Hydrostatic and uniaxial pressure tuning of iron-based superconductors: Insights into superconductivity, magnetism, nematicity and collapsed tetragonal transitions
Elena Gati, Li Xiang, Sergey L. Bud'ko, Paul C. Canfield
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31 pages, 17 figures, submitted to Annalen der Physik
Iron-based superconductors are well-known for their intriguing phase diagrams, which manifest a complex interplay of electronic, magnetic and structural degrees of freedom. Among the phase transitions observed are superconducting, magnetic, and several types of structural transitions, including a tetragonal-to-orthorhombic and a collapsed-tetragonal transition. In particular, the widely-observed tetragonal-to-orthorhombic transition is believed to be a result of an electronic order that is coupled to the crystalline lattice and is, thus, referred to as nematic transition. Nematicity is therefore a prominent feature of these materials, which signals the importance of the coupling of electronic and lattice properties. Correspondingly, these systems are particularly susceptible to tuning via pressure (hydrostatic, uniaxial, or some combination). We review efforts to probe the phase diagrams of pressure-tuned iron-based superconductors, with a strong focus on our own recent insights into the phase diagrams of several members of this material class under hydrostatic pressure. These studies on FeSe, Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$, Ca(Fe$_{1-x}$Co$_x$)$_2$As$_2$ and CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ were, to a significant extent, made possible by advances of what measurements can be adapted to the use under differing pressure environments. We point out the potential impact of these tools for the study of the wider class of strongly correlated electron systems.
Temperature dependent measurements of 57Fe Mossbauer spectra on CaFe2As2 single crystals in the tetragonal and collapsed tetragonal phases are reported. Clear features in the temperature dependencies of the isomer shift, relative spectra area and quadrupole splitting are observed at the transition from the tetragonal to the collapsed tetragonal phase. From the temperature dependent isomer shift and spectral area data, an average stiffening of the phonon modes in the collapsed tetragonal phase is inferred. The quadrupole splitting increases by ~25% on cooling from room temperature to ~100 K in …
In copper-oxide and iron-based high temperature (high-$T_{\rm c}$) superconductors, many physical properties exhibit in-plane anisotropy, which is believed to be caused by a rotational symmetry-breaking nematic order, whose origin and its relationship to superconductivity remain elusive. In many iron-pnictides, a tetragonal-to-orthorhombic structural transition temperature $T_{\rm s}$ coincides with the magnetic transition temperature $T_{\rm N}$, making the orbital and spin degrees of freedom highly entangled. NaFeAs is a system where $T_{\rm s}$ = 54 K is well separated from $T_{\rm N}$ = 42…
Recently, KFe$_2$As$_2$ was shown to exhibit a structural phase transition from a tetragonal to a collapsed tetragonal phase under applied pressure of about $15~\mathrm{GPa}$. Surprisingly, the collapsed tetragonal phase hosts a superconducting state with $T_c \sim 12~\mathrm{K}$, while the tetragonal phase is a $T_c \leq 3.4~\mathrm{K}$ superconductor. We show that the key difference between the previously known non-superconducting collapsed tetragonal phase in AFe$_2$As$_2$ (A= Ba, Ca, Eu, Sr) and the superconducting collapsed tetragonal phase in KFe$_2$As$_2$ is the qualitatively distinct e…
We present a study of the tetragonal to collapsed-tetragonal transition of CaFe2As2 using angle-resolved photoemission experiments and dynamical mean field theory-based electronic structure calculations. We observe that the collapsed-tetragonal phase exhibits reduced correlations and a higher coherence temperature due to the stronger Fe-As hybridization. Furthermore, a comparison of measured photoemission spectra and theoretical spectral functions shows that momentum-dependent corrections to the density functional band structure are essential for the description of low-energy quasiparticle dis…
A well-known feature of CaFe$_{2}$As$_{2}$-based superconductors is the pressure-induced collapsed tetragonal phase that is commonly ascribed to the formation of an interlayer As-As bond. Using detailed X-ray scattering and spectroscopy, we find that Rh-doped Ca$_{0.8}$Sr$_{0.2}$Fe$_{2}$As$_{2}$ does not undergo a first-order phase transition and that local Fe moments persist despite the formation of interlayer As-As bonds. Our density functional theory calculations reveal that the Fe-As bond geometry is critical for stabilizing magnetism and that the pressure-induced drop in the $c$ lattice p…
The structural properties of EuCo2As2 have been studied up to 35 GPa, through the use of x-ray diffraction in a diamond anvil cell at a synchrotron source. At ambient conditions, EuCo2As2 (I4/mmm) has a tetragonal lattice structure with a bulk modulus of 48 +/-4 GPa. With the application of pressure, the a-axis exhibits negative compressibility with a concurrent sharp decrease in c-axis length. The anomalous compressibility of the a-axis continues until 4.7 GPa, at which point the structure undergoes a second-order phase transition to a collapsed tetragonal (CT) state with a bulk modulus of 11…
Recent investigations of the superconducting iron-arsenide families have highlighted the role of pressure, be it chemical or mechanical, in fostering superconductivity. Here we report that CaFe2As2 undergoes a pressure-induced transition to a non-magnetic, volume "collapsed" tetragonal phase, which becomes superconducting at lower temperature. Spin-polarized total-energy calculations on the collapsed structure reveal that the magnetic Fe moment itself collapses, consistent with the absence of magnetic order in neutron diffraction.
Inelastic neutron scattering measurements of CaFe2As2 under applied hydrostatic pressure show that the antiferromagnetic spin fluctuations observed in the ambient pressure, paramagnetic, tetragonal (T) phase are strongly suppressed, if not absent, in the collapsed tetragonal (cT) phase. These results are consistent with a quenched Fe moment in the cT phase and the strong decrease in resistivity observed upon crossing the boundary from the T to cT phase. The suppression or absence of static antiferromagnetic order and dynamic spin fluctuations in the non-superconducting cT phase supports the no…
By performing pressure simulations within density functional theory for the family of iron-based superconductors $Ae{}A$Fe$_4$As$_4$ with $Ae$ = Ca, Sr, Ba and $A$ = K, Rb, Cs we predict in these systems the appearance of two consecutive half-collapsed tetragonal transitions at pressures $P_{c_1}$ and $P_{c_2}$, which have a different character in terms of their effect on the electronic structure. We find that, similarly to previous studies for CaKFe$_4$As$_4$, spin-vortex magnetic fluctuations on the Fe sublattice play a key role for an accurate structure prediction in these materials at zero…
The relationship between antiferromagnetic spin fluctuations and superconductivity has become a central topic of research in studies of superconductivity in the iron pnictides. We present unambiguous evidence of the absence of magnetic fluctuations in the non-superconducting collapsed tetragonal phase of CaFe2As2 via inelastic neutron scattering time-of-flight data, which is consistent with the view that spin fluctuations are a necessary ingredient for unconventional superconductivity in the iron pnictides. We demonstrate that the collapsed tetragonal phase of CaFe2As2 is non-magnetic, and dis…
We report the temperature-pressure phase diagram of CaKFe$_4$As$_4$ established using high pressure electrical resistivity, magnetization and high energy x-ray diffraction measurements up to 6 GPa. With increasing pressure, both resistivity and magnetization data show that the bulk superconducting transition of CaKFe$_4$As$_4$ is suppressed and then disappears at $p$ $\gtrsim$ 4 GPa. High pressure x-ray data clearly indicate a phase transition to a collapsed tetragonal phase in CaKFe$_4$As$_4$ under pressure that coincides with the abrupt loss of bulk superconductivity near 4 GPa. The x-ray da…
We report $^{75}$As NMR studies on single crystals of rare-earth doped iron pnictides superconductor Ca$_{1-x}$Pr$_{x}$Fe$_{2}$As$_{2}$ ($x$=0.075 and 0.15). The $^{75}$As spectra show a chemical pressure effect with doping and a first order structure transition to the collapsed tetragonal phase upon cooling. A sharp drop of the Knight shift is seen below the structural transition, whereas $1/T_1$ is strongly enhanced at low-temperatures. These evidences indicate quenching of Fe local magnetism and short-range ordering of Pr$^{3+}$ moment in the collapsed tetragonal phase. The quenched Fe mome…
The pressure dependence of a large number of phonon modes in CaFe2As2 with energies covering the full range of the phonon spectrum has been studied using inelastic x-ray and neutron scattering. The observed phonon frequency changes are in general rather small despite the sizable changes of the lattice parameters at the phase transition. This indicates that the bonding properties are not profoundly altered by the phase transition. The transverse acoustic phonons propagating along the c-direction are an exception because they stiffen very significantly in response to the large contraction of the…
Recent studies reveal a pressure induced transition from a paramagnetic tetragonal phase (T) to a collapsed tetragonal phase (CT) in $CaFe_2As_2$, which was found to be superconducting with non-hydrostatic pressure at low temperature. We have investigated the effects of electron correlation and local fluctuating moment in both tetragonal and collapsed tetragonal phases of the paramagnetic $CaFe_2As_2$ using self consistent DFT+DMFT with continuous time quantum Monte Carlo as the impurity solver. From the computed optical conductivity, we find a gain in the optical kinetic energy due to the los…
FeSe undergoes a transition from a tetragonal to a slightly orthorhombic phase at 90\,K, and becomes a superconductor below 8\,K. The orthorhombic phase is sometimes called a nematic phase because quantum oscillation, neutron, and other measurements detect a significant asymmetry in $x$ and $y$. How nematicity affects superconductivity has recently become a matter of intense speculation. Here we employ an advanced \emph{ab-initio} Green's function description of superconductivity and show that bulk tetragonal FeSe would, in principle, superconduct with almost the same T$_{c}$ as the nematic ph…
The static and the dynamic spin correlations in the low temperature collapsed tetragonal and the high temperature tetragonal phase in CaFe2As2 have been investigated by 75As nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements. Through the temperature (T) dependence of the nuclear spin lattice relaxation rates (1/T1) and the Knight shifts, although stripe-type antiferromagnetic (AFM) spin correlations are realized in the high temperature tetragonal phase, no trace of the AFM spin correlations can be found in the non-superconducting, low temperature, collapsed te…
We have found a remarkably large response of the transition temperature of CaFe2As2 single crystals grown out of excess FeAs to annealing / quenching temperature. Whereas crystals that are annealed at 400 C exhibit a first order phase transition from a high temperature tetragonal to a low temperature orthorhombic and antiferromagnetic state near 170 K, crystals that have been quenched from 960 C exhibit a transition from a high temperature tetragonal phase to a low temperature, non-magnetic, collapsed tetragonal phase below 100 K. By use of temperature dependent electrical resistivity, magneti…
NaFe$_2$As$_2$ is investigated experimentally using powder x-ray diffraction and Raman spectroscopy at pressures up to 23 GPa at room temperature and using ab-initio calculations. The results reveal a pressure-induced structural modification at 4 GPa from the starting tetragonal to a collapsed tetragonal phase. We determined the changes in interatomic distances under pressure that allowed us to connect the structural changes and superconductivity. The transition is related to the formation of interlayer As-As bonds at the expense of weakening of Fe-As bonds in agreement with recent theoretical…
FeSe has a unique ground state in which superconductivity coexists with a nematic order without long-range magnetic ordering at ambient pressure. Here, to study how the pairing interaction evolves with nematicity, we measured the thermal conductivity and specific heat of FeSe$_{1-x}$S$_x$, where the nematicity is suppressed by isoelectronic sulfur substitution. We find that in the whole nematic ($0\leq x \leq 0.17$) and tetragonal ($x=0.20$) regimes, the application of small magnetic field causes a steep increase of both quantities. This indicates the existence of deep minima or line nodes in …
Single crystals of Ca(Fe1-xRux)2As2 (0<x<0.065) and Ca1-yLay(Fe0.973Ru0.027)2As2 (0<y<0.2) have been synthesized and studied with respect to their structural, electronic and magnetic properties. The partial substitution of Fe by Ru induces a decrease of the c-axis constant leading for x<0.023 to a suppression of the coupled magnetic and structural (tetragonal to orthorhombic) transitions. At x_cr=0.023 a first order transition to a collapsed tetragonal (CT) phase is found, which behaves like a Fermi liquid and which is stabilized by further increase of x. The absence of superconductivity near …
Mechanical strain is a powerful technique for tuning electronic structure and interactions in quantum materials. In a system with tetragonal symmetry, a tunable uniaxial in-plane strain can be used to probe nematic correlations in the same way that a tunable magnetic field is used to probe magnetic correlations. Here, we present a new spectroscopic scanned probe technique that provides atomic-resolution insight into the effect of anisotropic strain on the electronic structure. We use this technique to study nematic fluctuations and nematic order across the phase diagram of a prototypical iron-…
Compounds with a tetragonal ThCr$_{2}$Si$_{2}$-type structure are characterized by the possibility of the isostructural phase transition from the tetragonal phase to the collapsed tetragonal phase induced by the external pressure. An example of a compound with such a phase transition is KFe$_{2}$As$_{2}$, which belongs to the family of the iron-based superconductors. In this paper, we investigate the effects of the phase transition on the structural, electronic, and dynamical properties of this compound. Performing the ab initio calculations, we reproduce the dependence of the lattice constant…
Using non-resonant Fe K-beta x-ray emission spectroscopy, we reveal that Sr-doping of CaFe2As2 decouples the Fe moment from the volume collapse transition, yielding a collapsed-tetragonal, paramagnetic normal state out of which superconductivity develops. X-ray diffraction measurements implicate the c-axis lattice parameter as the controlling criterion for the Fe moment, promoting a generic description for the appearance of pressure-induced superconductivity in the alkaline-earth-based 122 ferropnictides (AFe2As2). The evolution of the superconducting critical temperature with pressure lends s…
Recent observations of selective emergence (suppression) of superconductivity in the uncollapsed (collapsed) tetragonal phase of LaFe$_2$As$_2$ has rekindled interest in understanding what features of the band structure control the superconducting T$_c$. We show that the proximity of the narrow Fe-d$_{xy}$ state to the Fermi energy emerges as the primary factor. In the uncollapsed phase this state is at the Fermi energy, and is most strongly correlated and source of enhanced scattering in both single and two particle channels. The resulting intense and broad low energy spin fluctuations suppre…
The temperature dependence of in plane optical conductivity has been investigated for Ca0.86Pr0.14Fe2As2 which shows a structural transition from tetragonal (T) to collapsed tetragonal(cT) phase at TcT=73 K. Upon entering the cT phase, drastic change characterized by the formation of a midinfrared peak near 3200 cm-1(0.4 eV) in the optical conductivity is observed.Analysis of the spectral weight reveals reduced electron correlation after the cT phase transition.Based on the calculated band structure and simulated optical conductivity, we attribute the new feature around 0.4 eV to the formation…
We report a high-pressure study of simultaneous low-temperature electrical resistivity and Hall effect measurements on high quality single-crystalline KFe2As2 using designer diamond anvil cell techniques with applied pressures up to 33 GPa. In the low pressure regime, we show that the superconducting transition temperature T_c finds a maximum onset value of 7 K near 2 GPa, in contrast to previous reports that find a minimum T_c and reversal of pressure dependence at this pressure. Upon applying higher pressures, this T_c is diminished until a sudden drastic enhancement occurs coincident with a…
We report high-pressure $^{77}$Se NMR studies on FeSe single crystals that reveal a prominent inhomogeneous NMR linewidth broadening upon cooling, with the magnetic field applied along the tetragonal [110] direction. The data indicate the existence of short-range-ordered, inhomogeneous electronic nematicity, which has surprisingly long time scales over milliseconds. The short-range order survives temperatures up to $8$ times the structural transition temperature, and remains robust against pressure, in contrast to the strong pressure-dependence of the orbital ordering, structural transition, a…
In several families of iron-based superconducting materials, a d-wave pairing instability may compete with the leading s-wave instability. Here we show that when both states have comparable free energies, superconducting and nematic degrees of freedom are strongly coupled. While nematic order causes a sharp non-analytic increase in $T_{c}$, nematic fluctuations can change the character of the s-wave to d-wave transition, favoring an intermediate state that does not break time-reversal symmetry but does break tetragonal symmetry. The coupling between superconductivity and nematicity is also man…
We present an optical spectroscopy study on P-doped CaFe$_2$As$_2$ which experiences a structural phase transition from tetragonal to collapsed tetragonal (cT) phase near 75 K. The measurement reveals a sudden reduction of low frequency spectral weight and emergence of a new feature near 3200 \cm (0.4 eV) in optical conductivity across the transition, indicating an abrupt reconstruction of band structure. The appearance of new feature is related to the interband transition arising from the sinking of hole bands near $Γ$ point below Fermi level in the cT phase, as expected from the density func…
We use angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations to study the electronic structure of CaFe$_2$As$_2$ in previously unexplored collapsed tetragonal (CT) phase. This unusual phase of the iron arsenic high temperature superconductors was hard to measure as it exists only under pressure. By inducing internal strain, via the post growth, thermal treatment of the single crystals, we were able to stabilize the CT phase at ambient-pressure. We find significant differences in the Fermi surface topology and band dispersion data from the more commo…
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-degenerac…
We report the electronic structure reconstruction of Ca$_{1-x}$Pr$_x$Fe$_2$As$_2$ ($x$ = 0.1 and 0.15) in the low temperature collapsed tetragonal (CT) phase observed by angle-resolved photoemission spectroscopy. Different from Ca(Fe$_{1-x}$Rh$_x$)$_2$As$_2$ and the annealed CaFe$_2$As$_2$ where all hole Fermi surfaces are absent in their CT phases, the cylindrical hole Fermi surface can still be observed in the CT phase of Ca$_{1-x}$Pr$_x$Fe$_2$As$_2$. Furthermore, we found at least three well separated electron-like bands around the zone corner in the CT phase of Ca$_{1-x}$Pr$_x$Fe$_2$As$_2$…
We present high-energy x-ray diffraction data under applied pressures up to p = 29 GPa, neutron diffraction measurements up to p = 1.1 GPa, and electrical resistance measurements up to p = 5.9 GPa, on SrCo2As2. Our x-ray diffraction data demonstrate that there is a first-order transition between the tetragonal (T) and collapsed-tetragonal (cT) phases, with an onset above approximately 6 GPa at T = 7 K. The pressure for the onset of the cT phase and the range of coexistence between the T and cT phases appears to be nearly temperature independent. The compressibility along the a-axis is the same…
Using electronic Raman spectroscopy, we report direct measurements of charge nematic fluctuations in the tetragonal phase of strain-free Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$ single crystals. The strong enhancement of the Raman response at low temperatures unveils an underlying charge nematic state that extends to superconducting compositions and which has hitherto remained unnoticed. Comparison between the extracted charge nematic susceptibility and the elastic modulus allows us to disentangle the charge contribution to the nematic instability, and to show that charge nematic fluctuations are we…
We have performed high-resolution angle-resolved photoemission spectroscopy on FeSe superconductor (Tc ~ 8 K), which exhibits a tetragonal-to-orthorhombic structural transition at Ts ~ 90 K. At low temperature we found splitting of the energy bands as large as 50 meV at the M point in the Brillouin zone, likely caused by the formation of electronically driven nematic states. This band splitting persists up to T ~ 110 K, slightly above Ts, suggesting that the structural transition is triggered by the electronic nematicity. We have also revealed that at low temperature the band splitting gives r…
The structural properties of LaRu$_2$P$_2$ under external pressure have been studied up to 14 GPa, employing high-energy x-ray diffraction in a diamond-anvil pressure cell. At ambient conditions, LaRu$_2$P$_2$ (I4/mmm) has a tetragonal structure with a bulk modulus of $B=105(2)$ GPa and exhibits superconductivity at $T_c= 4.1$ K. With the application of pressure, LaRu$_2$P$_2$ undergoes a phase transition to a collapsed tetragonal (cT) state with a bulk modulus of $B=175(5)$ GPa. At the transition, the c-lattice parameter exhibits a sharp decrease with a concurrent increase of the a-lattice pa…
An SDW antiferromagnetic (SDW-AF) low temperature phase transition is generally observe and the AF spin fluctuations are considered to play an important role for the superconductivity paring mechanism in FeAs superconductors. However, a similar magnetic phase transition is not observed in FeSe superconductors, which has caused considerable discussion. We report on the intrinsic electronic states of FeSe as elucidated by transport measurements under magnetic fields using a high quality single crystal. A mobility spectrum analysis, an ab initio method that does not make assumptions on the transp…
Structural and electronic characterization of (Ca0.67Sr0.33)Fe2As2 has been performed as a func- tion of pressure up to 12 GPa using conventional and designer diamond anvil cells. The compound (Ca0.67Sr0.33)Fe2As2 behaves intermediate between its end members-CaFe2As2 and SrFe2As2- displaying a suppression of magnetism and the onset of superconductivity. Like other members of the AEFe2As2 family, (Ca0.67Sr0.33)Fe2As2 undergoes a pressure-induced isostructural volume collapse, which we associate with the development of As-As bonding across the mirror plane of the structure. This collapsed tetrag…
A fundamental issue concerning iron-based superconductivity is the roles of electronic nematicity and magnetism in realising high transition temperature ($T_{\rm c}$). To address this issue, FeSe is a key material, as it exhibits a unique pressure phase diagram involving nonmagnetic nematic and pressure-induced antiferromagnetic ordered phases. However, as these two phases in FeSe overlap with each other, the effects of two orders on superconductivity remain perplexing. Here we construct the three-dimensional electronic phase diagram, temperature ($T$) against pressure ($P$) and isovalent S-su…
We present detailed electronic structure calculations for CaFe2As2. We investigate in particular the `collapsed' tetragonal and orthorhombic regions of the temperature-pressure phase diagram and find properties that distinguish CaFe2As2 from other Fe-pnictide compounds. In contrast to the tetragonal phase of other Fe-pnictides the electronic structure in the `collapsed' tetragonal phase of CaFe2As2 is found to be strongly 3D. We discuss the influence of these properties on the formation of superconductivity and in particular we find evidence that both magnetic and lattice interactions may be i…
Superconducting iron chalcogenide FeSe has the simplest crystal structure among all the Fe-based superconductors. Unlike other iron pnictides, FeSe exhibits no long range magnetic order accompanying the tetragonal-to-orthorhombic structural distortion, which raises the fundamental question about the role of magnetism and its associated spin fluctuations in mediating both nematicity and superconductivity. The extreme sensitivity of FeSe to external pressure suggests that chemical pressure, induced by substitution of Se by the smaller ion S, could also a be good tuning parameter to further study…
At ambient pressure CaFe2As2 has been found to undergo a first order phase transition from a high temperature, tetragonal phase to a low temperature orthorhombic / antiferromagnetic phase upon cooling through T ~ 170 K. With the application of pressure this phase transition is rapidly suppressed and by ~ 0.35 GPa it is replaced by a first order phase transition to a low temperature collapsed tetragonal, non-magnetic phase. Further application of pressure leads to an increase of the tetragonal to collapsed tetragonal phase transition temperature, with it crossing room temperature by ~ 1.7 GPa. …
We report synthesis, crystal structure and superconductivity in ThCr2Si2-type LaFe2As2 (La122). La122 was synthesized at 960°C for 1.5 h under a pressure of 3.4 GPa. An as-synthesized La122 (non-superconductor) had a collapsed tetragonal structure with a short c-axis length of 11.0144(4) Å as observed in CaFe2As2 under pressure. The collapsed tetragonal transformed into an uncollapsed tetragonal by annealing the as-synthesized La122 at 500°C. The c-axis length remarkably extended to 11.7317(4) Å and superconductivity emerged at 12.1 K in the uncollapsed tetragonal La122. A cylindrical hole-lik…
Electronic nematicity, a correlated state that spontaneously breaks rotational symmetry, is observed in several layered quantum materials. In contrast to their liquid-crystal counterparts, the nematic director cannot usually point in an arbitrary direction (XY nematics), but is locked by the crystal to discrete directions (Ising nematics),resulting in strongly anisotropic fluctuations above the transition. Here, we report on the observation of nearly isotropic XY-nematic fluctuations, via elastoresistance measurements, in hole-doped Ba$_{1-x}$Rb$_{x}$Fe$_{2}$As$_{2}$ iron-based superconductors…
Impurity scattering is found to lead to quasi-one dimensional nanoscale modulation of the local density of states in the iron pnictides and chalcogenides. This `quasiparticle interference' feature is remarkably similar across a wide variety of pnictide and chalcogenide phases, suggesting a common origin. We show that a unified understanding of the experiments can be obtained by simply invoking a four-fold symmetry breaking $d_{xz}-d_{yz}$ orbital splitting, of a magnitude already suggested by the experiments. This can explain the one-dimensional characteristics in the local density of states o…
Understanding the interplay between nematicity, magnetism and superconductivity is pivotal for elucidating the physics of iron-based superconductors. Here we use neutron scattering to probe magnetic and nematic orders throughout the phase diagram of NaFe$_{1-x}$Ni$_x$As, finding that while both static antiferromagnetic and nematic orders compete with superconductivity, the onset temperatures for these two orders remain well-separated approaching the putative quantum critical points. We uncover local orthorhombic distortions that persist well above the tetragonal-to-orthorhombic structural tran…
The angular-dependent magnetoresistance (AMR) of the ab plane is measured on the single crystals of FeSe1-xSx (x = 0, 0.07, 0.13 and 1) and FeSe1-yTey (y = 0.06, 0.61 and 1) at various temperatures under fields up to 9 T. A pronounced twofold-anisotropic carrier-scattering effect is identified by AMR, and attributed to a magnetic-field-induced spin nematicity that emerges from the tetragonal normal-state regime below a characteristic temperature Tsn. This magnetically polarized spin nematicity is found to be ubiquitous in the isoelectronic FeSe1-xSx and FeSe1-yTey systems, no matter whether th…
We demonstrate that in iron-based superconductors, the extended S_{+-} SC state coexists with the d_{x^2-y^2} state under generic conditions. The mixed S_{+-} + d_{x^2-y^2} SC is a natural nematic state in which the tetragonal symmetry C_4 is broken to C_2 explaining puzzling findings of nematic SC in FeSe films [Science 332, 1410 (2011)]. Moreover, we report the possibility of a first order transition at low-T from the nematic S_{+-} + d_{x^2-y^2} state to the pure d_{x^2-y^2} state induced by the Zeeman magnetic field proposing an original experimental strategy for identifying our mixed nema…
The pseudogap phenomenon in cuprates is the most mysterious puzzle in the research of high-temperature superconductivity. In particular, whether the pseudogap is associated with a crossover or phase transition has been a long-standing controversial issue. The tetragonal cuprate HgBa$_2$CuO$_{4+δ}$, with only one CuO$_2$ layer per primitive cell, is an ideal system to tackle this puzzle. Here, we measure the anisotropy of magnetic susceptibility within the CuO$_2$ plane with exceptionally high-precision magnetic torque experiments. Our key finding is that a distinct two-fold in-plane anisotropy…
Strongly interacting electrons can exhibit novel collective phases, among which the electronic nematic phases are perhaps the most surprising as they spontaneously break rotational symmetry of the underlying crystal lattice. The electron nematicity has been recently observed in the iron-pnictide and cuprate high-temperature superconductors. Whether such a tendency of electrons to self-organise unidirectionally has a common feature in these superconductors is, however, a highly controversial issue. In the cuprates, the nematicity has been suggested as a possible source of the pseudogap phase, w…
The large anisotropy in the electronic properties across a structural transition in several correlated systems has been identified as the key manifestation of electronic nematic order, breaking rotational symmetry. In this context, FeSe is attracting tremendous interest, since electronic nematicity develops over a wide range of temperatures, allowing accurate experimental investigation. Here we combine angle-resolved photoemission spectroscopy and theoretical calculations based on a realistic multi-orbital model to unveil the microscopic mechanism responsible for the evolution of the electroni…
The antiferromagnet CaFe$_2$As$_2$ does not become superconducting when subject to ideal hydrostatic pressure conditions, where crystallographic and magnetic states also are well defined. By measuring electrical resistivity and magnetic susceptibility under quasi-hydrostatic pressure, however, we find that a substantial volume fraction of the sample is superconducting in a narrow pressure range where collapsed tetragonal and orthorhombic structures coexist. At higher pressures, the collapsed tetragonal structure is stabilized, with the boundary between this structure and the phase of coexistin…
Superconductivity of high critical temperature ($T_{c}$) superconductors is usually realized through chemical dopant or application of pressure in a similar way to induce charge carriers of either electrons or holes into their parent compounds. For chemical doping, superconductivity behaves asymmetrically with the maximum $T_{c}$ often higher for optimal hole-doping than that of optimal electron-doping on the same parent compound. However, whether electron carriers could be in favour of higher $T_{c}$ than holes in such high-$T_{c}$ superconductors is unknown but attractive. Here we show that …
The driving forces behind electronic nematicity in the iron pnictides remain hotly debated. We use atomic-resolution variable-temperature scanning tunneling spectroscopy to provide the first direct visual evidence that local electronic nematicity and unidirectional antiferroic (stripe) fluctuations persist to temperatures almost twice the nominal structural ordering temperature in the parent pnictide NaFeAs. Low-temperature spectroscopic imaging of nematically-ordered NaFeAs shows anisotropic electronic features that are not observed for isostructural, non-nematic LiFeAs. The local electronic …
Magnetic interactions are generally believed to play a key role in mediating electron pairing for superconductivity in iron arsenides; yet their character is only partially understood. Experimentally, the antiferromagnetic (AF) transition is always preceded by or coincident with a tetragonal to orthorhombic structural distortion. Although it has been suggested that this lattice distortion is driven by an electronic nematic phase, where a spontaneously generated electronic liquid crystal state breaks the C4 rotational symmetry of the paramagnetic state, experimental evidence for electronic anis…
Single crystals of LaFeAsO were successfully grown out of KI flux. Temperature dependent electrical resistivity was measured with current flow along the basal plane, ρ_perpend(T), as well as with current flow along the crystallographic c-axis, ρ_parallel(T), the latter one utilizing electron beam lithography and argon ion beam milling. The anisotropy ratio was found to lie between ρ_parallel/ρ_perpend = 20 - 200. The measurement of ρ_perpend(T) was performed with current flow along the tetragonal [1 0 0] direction and along the [1 1 0] direction and revealed a clear in-plane anisotropy already…
The role of nematic order for the mechanism of high-temperature superconductivity is highly debated. In most iron-based superconductors (IBS) the tetragonal symmetry is broken already in the normal state, resulting in orthorhombic lattice distortions, static stripe magnetic order, or both. Superconductivity then emerges, at least at weak doping, already from the state with broken $C_4$ rotational symmetry. One of the few stoichiometric IBS, lithium iron arsenide, superconducts below 18 K and does not display either structural or magnetic transition in the normal state. Here we demonstrate, usi…
We have grown single crystal samples of Co substituted CaFe2As2 using an FeAs flux and systematically studied the effects of annealing/quenching temperature on the physical properties of these samples. Whereas the as-grown samples (quenched from 960C) all enter the collapsed tetragonal phase upon cooling, annealing/quenching temperatures between 350C and 800C can be used to tune the system to low temperature antiferromagnetic/orthorhomic or superconducting states as well. The progression of the transition temperature versus annealing/quenching temperature (T-T$_{anneal}$) phase diagrams with i…
