We performed electron energy-loss spectroscopy studies in order to get a deeper insight into the electronic properties of potassium intercalated picene, a recently discovered superconductor. A comparison of the loss function of the undoped and doped compound shows the appearance of a new peak in the optical gap, which we attribute to the charge carrier plasmon. We find a dramatic increase for the value of the background dielectric constant $ε_{\infty}$ upon doping. Our core level excitation data clearly signal filling of the conduction bands with electrons upon potassium addition.
By the first principles calculations and X-ray diffraction simulations, we perform a systematic study of multiple superconducting phases of potassium-doped picene [Nature {\bf464} 76, 2010]. The combination of optimized lattice parameters, formation energy, and simulated X-ray diffraction spectra indicates that the superconducting phase with transition temperature (T$_c$) of 7 K corresponds to a charge doped K$_2$picene, which is semiconducting with a 0.1 eV energy gap, while the superconducting phase with T$_c$=18 K corresponds to a metallic K$_3$picene. The distinct crystal and electronic st…
The electronic structure of potassium intercalated picene and coronene films has been studied using photoemission spectroscopy. Picene has additionally been intercalated using sodium. Upon alkali metal addition core level as well as valence band photoemission data signal a filling of previously unoccupied states of the two molecular materials due to charge transfer from potassium. In contrast to the observation of superconductivity in K_xpicene and K_xcoronene (x ~ 3), none of the films studied shows emission from the Fermi level, i.e. we find no indication for a metallic ground state. Several…
The electronic structure of the unoccupied and occupied states of potassium (K)-doped and undoped picene crystalline films has been investigated by using the element-selective and bulk-sensitive photon-detection methods of X-ray absorption and emission spectroscopies. We observed the formation of the doping-induced unoccupied and occupied electronic states in K-doped picene. By applying the inner-shell resonant-excitation experiments, we observed the evidence for the orbital hybridization between K and picene near the Fermi energy. Furthermore, the resonant X-ray emission experiment suggests t…
The crystal structure of potassium doped picene with an exact stoichiometry (K3C22H14, K3picene from here onwards) has been theoretically determined within Density Functional Theory allowing complete variational freedom of the crystal structure parameters and the molecular atomic positions. A modified herringbone lattice is obtained in which potassium atoms are intercalated between two paired picene molecules displaying the two possible orientations in the crystal.Along the c-axis, organic molecules alternate with chains formed by three potassium atoms. The electronic structureof the doped mat…
We theoretically explore the crystal structures of K$_x$picene, for which a new aromatic superconductivity has recently been discovered for $x=3$, by systematically performing first-principles full structural optimization covering the concentration range $x=1$-4. The crystal symmetry (space group) of the pristine picene is shown to be preserved in all the optimized structures despite significant deformations of each picene molecule and vast rearrangements of herringbone array of molecules. For K$_x$picene ($x=1$-4) optimization indicates that (i) multiple structures exist in some cases, and (i…
We show, by means of ab-initio calculations, that electron-electron correlations play an important role in potassium-doped picene ($K_x$-picene), recently characterized as a superconductor with $T_c = 18K$. The inclusion of exchange interactions by means of hybrid functionals reproduces the correct gap for the undoped compound and predicts an antiferromagnetic state for $x=3$, where superconductivity has been observed. The latter finding is compatible with a sizable value of the correlation strength, in agreement with simple estimates. Our results highlight the similarity between potassium-dop…
K$_3$-picene is a superconducting molecular crystal with critical temperature T$_c=7$K or 18K, depending on preparation conditions. Using density functional theory we show that electron-phonon interaction accounts for T$_c ~ 3-8$ K. The average electron-phonon coupling, calculated by including the phonon energy scale in the electron-phonon scattering, is $λ=0.73$ and $ω_{\rm log}=18.0\,$ meV. Intercalant and intermolecular phonon-modes contribute substantially (40%) to $λ$ as also shown by the isotope exponents of potassium (0.19) and carbon (0.31). The relevance of these modes makes supercond…
We study superconductivity in doped solid picene (C22H14) with linear response calculations of the phonon spectrum and electron-phonon (ep) interaction. We show that the coupling of the high-energy C bond-stretching phonons to the π molecular orbitals for a doping of ~3 electrons per picene molecule is sufficiently strong to reproduce the experimental Tc of 18 K within Migdal-Eliashberg theory. For hole doping, we predict a similar coupling leading to a maximum Tc of 6 K. However, we argue that, due to its molecular nature, picene may belong to the same class of strongly correlated ep supercon…
We report electronic structure and physical properties of metal doped picene as well as selective synthesis of the phase exhibiting 18 K superconducting transition. First, Raman scattering is used to characterize the number of electrons transferred from the dopants to picene molecules. The charge transfer leads to a softening of Raman scattering peaks, which enables us to determine the number of transferred electrons. From this we have identified that three electrons are transferred to each picene molecule in the superconducting doped-picene solids. Second, we report the pressure dependence of…
Potassium-doped picene (K$_x$picene) has recently been reported to be a superconductor at $x=3$ with critical temperatures up to 18 K. Here we study the electronic structure of K-doped picene films by photoelectron spectroscopy and {\it ab initio} density functional theory combined with dynamical mean-field theory (DFT+DMFT). Experimentally we observe that, except for spurious spectral weight due to the lack of a homogeneous chemical potential at low K-concentrations ($x \approx 1$), the spectra always display a finite energy gap. This result is supported by our DFT+DMFT calculations which pro…
To explore the electronic structure of the first aromatic superconductor, potassium-doped solid picene which has been recently discovered by Mitsuhashi et al with the transition temperatures $T_c=7 - 20$ K, we have obtained a first-principles electronic structure of solid picene as a first step toward the elucidation of the mechanism of the superconductivity. The undoped crystal is found to have four conduction bands, which are characterized in terms of the maximally localized Wannier orbitals. We have revealed how the band structure reflects the stacked arrangement of molecular orbitals for b…
Alkali doped aromatic compounds have shown evidence of metallic and superconducting phases whose precise nature is still mysterious. In potassium and rubidium doped phenanthrene, superconducting temperatures around 5 K have been detected, but such basic elements as the stoichiometry, crystal structure, and electronic bands are still speculative. We seek to predict the crystal structure of M3-phenanthrene (M = K, Rb) using ab-initio evolutionary simulation in conjunction with density functional theory (DFT), and find metal but also insulator phases with distinct structures. The original P21 her…
We have obtained the first-principles electronic structure of solid coronene, which has been recently discovered to exhibit superconductivity with potassium doping. Since coronene, along with picene, the first aromatic superconductor, now provide a class of superconductors as solids of aromatic compounds, here we compare the two cases in examining the electronic structures. In the undoped coronene crystal, where the molecules are arranged in a herringbone structure with two molecules in a unit cell, the conduction band above an insulating gap is found to comprise four bands, which basically or…
We propose an electron-phonon parameterization which reliably reproduces the geometry and harmonic frequencies of a real system. With respect to standard electron-phonon models, it adds a "double-counting" correction, which takes into account the lattice deformation as the system is dressed by low-energy electron-phonon processes. We show the importance of this correction by studying potassium-doped picene (K$_3$Picene), recently claimed to be a superconductor with a $T_c$ of up to 18 K. The Hamiltonian parameters are derived from ab-initio density functional theory, and the lattice model is s…
We performed electron energy-loss spectroscopy studies in transmission in order to obtain insight into the electronic properties of potassium intercalated coronene, a recently discovered superconductor with a rather high transition temperature of about 15\,K. A comparison of the loss function of undoped and potassium intercalated coronene shows the appearance of several new peaks in the optical gap upon potassium addition. Furthermore, our core level excitation data clearly signal filling of the conduction bands with electrons.
The potassium-doped p-terphenyl compounds were synthesized in recent experiments and the superconductivity with high transition temperatures were reported, but the atomic structure of potassium-doped p-terphenyl is unclear. In this paper, we studied the structural and electronic properties of potassium-doped p-terphenyl with various doping levels by the first-principles simulation. We first find out the low energy position of K atom in intralayer interstitial space of the molecular layer, then examine whether two rows of K atoms can be accommodated in this one space, at last the effect of the …
Using a new two-step synthesis method - ultrasound treatment and low temperature annealing, we explore superconductivity in potassium-doped triphenylbismuth, which is composed of one bismuth atom and three phenyl rings. The combination of dc and ac magnetic measurements reveals that one hundred percent of synthesized samples exhibit superconductivity at 3.5 K and/or 7.2 K at ambient pressure. The magnetization hysteresis loops provide a strong evidence of type-II superconductor, with the upper critical magnetic field up to 1.0 Tesla. Both calculated electronic structure and measured Raman spec…
We report on the emergence of two disconnected superconducting domes in alkali-metal potassium (K)-doped FeSe ultra-thin films grown on graphitized SiC(0001). The superconductivity exhibits hypersensitivity to K dosage in the lower-Tc dome, whereas in the heavily electron-doped higher-Tc dome it becomes spatially homogeneous and robust against disorder, supportive of a conventional Cooper-pairing mechanism. Furthermore, the heavily K-doped multilayer FeSe films all reveal a large superconducting gap of ~ 14 meV, irrespective of film thickness, verifying the higher-Tc superconductivity only in …
We report the growth of potassium-doped BaFe2As2 thin films, where the major charge carriers are holes, on Al2O3 (0001) and LaAlO3 (001) substrates by using an ex-situ pulsed laser deposition technique. The measured Tc's are 40 and 39 K for the films grown on Al2O3 and LaAlO3, respectively and diamagnetism indicates that the films have good bulk superconducting properties below 36 and 30 K, respectively. The X-ray diffraction patterns for both films indicated a preferred c-axis orientation, regardless of the substrate structures of LaAlO3 and Al2O3. The upper critical field at zero temperature…
Organic materials are believed to be potential superconductor with high transition temperature (TC). Organic superconductors mainly have two families: the quasi-one dimensional (TMTSF)2X and two dimensional (BEDT-TTF)2X (Ref. 1 and 2), in which TMTSF is tetramethyltetraselenafulvalene (C10H12Se4) and BEDT-TTF or "ET" is bis(ethylenedithio)tetrathiafulvalene (C10H8S8). One key feature of the organic superconductors is that they have π-molecular orbitals, and the π-electron can delocalize throughout the crystal giving rise to metallic conductivity due to a π-orbital overlap between adjacent mole…
By using high pressure synthesis method, we have fabricated the potassium doped para-terphenyl. The temperature dependence of magnetization measured in both zero-field-cooled and field-cooled processes shows step like transitions at about 125 K. This confirms earlier report about the possible superconductivity like transition in the same system. However, the magnetization hysteresis loop exhibits a weak ferromagnetic background. After removing this ferromagnetic background, a Meissner effect like magnetic shielding can be found. A simple estimate on the diamagnetization of this step tells that…
We have prepared potassium intercalated 1,2;8,9-dibenzopentacene films under vacuum conditions. The evolution of the electronic excitation spectra upon potassium addition as measured using electron energy-loss spectroscopy clearly indicate the formation of particular doped phases with compositions K$_x$dibenzopentacene ($x$ = 1,2,3). Moreover, the stability of these phases as a function of temperature has been explored. Finally, the electronic excitation spectra also give insight into the electronic ground state of the potassium doped 1,2;8,9-dibenzopentacene films.
The geometrical and electronic structure of potassium doped phenanthrene, \ce{K3C14H10}, have been studied by first-principles density functional theory. The main effect of potassium doping is to inject charge in the narrow phenanthrene conduction band, rendering the system metallic. The Fermi surface for the experimental X-rays structure is composed of two sheets with marked one and two dimensional character respectively.
Superconducting layered transition metal dichalcogenides (TMDs) stand out among other superconductors due to the tunable nature of the superconducting transition, coexistence with other collective electronic excitations (charge density waves) and strong intrinsic spin-orbit coupling. Molybdenum disulphide (MoS2) is the most studied representative of this family of materials, especially since the recent demonstration of the possibility to tune its critical temperature, Tc, by electric-field doping. However, just one of its polymorphs, band-insulator 2H-MoS2, has so far been explored for its pot…
We describe a new methodology of synthesizing the oxypnictide superconductors with potassium fluoride as a source as a source of fluorine instead of LaF3. This route also allows the substitution of potassium at lanthanum sites which leads to an increase in the upper critical field as would be expected for a multiband superconductor. We also report the highest reported Tc onset of 28.5K and highest upper critical field in these superconductors.
Inspired by the discovery of high temperature superconductivity in potassium-doped $p$-terphenyl, we examine the possibility of superconductivity in $p$-quaterphenyl with one more phenyl ring than $p$-terphenyl. The Meissner effect with critical temperatures ranging from 3.5 K to 120 K is found by the magnetic susceptibility measurements in $p$-quaterphenyl upon doping potassium in the condition of annealing or just pestling. The primary superconducting phase with critical temperature of 7.2 K can be reduplicated in several superconducting samples. In both the annealed and pestled superconduct…
Recently, there is a series of reports by Wang et al. on the superconductivity in K-doped p-terphenyl (KxC18H14) with the transition temperatures range from 7 to 123 Kelvin. Identifying the structural and bonding character is the key to understand the superconducting phases and the related properties. Therefore we carried out an extensive study on the crystal structures with different doping levels and investigate the thermodynamic stability, structural, electronic, and magnetic properties by the first-principles calculations. Our calculated structures capture most features of the experimental…
We report the observation of superconductivity at 33 K in K-doped 1,2:8,9-dibenzopentacene (C30H18). This is higher than any Tc reported previously for an organic superconductor besides the alkali-metal doped C60. This finding provides an indication that superconductivity at much higher temperature may be possible in such system, if PAHs with longer benzene rings can be synthesized.
To explore underlying mechanism for the superconducting phase in recent discovered aromatic hydrocarbons, we carry out the first-principles calculations on benzene, the basic and the simplest unit of the series and examine the structural and phase stability when doped by potassium, K$_x$C$_6$H$_6$ ($x=1,2,3$). We find that K$_2$C$_6$H$_6$ with the space group of $Pbca$ is the most stable phase with superconducting transition temperature around 6.2 K. Moreover, we argue that all existing hydrocarbons should have a unified superconducting phase in the same temperature range of 5$-$7 K, when dope…
The chain-like organic compounds with conjugated structure have the potential to become high temperature superconductors. We examine this idea by choosing p-quinquephenyl with five phenyl rings connected in para position. The dc magnetic susceptibility measurements provide solid evidence for the presence of Meissner effect when the compound is doped by potassium. The real part of the ac susceptibility shows exactly same transition temperature as that in dc magnetization, and the imaginary part of nearly zero value after transition implies the realization of zero-resistivity. All these features…
Recently, superconductivity in potassium (K) doped p-terphenyl (C18H14) has been suggested by the possible observation of the Meissner effect and subsequent photoemission spectroscopy measurements, but the detailed lattice structure and more-direct evidence are still lacking. Here we report a low temperature scanning tunneling microscopy/spectroscopy (STM/STS) study on K-doped single layer p-terphenyl films grown on Au (111). We observe several ordered phases with different morphologies and electronic behaviors, in two of which a sharp and symmetric low-energy gap of about 11 meV opens below 5…
Organic compounds are always promising candidates of superconductors with high transition temperatures. We examine this proposal by choosing 2,2$'$-bipyridine solely composed by C, H, and N atoms. The presence of Meissner effect with a transition temperature of 7.2 K in this material upon potassium doping is demonstrated by the $dc$ magnetic susceptibility measurements. The real part of the $ac$ susceptibility exhibits the same transition temperature as that in $dc$ magnetization, and a sharp peak appeared in the imaginary part indicates the formation of the weakly linked superconducting vorte…
Preliminary evidence for the occurrence of high-Tc superconductivity in alkali-doped organic materials, such as potassium-doped p-terphenyl (KPT), were recently obtained by magnetic susceptibility measurements and by the opening of a large superconducting gap as measured by ARPES and STM techniques. In this work, KPT samples have been synthesized by a chemical method and characterized by low-temperature Raman scattering and resistivity measurements. Here, we report the occurrence of a resistivity drop of more than 4 orders of magnitude at low temperatures in KPT samples in the form of compress…
The possibility of high temperature superconductivity in organic compounds has been discussed since the pioneering work of Little in 1964, with unsatisfactory progress until the recent report of a weak Meissner shielding effect at 120 Kelvin in potassium-doped para-terphenyl samples. To date however, no other signals of the superconductivity have been shown, including the zero-resistance state or evidence for the formation of the Cooper pairs that are inherent to the superconducting state. Here, using high-resolution photoemission spectroscopy on potassium surface-doped para-terphenyl crystals…
Synthesis methodology for flakes of p-terphenyl through sublimation under inert atmosphere of argon is presented. Flake morphology of p-terphenyl provides a favourable environment for efficient intercalation of potassium. Ratio of potassium and p-terphenyl is adjusted so as to obtain the desired superconducting phase i.e. potassium doped p-terphenyl (K3C18H14). A clear transition is observed at 107 K under Zero Field Cooled (ZFC) and Field Cooled (FC) mode. But overall the moment is positive possibly due to impurity phase dominating characteristics in the presence of negligible superconducting…
We have investigated correlated electronic structures and the phase diagram of electron-doped hydrocarbon molecular solids, based on the dynamical mean-field theory. We have found that the ground state of hydrocarbon-based superconductors such as electron-doped picene and coronene is a multi-band Fermi liquid, while that of non-superconducting electron-doped pentacene is a single-band Fermi liquid in the proximity of the metal-insulator transition. The size of the molecular orbital energy level splitting plays a key role in producing the superconductivity of electron-doped hydrocarbon solids. …
Superconductivity originates from pairing of electrons. Pairing channel on Fermi surface and pairing glue are thus two pivotal issues for understanding a superconductor. Recently, high-temperature superconductivity over 40 K was found in electron-doped FeSe superconductors including K$_x$Fe$_{2-y}$Se$_2$, Li$_{0.8}$Fe$_{0.2}$OHFeSe, and 1 monolayer FeSe thin film. However, their pairing mechanism remains controversial. Here, we studied the systematic evolution of electronic structure in potassium-coated FeSe single crystal. The doping level is controlled precisely by in situ evaporating potass…
We present a systematic study for understanding the relation between electronic correlation and superconductivity in C60 and aromatic compounds. We derived, from first principles, extended Hubbard models for twelve compounds; fcc K3C60, Rb3C60, Cs3C60 (with three different lattice constants), A15 Cs3C60 (with four different lattice constants), doped solid picene, coronene, and phenanthrene. We show that these compounds are strongly correlated and have a similar energy scale of the bandwidth and interaction parameters. However, they have a different trend in the relation between the strength of…
By the first principles calculations based on the van der Waals density functional theory, we study the crystal structures and electronic properties of La-doped phenanthrene. Two stable atomic geometries of La$_1$phenanthrene are obtained by relaxation of atomic positions from various initial structures. The structure-\uppercase\expandafter{\romannumeral1} is a metal with two energy bands crossing the Fermi level, while the structure-\uppercase\expandafter{\romannumeral2} displays a semiconducting state with an energy gap of 0.15 eV, which has an energy gain of 0.42 eV per unit cell compared t…
Sr2IrO4 was predicted to be a high temperature superconductor upon electron doping since it highly resembles the cuprates in crystal structure, electronic structure and magnetic coupling constants. Here we report a scanning tunneling microscopy/spectroscopy (STM/STS) study of Sr2IrO4 with surface electron doping by depositing potassium (K) atoms. At the 0.5-0.7 monolayer (ML) K coverage, we observed a sharp, V-shaped gap with about 95% loss of density of state (DOS) at EFand visible coherence peaks. The gap magnitude is 25-30 meV for 0.5-0.6 ML K coverage and it closes around 50 K. These behav…
The origin of enhanced superconductivity over 50 K in the recently discovered FeSe monolayer films grown on SrTiO$_{3}$ (STO), as compared to 8 K in bulk FeSe, is intensely debated. As with the ferrochalcogenides A$_{x}$Fe$_{2-y}$Se$_{2}$ and potassium doped FeSe, which also have a relatively high superconducting critical temperature ($T_c$), 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 $T_c$. However, the fundamental reasons explaining this increase of $T_c$ remain uncle…
We present results of precise measurements of the thermal and electrical transport in the optimally- and over-doped Ba1-xKxFe2As2 single crystals (x = 0.35, 0.55, 0.88) and compare them to the previously reported data on Ba(Fe1-yCoy)2As2. A contraction of the electron pocket is observed upon substitution potassium for barium, but even at the extreme doping (x = 0.88) there is still a noticeable contribution from negative charge carriers to the electronic transport. The size of the electron pocket in all K-doped samples is small enough to cause a significant enhancement of the respective Hall-L…
Resistivity, Hall effect and magnetoresistance have been investigated systematically on single crystals of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ ranging from undoped to optimally doped regions. A systematic evolution of the quasiparticle scattering has been observed. It is found that the resistivity in the normal state of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ is insensitive to the potassium doping concentration, which is very different from the electron doped counterpart Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$, where the resistivity at 300 K reduces to half value of the undoped one when the system is optimally doped…
Alkali-doped iron selenide is the latest member of high Tc superconductor family, and its peculiar characters have immediately attracted extensive attention. We prepared high-quality potassium-doped iron selenide (KxFe2-ySe2) thin films by molecular beam epitaxy and unambiguously demonstrated the existence of phase separation, which is currently under debate, in this material using scanning tunneling microscopy and spectroscopy. The stoichiometric superconducting phase KFe2Se2 contains no iron vacancies, while the insulating phase has a \surd5\times\surd5 vacancy order. The iron vacancies are …
We report comprehensive angle-resolved photoemission investigations on the electronic structure of single crystal multiple-layer FeSe films grown on CaF2 substrate by pulsed laser deposition (PLD) method. Measurements on FeSe/CaF2 samples with different superconducting transition temperatures Tc of 4 K, 9 K and 14 K reveal electronic difference in their Fermi surface and band structure. Indication of the nematic phase transition is observed from temperature-dependent measurements of these samples; the nematic transition temperature is 140-160 K, much higher than 90 K for the bulk FeSe. Potassi…
In Ba(Fe0.95Co0.05)2As2 all of the 75As NMR intensity at the paramagnetic resonance position vanishes abruptly below Tonset(SDW)=56 K, indicating that magnetic (spin density wave) order is present in all of the sample volume, despite bulk superconductivity below Tc=15 K. The two phases thus coexist homogeneously at the microscopic scale. In Ba0.6K0.4Fe2As2, on the other hand, the signal loss below Tonset(SDW)~75 K is not complete, revealing that magnetic order is bound to finite-size areas of the sample, while the remaining NMR signal shows a clear superconducting response below Tc=37 K. Thus,…
The geometrical and electronic structure of tripotassium doped phenanthrene, \ce{K3C14H10}, have been studied by first-principles density functional theory. The main effect of potassium doping is to inject charge in the narrow phenanthrene conduction band, rendering the system metallic. The Fermi surface for the experimental X-rays unit cell is composed of two sheets with marked one and two dimensional character respectively.
We used \emph{in-situ} potassium (K) evaporation to dope the surface of the iron-based superconductor FeTe$_{0.55}$Se$_{0.45}$. The systematic study of the bands near the Fermi level confirms that electrons are doped into the system, allowing us to tune the Fermi level of this material and to access otherwise unoccupied electronic states. In particular, we observe an electron band located above the Fermi level before doping that shares similarities with a small three-dimensional pocket observed in the cousin, heavily-electron-doped KFe$_{2-x}$Se$_2$ compound.
This is a report on the new 122 ternary transition-metal pnictide of BaMn2Bi2, which is crystallized from bismuth flux. BaMn2Bi2 adopts ThCr2Si2-type structure (I4/mmm) with a = 4.4902(3) Å and c = 14.687(1) Å; it is antiferromagnetic with anisotropic magnetic susceptibility and semiconducting with a band gap of Eg = 6 meV. Heat capacity result confirms the insulating ground state in BaMn2Bi2 with the electronic residual Sommerfeld coefficient of γ ~ 0. The high temperature magnetization results show that magnetic ordering temperature is TN ~ 400 K. Hole-doping in BaMn2Bi2 via potassium in Ba1…
We have studied electronic and magnetic structures of K$_{0.8+x}$Fe$_{1.6}$Se$_2$ by performing the first-principles electronic structure calculations. The ground state of the Fe-vacancies ordered K$_{0.8}$Fe$_{1.6}$Se$_2$ is found to be a quasi-two-dimensional blocked checkerboard antiferromagnetic (AFM) semiconductor with an energy gap of 594 meV and a large ordering magnetic moment of 3.37 $μ_B$ for each Fe atom, in excellent agreement with the neutron scattering measurement. The underlying mechanism is the chemical-bonding-driven tetramer lattice distortion. K$_{0.8+x}$Fe$_{1.6}$Se$_2$ wit…
