4395; Kulić 2000 Phys. Rep. 38 1–264; Kulić and Dolgov 2005 Phys. Status Solidi b 242 151; Danylenko et al 1999 Eur. Phys. J. B 9 201) is recently applied in (Lee et al 2014 Nature 515 245; Rademaker et al 2016 New J. Phys. 18 022001; Wang et al 2016 Supercond. Sci. Technol. 29 054009) for the explanation of high in a monolayer FeSe grown on (Lee et al 2014 Nature 515 245) and TiO2 (Rebec et al 2016 arXiv:1606.09358v1) substrates. The EPI is due to a long-range dipolar electric field created by high-energy oxygen vibrations ( meV) at the interface (Lee et al 2014 Nature 515 245; Rademaker et al 2016 New J. Phys. 18 022001; Wang et al 2016 Supercond. Sci. Technol. 29 054009). In leading order (with respect to ) the mean-field critical temperature ∼ and the gap are due to an interplay between the maximal EPI pairing potential and the FSP-width qc. For K one has meV in a satisfactory agreement with ARPES experiments. In leading order Tc0 is mass-independent and a very small oxygen isotope effect is expected in next to leading order. In clean systems Tc0 for s-wave and d-wave pairing is degenerate but both are affected by non-magnetic impurities, which are pair-weakening in the s-channel and pair-breaking in the d-channel. The self-energy and replica bands at T = 0 and at the Fermi surface are calculated and compared with experimental results at ( Rademaker et al 2016 New J. Phys. 18 022001; Wang et al 2016 Supercond. Sci. Technol. 29 054009). The EPI coupling constant is mass-dependent () and at makes the slope of the self-energy and the replica intensities mass-dependent. This result, overlooked in the literature, is contrary to the prediction of the standard Migdal–Eliashberg theory for EPI. The small oxygen isotope effect in and pronounced isotope effect in and ARPES spectra Ai of the replica bands in FeSe films on SrTiO3 and TiO2 is a smoking-gun experiment for validity of the EPI–FSP theory to these systems. The EPI–FSP theory predicts a large number of low-laying pairing states, thus causing internal pair fluctuations. The latter reduce Tc0 additionally, by creating a pseudogap state for . Possibilities to increase Tc0, by designing novel structures are discussed in the framework of the EPI–FSP theory.

Superconductivity in FeSe Thin Films Driven by the Interplay between Nematic Fluctuations and Spin-Orbit Coupling.

The origin of the high-temperature superconducting state observed in FeSe thin films, whose phase diagram displays no sign of magnetic order, remains a hotly debated topic. Here we investigate whether fluctuations arising due to the proximity to a nematic phase, which is observed in the phase diagram of this material, can promote superconductivity. We find that nematic fluctuations alone promote a highly degenerate pairing state, in which both s-wave and d-wave symmetries are equally favored, and T_{c} is consequently suppressed. However, the presence of a sizable spin-orbit coupling or inversion symmetry breaking at the film interface lifts this harmful degeneracy and selects the s-wave state, in agreement with recent experimental proposals. The resulting gap function displays a weak anisotropy, which agrees with experiments in monolayer FeSe and intercalated Li_{1-x}(OH)_{x}FeSe.

Hidden sign-changing s -wave superconductivity in monolayer FeSe

Combining the recent scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES) measurements, we construct a tight-binding model suitable for describing the band structure of monolayer FeSe grown on SrTiO$_{3}$. Then we propose a possible pairing function, which can well describe the gap anisotropy observed by ARPES and has a hidden sign-changing characteristic. At last, as a test of this pairing function we further study the nonmagnetic impurity-induced bound states, to be verified by future STM experiments.

Superconductivity and nematic fluctuations in a model of doped FeSe monolayers: Determinant quantum Monte Carlo study

In contrast to bulk FeSe, which exhibits nematic order and low temperature superconductivity, atomic layers of FeSe reverse the situation, having high temperature superconductivity appearing alongside a suppression of nematic order. To investigate this phenomenon, we study a minimal electronic model of FeSe, with interactions that enhance nematic fluctuations. This model is sign problem free, and is simulated using determinant quantum Monte Carlo (DQMC). We developed a DQMC algorithm with parallel tempering, which proves to be an efficient source of global updates and allows us to access the region of strong interactions. Over a wide range of intermediate couplings, we observe superconductivity with an extended s-wave order parameter, along with enhanced, but short ranged, $q=(0,0)$ ferro-orbital (nematic) order. These results are consistent with approximate weak coupling treatments that predict that nematic fluctuations lead to superconducting pairing. Surprisingly, in the parameter range under study, we do not observe nematic long range order. Instead, at stronger coupling an unusual insulating phase with $q=(\pi,\pi)$ antiferro-orbital order appears, which is missed by weak coupling approximations.

Electronic structure of FeSe monolayer superconductors

We review a variety of theoretical and experimental results concerning electronic band structure of superconducting materials based on FeSe monolayers. Three type of systems are analyzed: intercalated FeSe systems AxFe2Se2–xSx and [Li1–xFexOH]FeSe as well as the single FeSe layer films on SrTiO3 substrate. We present the results of detailed first principle electronic band structure calculations for these systems together with comparison with some experimental ARPES data. The electronic structure of these systems is rather different from that of typical FeAs superconductors, which is quite significant for possible microscopic mechanism of superconductivity. This is reflected in the absence of hole pockets of the Fermi surface at T-point in Brillouin zone, so that there are no “nesting” properties of different Fermi surface pockets. LDA + DMFT calculations show that correlation effects on Fe-3d states in the single FeSe layer are not that strong as in most of FeAs systems. As a result, at present there is no theoretical understanding of the formation of rather “shallow” electronic bands at M-points. LDA calculations show that the main difference in electronic structure of FeSe monolayer on SrTiO3 substrate from isolated FeSe layer is the presence of the band of O-2p surface states of TiO2 layer on the Fermi level together with Fe-3d states, which may be important for understanding the enhanced Tc values in this system. We briefly discuss the implications of our results for microscopic models of superconductivity.

Superconducting Gap Anisotropy in Monolayer FeSe Thin Film.

Superconductivity originates from pairing of electrons near the Fermi energy. The Fermi surface topology and pairing symmetry are thus two pivotal characteristics of a superconductor. Superconductivity in one monolayer (1ML) FeSe thin film has attracted great interest recently due to its intriguing interfacial properties and possibly high superconducting transition temperature over 65K. Here, we report high-resolution measurements of the Fermi surface and superconducting gaps in 1ML FeSe using angle-resolved photoemission spectroscopy. Two ellipselike electron pockets are clearly resolved overlapping with each other at the Brillouin zone corner. The superconducting gap is nodeless but moderately anisotropic, which puts strong constraint on determining the pairing symmetry. The gap maxima locate on the d_{xy} bands along the major axis of the ellipse and four gap minima are observed at the intersections of electron pockets. The gap maximum location combined with the Fermi surface geometry deviate from a single d-wave, extended s-wave or s_{±} gap function, suggesting an important role of the multiorbital nature of Fermi surface and orbital-dependent pairing in 1ML FeSe. The gap minima location may be explained by a sign change on the electron pockets, or a competition between intra- and interorbital pairing.

Electronic properties of the FeSe/STO interface from first-principle calculations

We perform first-principle calculations of the FeSe monolayer on STO with the focus on three central aspects. First, compared to experiment, the bulk lattice constant of FeSe is too small in LDA, PBEsol and Perdew–Burgke–Ernzerhof (PBE) type exchange-correlation (xc) functionals while in bulk SrTiO3 (STO) LDA over-binds, PBE under-binds and PBEsol agrees best with experiment. Thus, the strain in the FeSe monolayer on STO depends on the xc functional and, especially in the non-magnetic state, is strongly overestimated and best described in PBEsol. In agreement with earlier work, we find that the band structure of the checkerboard antiferromagnetic configuration agrees best with experiment where, in addition, the relative strain on FeSe is best described. Second, our focus is on the crystal structure of the interface itself. The FeSe/STO distance depends weakly on the presence of magnetism and PBE results agree best with recent experimental data. We find that a double -layer below the FeSe relaxes to a structure in disagreement with experimental data. On the other hand, considering the effect of oxygen-vacancies in the single terminated slab within the virtual crystal approximation, in agreement with recent experiment, the FeSe monolayer Ti layer distance increases for a small vacancy concentration (<20%). Third, we investigate the charge-transfer to FeSe due to oxygen-vacancies in STO. Interestingly, we find negligible charge transfer for small concentrations—only above 20% a significant charge transfer is observed.