Polarized inelastic neutron scattering experiments were performed to study magnetic excitations in the normal and superconducting phases of Co-underdoped BaFe$_2$As$_2$, which exhibits coexistence of antiferromagnetic order and superconductivity. In the normal state the antiferromagnetic order results in broadened spin gaps opening in all three spin directions that are reminiscent of the magnetic response in pure antiferromagnetic BaFe$_2$As$_2$. In particular longitudinal excitations exhibit a large gap. In the superconducting state we find two distinct resonance excitations, which both are anisotropic in spin-space, and which both do not appear in the longitudinal polarization channel. This behavior contrasts to previous polarized neutron results on samples near optimum or higher doping. The gap in the longitudinal fluctuations arising from the antiferromagnetic order seems to be sufficiently larger than twice the superconducting gap to suppress any interplay with the superconducting state. This suppressed low-energy weight of longitudinal fluctuations can explain the reduced superconducting transition temperature in underdoped BaFe$_2$As$_2$ and indicates that the coexistence of antiferromagnetism and superconductivity occurs locally.
A nematic quantum critical point is anticipated to exist in the superconducting dome of some high-temperature superconductors. The nematic order competes with the superconducting order and hence reduces the superconducting condensate at $T = 0$. Moreover, the critical fluctuations of nematic order can excite more nodal quasiparticles out of the condensate. We address these two effects within an effective field theory and show that superfluid density $ρ^s(T)$ and superconducting temperature $T_c$ are both suppressed strongly by the critical fluctuations. The strong suppression of superconductiv…
In underdoped YBa_2Cu_3O_x (YBCO) with x = 6.63, the opening of the pseudogap at T^* ~ 160 K has a strong effect on the Hall angle tan(theta). While the Hall response is significantly reduced, the diagonal current is relatively unaffected. The Hall conductivity suppression continues deep into the flux-flow state (from T_c to 40 K), as an anomalous suppression of the vortex Hall current.
Generally strong charge and magnetic inhomogeneities are observed in NQR/NMR experiments on underdoped cuprates. It is not the case for the underdoped HgBa$_2$CuO$_{4+δ}$, the most symmetric and highest T$_c$ single layer cuprate, whose magnetic inhomogeneity is strongly suppressed. Also neutron scattering experiments reveal a unique pair of weakly dispersive magnetic modes in this material. We propose that these special properties stem from the symmetric positioning of the O-dopants between adjacent CuO$_2$ layers that lead to a strong superexchange interaction between a pair of hole spins. I…
The normal state of optimally doped cuprates is dominated by the "strange metal" phase that shows a linear temperature ($T$) dependence of the resistivity persisting down to the lowest $T$. For underdoped cuprates this behavior is lost below the pseudogap temperature $T^*$, where Charge Density Waves (CDW) together with other intertwined local orders characterize the ground state. Here we show that the $T$-linear resistivity of highly strained, ultrathin and underdoped YBa$_2$Cu$_3$O$_{7-δ}$ films is restored when the CDW amplitude, detected by Resonant Inelastic X-ray scattering, is suppresse…
We use inelastic neutron scattering to study the fate of the two spin resonance modes in underdoped superconducting NaFe$_{1-x}$Co$_x$As ($x=0.0175$) under applied magnetic fields. While an applied in-plane magnetic field of $B=12$ T only modestly suppresses superconductivity and enhances static antiferromagnetic order, the two spin resonance modes display disparate responses. The spin resonance mode at higher energy is mildly suppressed, consistent with the field effect in other unconventional superconductors. The spin resonance mode at lower energy, on the other hand, is almost completely su…
Low-temperature (22~K) irradiation with 2.5~MeV electrons was used to study the competition between stripe ${\rm C_2}$ and tetragonal ${\rm C_4}$ antiferromagnetic phases which exist in a narrow doping range around $x=$0.25 in hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$. In nearby compositions outside of this range, at $x=$0.22 and $x=$0.19, the temperatures of both the concomitant orthorhombic/stripe antiferromagnetic transition $T_{\rm C2}$ and the superconducting transition $T_{\rm c}$ are monotonically suppressed by added disorder at similar rates of about 0.1~K/$μΩ$cm, as revealed through usin…
Polarized and unpolarized triple-axis spectrometry has been used to study an underdoped YBa_2Cu3O6.6. Our results indicate that spin excitations in the superconducting state are essentially the same as those in the fully doped material except that the unusual 41 meV resonance is observed at 34.8 meV. The normal state spin excitations are characterized by a weakly energy-dependent continuum whose temperature dependence shows the clear signature of a superconducting gap at Tc. The enhancement at the resonance is accompanied by a suppression of magnetic fluctuations at both higher and lower energ…
We present x-ray powder diffraction (XRPD) and neutron diffraction measurements on the slightly underdoped iron pnictide superconductor Ba(1-x)K(x)Fe2As2, Tc = 32K. Below the magnetic transition temperature Tm = 70K, both techniques show an additional broadening of the nuclear Bragg peaks, suggesting a weak structural phase transition. However, macroscopically the system does not break its tetragonal symmetry down to 15 K. Instead, XRPD patterns at low temperature reveal an increase of the anisotropic microstrain proportionally in all directions. We associate this effect with the electronic ph…
We propose a hybridization phenomenology to describe the pseudogap state of the underdoped cuprates. We show how a momentum independent pseudogap opens asymmetrically from the Fermi-surface but symmetric to the zeroes of the hybridized bonding dispersion, which results in false d-wave characteristics of the pseudogap at the Fermi level. By comparing against a d-wave form factor we illustrate the difficulty in identifying a momentum independent order in momentum averaged quantities such as the electronic Raman response. We identify a suppression in the single-particle density of states which pr…
We characterize the spontaneous magnetic field, and determine the associated temperature Tg, in the superconducting state of Ca(x)La(1-x)Ba(1.75-x)La(0.25+x)Cu(3)O(y) using zero and longitudinal field MuSR measurements for various values of x and y. Our major findings are: (I) Tg and Tc are controlled by the same energy scale, (II) the phase separation between hole poor and hole rich regions is a microscopic one, and (III) spontaneous magnetic fields appear gradually with no moment size evolution.
High temperature superconductivity emerges in the vicinity of competing strongly correlated phases. In the iron-based superconductor $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$, the superconducting state shares the composition-temperature phase diagram with an electronic nematic phase and an antiferromagnetic phase that break the crystalline rotational symmetry. Symmetry considerations suggest that anisotropic strain can enhance these competing phases and thus suppress the superconductivity. Here we study the effect of anisotropic strain on the superconducting transition in single crystals of $Ba(Fe_{1-x}C…
Measurements of thermal conductivity ($κ$) versus temperature and doping for several cuprate superconductors are discussed. Suppressed values of the normal-state $κ$ and the slope change in $κ$ at $T_c$, observed near 1/8 doping in both YBa$_2$Cu$_3$O$_{6+x}$ and Hg cuprates, are attributed to local lattice distortions and the suppression of the superconducting condensate, respectively. Both phenomena are proposed to arise from small domains of localized planar holes, presumably a manifestation of phase separation. It is suggested that the phase behavior of $κ$ reflects stripe dynamics and the…
The normal state in the hole underdoped copper oxide superconductors has proven to be a source of mystery for decades. The measurement of a small Fermi surface by quantum oscillations on suppression of superconductivity by high applied magnetic fields, together with complementary spectroscopic measurements in the hole underdoped copper oxide superconductors, point to a nodal electron pocket from charge order in YBa2Cu3O6+x. Here we report quantum oscillation measurements in the closely related stoichiometric material YBa2Cu4O8, which reveal similar Fermi surface properties to YBa2Cu3O6+x, desp…
An intriguing aspect of unconventional superconductivity is that it always appears in the vicinity of other competing phases, whose suppression brings the full emergence of superconductivity. In the iron-pnictides, these competing phases are marked by a tetragonal-to-orthorhombic structural transition and a collinear spin-density-wave (SDW) transition. There has been macroscopic evidence for competition between these phases and superconductivity as the magnitude of both the orthorhombicity and magnetic moment are suppressed in the superconducting state. Here, using angle-resolved photoemission…
We use quantum oscillation measurements to distinguish between spin and orbital components of the lowest energy quasiparticle excitations in YBa2Cu3O6.54, each of which couple differently to a magnetic field. Our measurements reveal the phase of the observed quantum oscillations to remain uninverted over a wide angular range, indicating that the twofold spin degeneracy of the Landau levels is virtually unaltered by the magnetic field. The inferred suppression of the spin degrees of freedom indicates a spin density-wave is responsible for creation of the small Fermi surface pockets in underdope…
The recent discovery of superconductivity in infinite-layer nickelates generates tremendous research endeavors, but the ground state of their parent compounds is still under debate. Here, we report experimental evidences for the dominant role of Kondo scattering in the underdoped Nd1-xSrxNiO2 thin films. A resistivity minimum associated with logarithmic temperature dependence in both longitudinal and Hall resistivities are observed in the underdoped Nd1-xSrxNiO2 samples before the superconducting transition. A linear scaling behavior $σ_{xy}^{AHE}\simσ_{xx}$ between anomalous Hall conductivity…
We report the first NMR investigation of spin dynamics in the overdoped non-superconducting regime of Ba(Fe[1-x]Co[x])2As2 up to x =0.26. We demonstrate that the absence of inter-band transitions with large momentum transfer Q(AF) ~ (pi, 0) between the hole and electron Fermi surfaces results in complete suppression of antiferromagnetic spin fluctuations for x > 0.15. Our experimental results provide direct evidence for a correlation between Tc and the strength of Q(AF) antiferromagnetic spin fluctuations.
We analyze how disorder affects the transition temperature $T_{c}$ of the $s^{+-}$superconducting state in the iron pnictides. The conventional wisdom is that $T_{c}$ should rapidly decrease with increasing inter-band non-magnetic impurity scattering, but we show that this behavior holds only in the overdoped region of the phase diagram. In the underdoped regime, where superconductivity emerges from a pre-existing magnetic state, disorder gives rise to two competing effects: breaking of the Cooper pairs, which tends to reduce $T_{c}$, and suppression of the itinerant magnetic order, which tend…
We investigate the nature of the SDW (Spin Density Wave) transition in the underdoped regime of an iron-based high Tc superconductor Ba(Fe1-xCox)2As2 by 75As NMR, with primary focus on a composition with x = 0.02 (T_SDW = 99 K).We demonstrate that critical slowing down toward the three dimensional SDW transition sets in at the tetragonal to orthorhombic structural phase transition, Ts = 105 K, suggesting strong interplay between structural distortion and spin correlations. In the critical regime between Ts and T_SDW, the dynamical structure factor of electron spins S(q,Wn) measured with the lo…
We introduce a simple phenomenological form for the self-energy which allows us to extract important information from angle resolved photoemission data on the high Tc superconductor Bi2212. First, we find a rapid suppression of the single particle scattering rate below Tc for all doping levels. Second, we find that in the overdoped materials the gap Delta at all k-points on the Fermi surface has significant temperature dependence and vanishes near Tc. In contrast, in the underdoped samples such behavior is found only at k-points close to the diagonal. Near (pi,0), Delta is essentially T-indepe…
Using neutron scattering we have determined the magnetic structure and fluctuations in the YBa2Cu3O6.35 superconductor (Tc=18 K). The long-range ordered collinear spins of the insulating antiferromagnet are replaced by a commensurate central mode arising from slow, isotropically polarized, short-range spin correlations. The inelastic spectrum up to 30 meV is broad in wave vector and commensurate. In contrast to the the resonance peak of higher Tc superconductors, the spins exhibit a single overdamped spectrum whose rate of relaxation decreases on cooling and saturates at 5 meV below 50 K. As t…
We report properties of topological insulator - ferromagnet - superconductor trilayers comprised of thin films of 20 nm thick $\rm Bi_2Se_3$ on 10 nm $\rm SrRuO_3$ on 30 nm $\rm YBa_2Cu_3O_x$. As deposited trilayers are underdoped and have a superconductive transition with $\rm T_c$ onset at 75 K, zero resistance at 65 K, $\rm T_{Cueri}$ at 150 K and $\rm T^*$ of about 200 K. Further reannealing under vacuum yields the 60 K phase of $\rm YBa_2Cu_3O_x$ which still has zero resistance below about 40 K. Only when $10\times 100$ micro-bridges were patterned in the trilayer, some of the bridges sho…
The central puzzle of the cuprate superconductors at low hole density is the nature of the pseudogap regime. It has a number of seemingly distinct experimental signatures: a suppression of the paramagnetic spin susceptibility at high temperatures, low energy electronic excitations that extend over arcs in the Brillouin zone, X-ray detection of charge density wave order at intermediate temperatures, and quantum oscillations at high magnetic fields and low temperatures. We show that a model of competing charge density wave and superconducting orders provides a unified description of the intermed…
Zero-field and longitudinal-field muon-spin-relaxation measurements have been performed in partially Fe-substituted La2-xSrxCu1-yFeyO4 in a wide range of hole concentration, to investigate the magnetic state induced by the Fe substitution recently suggested from the neutron-scattering measurements [Phys. Rev. Lett. 107, 127002 (2011)]. It has been found that the magnetic transition temperature is notably enhanced through the 1% Fe substitution in a wide range of hole concentration where superconductivity appears in Fe-free La2-xSrxCuO4. In the underdoped regime, the Fe-induced magnetic order c…
We measured the optical conductivity of superconducting single crystals of Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ with $x$ ranging from 0.40 (optimal doping, $T_c = 39$ K) down to 0.20 (underdoped, $T_c = 16$ K), where a magnetic order coexists with superconductivity. In the normal state, the low-frequency optical conductivity can be described by an incoherent broad Drude component and a coherent narrow Drude component: the broad one is doping-independent, while the narrow one shows strong scattering in the heavily underdoped compound. In the superconducting state, the formation of the condensate l…
We have studied in fields up to 60T the variation of the transverse magnetoresistance (MR) of underdoped YBCO6.6 crystals either pure or with Tc reduced down to 3.5K by electron irradiation. We evidence that the normal state MR is restored above a threshold field H'c(T), which is found to vanish at T'c>>Tc. In the pure YBCO6.6 sample a 50 Tesla field is already required to completely suppress the superconducting fluctuations at Tc. While disorder does not depress the pseudogap temperature, it reduces drastically the phase coherence established at Tc and weakly H'c(0), T'c and the onset Tnu of …
We report the results of Raman scattering experiments on single crystals of La(2-x)Sr(x)CuO(4) [La214] as a function of temperature and doping. In underdoped compounds low-energy B1g spectral weight is depleted in association with the opening of a pseudogap on regions of the Fermi surface located near (pi, 0) and (0, pi). The magnitude of the depletion increases with decreasing doping, and in the most underdoped samples, with decreasing temperature. The spectral weight that is lost at low-energies (omega < 800 cm-1) is transferred to the higher energy region normally occupied by multi-magnon s…
Neutron diffraction and high-resolution x-ray diffraction studies find that, similar to the closely related underdoped Ba(Fe[1-x]Cox)2As2 superconducting compounds, Ba(Fe0.961Rh0.039)2As2 shows strong evidence of competition and coexistence between superconductivity and antiferromagnetic order below the superconducting transition, Tc = 14 K. The transition temperatures for both the magnetic order and orthorhombic distortion are in excellent agreement with those inferred from resistivity measurements, and both order parameters manifest a distinct decrease in magnitude below Tc. These data sugge…
Temperature-dependent inter-plane resistivity, $ρ_c(T)$, was measured in hole-doped iron-arsenide superconductor (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ over a doping range from parent compound to optimal doping $T_c\approx 38~K$, $0\leq x \leq 0.34$. Measurements were undertaken on high-quality single crystals grown from FeAs flux. The coupled magnetic/structural transition at $T_{SM}$ leads to clear accelerated decrease of $ρ_c(T)$ on cooling in samples with $T_c <$26~K ($x <0.25$). This decrease in hole-doped material is in notable contrast to an increase in $ρ_c(T)$ in the electron-doped Ba(Fe$_{1-x…
We reveal the full energy-momentum structure of the pseudogap of underdoped high-Tc cuprate superconductors. Our combined theoretical and experimental analysis explains the spectral-weight suppression observed in the B2g Raman response at finite energies in terms of a pseudogap appearing in the single-electron excitation spectra above the Fermi level in the nodal direction of momentum space. This result suggests an s-wave pseudogap (which never closes in the energy-momentum space), distinct from the d-wave superconducting gap. Recent tunneling and photoemission experiments on underdoped cuprat…
We generalize the theory of Cooper pairing by spin excitations in the metallic antiferromagnetic state to include situations with electron and/or hole pockets. We show that Cooper pairing arises from transverse spin waves and from gapped longitudinal spin fluctuations of comparable strength. However, each of these interactions, projected on a particular symmetry of the superconducting gap, acts primarily within one type of pocket. We find a nodeless $d_{x^2-y^2}$-wave state is supported primarily by the longitudinal fluctuations on the electron pockets, and both transverse and longitudinal flu…
The cuprates exhibit a prominent charge-density-wave (CDW) instability with wavevector along [100], i.e., the Cu-O bond direction. Whereas CDW order is most prominent at moderate doping and low temperature, there exists increasing evidence for dynamic charge correlations throughout a large portion of the temperature-doping phase diagram. In particular, signatures of incipient charge order have been observed as phonon softening and/or broadening near the CDW wavevector approximately half-way through the Brillouin zone. Most of this work has focused on moderately-doped cuprates, for which the CD…
Scanning tunneling spectroscopy (STS) studies reveal long-range (~100 nm) spatial homogeneity in optimally and underdoped superconducting YBa_2Cu_3O_{7-δ} (YBCO) single crystals and thin films, and macroscopic spatial modulations in overdoped (Y_{0.7}Ca_{0.3})Ba_2Cu_3O_{7-δ} (Ca-YBCO) epitaxial films. In contrast, STS on an optimally doped YBa_2(Cu_{0.9934}Zn_{0.0026}Mg_{0.004})_3O_{6.9} single crystal exhibits strong spatial modulations and suppression of superconductivity over a microscopic scale near the Zn or Mg impurity sites, and the global pairing potential is also reduced relative to t…
We studied low-frequency spin dynamics near the impurity-induced superconductor-to-insulator transition for underdoped high-Tc superconductor YBa2(Cu1-xMx)4O8 (M=Ni, Zn) using the Cu nuclear quadrupole resonance (NQR) spin-echo technique. We observed remarkable suppression of the normal-state pseudo spin-gap and a loss of Cu NQR spectrum intensity at low temperatures around the critical impurity concentration.
We investigate parity-mixing superconductivity in the two-dimensional Hubbard model with Rashba spin-orbit coupling, using Cellular Dynamical Mean-Field Theory (CDMFT). A superconducting state with mixed singlet $d$-wave and triplet $p$-wave character is found in a wide range of doping. The singlet component decreases with the amplitude of the Rashba spin-orbit coupling, whereas the triplet component increases, but both disappear at about 20\% doping. The effect of a Zeeman field is also investigated; it tends to suppress both types of superconductivity, but induces nontrivial topological prop…
Critical behavior of the infrared reflectivity of RuSr_2GdCu_2O_8 ceramics is observed near the superconducting T_{SC} = 45 K and magnetic T_M = 133 K transition temperatures. The optical conductivity reveals the typical features of the c-axis optical conductivity of strongly underdoped multilayer superconducting cuprates. The transformation of the Cu-O bending mode at 288 cm^{-1} to a broad absorption peak at the temperatures between T^* = 90 K and T_{SC} is clearly observed, and is accompanied by the suppression of spectral weight at low frequencies. The correlated shifts to lower frequencie…
We report inelastic neutron scattering on single crystals of the bilayer cuprate family La$_{2-x}$Ca$_{1+x}$Cu$_{2}$O$_{6+δ}$, including two crystals made superconducting (transitions at 45 and 55 K) by high-pressure annealing in an oxygen-containing atmosphere. The magnetic excitations in the non-superconducting crystal have a similar temperature-dependence as those in weakly hole-doped cuprates. In the superconducting crystals, there is a near-uniform suppression of the magnetic spectral weight with increasing temperature; in particular, there are no signs of a spin gap or "resonance" peak. …
The longitudinal in-plane magnetoresistance (LMR) has been measured in different Ba(Fe_(1-x)Co_x)2As2 single crystals and in LiFeAs. For all these compounds, we find a negative LMR in the paramagnetic phase whose magnitude increases as H^2. We show that this negative LMR can be readily explained in terms of suppression of the spin fluctuations by the magnetic field. In the Co-doped samples, the absolute value of the LMR coefficient is found to decrease with doping content in the paramagnetic phase. The analysis of its T dependence in an itinerant nearly antiferromagnetic Fermi liquid model evi…
We study out-of-equilibrium transport in disordered superconductors close to the superconducting transition. We consider a thin film connected by resistive tunnel interfaces to thermal reservoirs having different chemical potentials and temperatures. The nonequilibrium longitudinal current-current correlation function is calculated within the nonlinear sigma model description and nonlinear dependence on temperatures and chemical potentials is obtained. Different contributions are calculated, originating from the fluctuation-induced suppression of the quasiparticle density of states, Maki- Thom…
We find excitations lower in energy than known phonon modes in underdoped La$\_{2-x}$Sr$\_x$CuO$\_{4+δ}$ (x=0.08), with both inelastic X-Ray scattering (IXS) and inelastic neutron scattering (INS). A non dispersive excitation at 9 meV is identified and is also seen by INS in (La,Nd)$\_{2-x}$Sr$\_x$CuO$\_{4+δ}$, with 40$\%$ Nd substitution. INS also identifies a still lower energy dispersive mode at low q in the Nd free sample. These modes are clearly distinct from the longitudinal acoustic phonon and correspond in energy to the Zone Centre modes measured by optical spectroscopy and associated …
We use inelastic neutron scattering to systematically investigate the Ni-doping evolution of the low-energy spin excitations in BaFe2-xNixAs2 spanning from underdoped antiferromagnet to overdoped superconductor (0.03< x < 0.18). In the undoped state, the low-energy (<80 meV) spin waves of BaFe2As2 form transversely elongated ellipses in the [H, K] plane of the reciprocal space. Upon Ni-doping, the c-axis magnetic exchange coupling is rapidly suppressed and the momentum distribution of spin excitations in the [H, K] plane is enlarged in both the transverse and longitudinal directions with respe…
Effects of high-pressure synthesis on phase formation and superconducting properties of PrFeAsO1-xFx
Institute of High Pressure Physics (IHPP), Polish Academy of Sciences（波兰科学院高压物理研究所）；Faculty of Physics, Warsaw University of Technology（华沙理工大学物理学院）；Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）
