We investigate the electronic specific heat of overdoped BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ single crystals in the superconducting state using high-resolution nanocalorimetry. From the measurements, we extract the doping dependence of the condensation energy, superconducting gap $Δ$, and related microscopic parameters. We find that the anomalous scaling of the specific heat jump $ΔC \propto T_{\mathrm{c}}^3$, found in many iron-based superconductors, in this system originates from a $T_\mathrm{c}$-dependent ratio $Δ/k_\mathrm{B}T_\mathrm{c}$ in combination with a doping-dependent density of states $N(\varepsilon_\mathrm{F})$. A clear enhancement is seen in the effective mass $m^{*}$ as the composition approaches the value that has been associated with a quantum critical point at optimum doping. However, a simultaneous increase in the superconducting carrier concentration $n_\mathrm{s}$ maintains the superfluid density, yielding an apparent penetration depth $λ$ that decreases with increasing $T_\mathrm{c}$ without sharp divergence at the quantum critical point. Uemura scaling indicates that $T_\mathrm{c}$ is governed by the Fermi temperature $T_\mathrm{F}$ for this multi-band system.
We use polarized inelastic neutron scattering to study low-energy spin excitations and their spatial anisotropy in electron-overdoped superconducting BaFe$_{1.85}$Ni$_{0.15}$As$_{2}$ ($T_c=14$ K). In the normal state, the imaginary part of the dynamic susceptibility, $χ^{\prime\prime}(Q,ω)$, at the antiferromagnetic (AF) wave vector $Q=(0.5,0.5,1)$ increases linearly with energy for $E\le 13$ meV. Upon entering the superconducting state, a spin gap opens below $E\approx 3$ meV and a broad neutron spin resonance appears at $E\approx 7$ meV. Our careful neutron polarization analysis reveals that…
Using multiple Andreev reflection (MAR) spectroscopy, we studied superconductor - normal metal - superconductor (SnS) semiballistic contacts with incoherent transport in overdoped pnictide superconductors BaFe$_{1.86}$Ni$_{0.14}$As$_2$ with critical temperature $T_c \approx 12$ K. We directly determined an anisotropic large gap with the characteristic ratios $2Δ_L^{\rm out}(0)/k_BT_c \approx 6$ and $2Δ_L^{\rm in}(0)/k_BT_c \approx 4$, almost isotropic small gap with $2Δ_S(0)/k_BT_c \approx 2$, and the temperature dependence of the resolved superconducting order parameters. Above the large gap …
We report on specific heat measurements on clean overdoped $\mathrm{BaFe_{2}(As_{1-x}P_x)_2}$ single crystals performed with a high resolution membrane-based nanocalorimeter. A nonzero residual electronic specific heat coefficient at zero temperature $γ_\mathrm{r}={C/T}|_{T \to 0}$ is seen for all doping compositions, indicating a considerable fraction of the Fermi surface ungapped or having very deep minima. The remaining superconducting electronic specific heat is analyzed through a two-band s-wave $α$ model in order to investigate the gap structure. Close to optimal doping we detect a singl…
The in-plane thermal conductivity $κ$ of overdoped FeAs-based superconductor BaFe$_{1.73}$Co$_{0.27}$As$_2$ ($T_c$ = 8.1 K) single crystal was measured down to 80 mK. In zero field, the residual linear term $κ_0/T$ is negligible, suggesting a nodeless superconducting gap in the $ab$-plane. In magnetic field, $κ_0/T$ increases rapidly, very different from that of conventional s-wave superconductors. This anomalous $κ_0/T(H)$ may reveal an exotic superconducting gap structure in overdoped BaFe$_{1.73}$Co$_{0.27}$As$_2$: the vanishing hole ($β$) pocket has a much larger gap than the electron ($γ$…
Low temperature specific heat has been measured in optimally doped and highly overdoped non-superconducting BaFe$_{2-x}$TM$_x$As$_{2}$ ($TM$ = Co and Ni) single crystals. By using the data of the overdoped samples, we successfully removed the phonon contribution of the optimally doped ones, and derived the electronic specific heat coefficient $γ_e$. Remarkably, we found a continuing temperature dependent $γ_e(T)$ which follows the quadratic relation $γ_e=γ_0+αT^2$ in the low temperature limit. Together with the very small residual term $γ_0$, linear magnetic field dependence of $γ_e$, it is co…
We use elastic and inelastic neutron scattering to systematically investigate the evolution of the low-energy spin excitations of the iron arsenide superconductor BaFe2-xNixAs2 as a function of nickel doping x. In the undoped state, BaFe2As2 exhibits a tetragonal-to-orthorhombic structural phase transition and simultaneously develops a collinear antiferromagnetic (AF) order below TN = 143 K. Upon electron-doping of x = 0.075 to induce bulk superconductivity with Tc = 12.3 K, the AF ordering temperature reduces to TN = 58 K.We show that the appearance of bulk superconductivity in BaFe1.925Ni0.0…
In order to establish the doping dependence of the critical current properties in the iron-based superconductors, the in-plane critical current density (Jc) of BaFe2As2-based superconductors, Ba1-xKxFe2As2 (K-Ba122), Ba(Fe1-xCox)2As2 (Co-Ba122), and BaFe2(As1-xPx)2 (P-Ba122) in a wide range of doping concentration (x) was investigated by means of magnetization hysteresis loop (MHL) measurements on single-crystal samples. Depending on the dopant elements and their concentration, Jc exhibits a variety of magnetic-field (H) and temperature (T) dependences. (1) In the case of K-Ba122, MHL of the u…
The disordered flux line lattice in single crystals of the slightly overdoped aFe_{2-x}Co_xAs_2 (x = 0.19, Tc = 23 K) superconductor is studied by magnetization measurements, small-angle neutron scattering (SANS), and magnetic force microscopy (MFM). In the whole range of magnetic fields up to 9 T, vortex pinning precludes the formation of an ordered Abrikosov lattice. Instead, a vitreous vortex phase (vortex glass) with a short-range hexagonal order is observed. Statistical processing of MFM datasets lets us directly measure its radial and angular distribution functions and extract the radial…
A series of high quality BaFe$_{2-x}$Ni$_x$As$_2$ pnictide superconductors were studied using magnetic relaxation and isothermal magnetic measurements in order to study the second magnetization peak (SMP) and critical current behaviour in Ni-doped 122 family. The temperature dependence of the magnetic relaxation rate suggests a pinning crossover, whereas, it's magnetic field dependence hints a vortex-lattice structural phase-transition. The activation energy ($U$) estimated using the magnetic relaxation data was analyzed in detail for slightly-underdoped, slightly-overdoped and an overdoped sa…
The superconducting fluctuations well inside the normal state of Fe-based superconductors were studied through measurements of the in-plane paraconductivity and magnetoconductivity in high quality BaFe(2-x)NixAs2 crystals with doping levels from the optimal (x=0.10) up to the highly overdoped (x=0.20). These measurements, performed in magnetic fields up to 9 T perpendicular to the ab (Fe) layers, allowed a reliable check of the applicability to iron-based superconductors of Ginzburg-Landau approaches for 3D anisotropic compounds, even at high reduced temperatures and magnetic fields. Our resul…
We propose a phenomenological model for high-$T_{c}$ superconductors (HTSC) assuming: (1) a microscopic phase separation between superconducting and normal-metal areas in the overdoped region; and (2) existence of a homogeneous superconducting phase only below the pseudo-gap $T^{*}$ line, which shows a sharp reduction towards $T^{*}\sim 0$ at a mildly overdoped critical concentration $x_{c}$. This model explains anomalous doping and temperature dependences of $n_{s}/m^{*}$ (superconducting carrier density / effective mass) observed in several overdoped HTSC systems. We point out an analogy to …
We performed polarization- and photon-energy-dependent angle-resolved photoemission spectroscopy of a slightly overdoped iron pnictide superconductor, BaFe$_{1.8}$Co$_{0.2}$As$_{2}$, to clarify the three-dimensional electronic structure including its orbital characters at the Brillouin zone center. Two hole Fermi surfaces (FSs) with $d_{xz/yz}$ and $d_{xy/x^2-y^2}$ orbitals were observed but $d_{z^2}$ hole FS, which has nodes according to a theory of the spin-fluctuation superconductivity mechanism, did not appear. These results suggest that no node will appear at hole FSs at the zone center.
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…
We report a systematic investigation on c-axis point-contact Andreev reflection (PCAR) in BaFe$_{2-x}$Ni$_x$As$_2$ superconducting single crystals from underdoped to overdoped regions (0.075 $\leq x\leq 0.15$). At optimal doping ($x=0.1$) the PCAR spectrum feature the structures of two superconducting gap and electron-boson coupling mode. In the $s\pm$ scenario, quantitative analysis using a generalized Blonder-Tinkham-Klapwijk (BTK) formalism with two gaps: one isotropic and another angle dependent, suggest a nodeless state in strong-coupling limit with gap minima on the Fermi surfaces. Upon …
We have systematically studied the low-temperature specific heat of the BaFe$_{2-x}$Ni$_x$As$_2$ single crystals covering the whole superconducting dome. Using the nonsuperconducting heavily overdoped x = 0.3 sample as a reference for the phonon contribution to the specific heat, we find that the normal-state electronic specific heats in the superconducting samples may have a nonlinear temperature dependence, which challenges previous results in the electron-doped Ba-122 iron-based superconductors. A model based on the presence of ferromagnetic spin fluctuations may explain the data between x …
The coexistence of magnetism and superconductivity in the isovalent-P-substituted BaFe$_2$(As$_{1-x}$P$_x$)$_2$ has been investigated microscopically by $^{31}$P-NMR measurements. We found that superconducting (SC) transition occurs in a magnetic region with static ordered moments and that the moments are reduced below the SC transition temperature $T_{\rm c}$ in the samples near the phase boundary of magnetism and superconductivity. Our results indicate that magnetism and superconductivity coexist spatially but compete with each other on the same Fermi surfaces. The coexistence state is quali…
We report elastic neutron scattering and transport measurements on the Ni and Cr equivalently doped iron pnictide BaFe$_{2-2x}$Ni$_{x}$Cr$_{x}$As$_{2}$. Compared with the electron-doped BaFe$_{2-x}$Ni$_{x}$As$_{2}$, the long-range antiferromagnetic (AF) order in BaFe$_{2-2x}$Ni$_{x}$Cr$_{x}$As$_{2}$ is gradually suppressed with vanishing ordered moment and Néel temperature near $x= 0.20$ without the appearance of superconductivity. A detailed analysis on the transport properties of BaFe$_{2-x}$Ni$_{x}$As and BaFe$_{2-2x}$Ni$_{x}$Cr$_{x}$As$_{2}$ suggests that the non-Fermi-liquid behavior asso…
We report on the nonequilibrium quasiparticle dynamics in BaFe$_2$As$_2$ on both the hole doped (Ba$_{1-x}$K$_x$Fe$_2$As$_2$) and electron doped (BaFe$_{2-y}$Co$_y$As$_2$) sides of the phase diagram using ultrafast pump-probe spectroscopy. Below $T_c$, measurements conducted at low photoinjected quasiparticle densities in the optimally and overdoped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ samples reveal two distinct relaxation processes: a fast component whose decay rate increases linearly with excitation density and a slow component with an excitation density independent decay rate. We argue that these t…
Temperature-dependent inter-plane resistivity, $ρ_c(T)$, was measured for the iron-based superconductor BaFe$_2$(As$_{1-x}$P$_x$)$_2$ over a broad isoelectron phosphorus substitution range from $x$=0 to $x$=0.60, from non-superconducting parent compound to heavily overdoped superconducting composition with $T_c\approx 10 K$. The features due to structural and magnetic transitions are clearly resolved in $ρ_c(T)$ of the underdoped crystals. A characteristic maximum in $ρ_c(T)$, found in the parent BaFe$_2$As$_2$ at around 200 K, moves rapidly with phosphorus substitution to high temperatures. A…
We report an $^{75}$As NMR study of BaFe$_2$As$_2$ in both single crystals and polycrystal forms. We find that Sn impurities in the single crystal dramatically alter the low energy spin fluctuations and suppress the ordering temperature from 138 K to 85 K. In contrast to Sn-free samples, we find that the temperature dependence of the $^{75}$As NMR spectra and spin lattice relaxation rates reveal a second order phase transition to a state of incommensurate magnetic order.
In order to investigate the inhomogeneity of the superconducting (SC) state in the overdoped high-$T_{\rm c}$ cuprates, we have measured the magnetic susceptibility, $χ$, of La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) single crystals in the overdoped regime in magnetic fields parallel to the c-axis up to 7 T on warming after zero-field cooling. It has been found for $x$ = 0.198 and 0.219 that the temperature dependence of $χ$ in 1 T shows a plateau, that is, $χ$ is almost independent of temperature in a moderate temperature-range in the SC state. Moreover, a so-called second peak in the magnetization curve…
We present a comprehensive overview of vortex pinning in single crystals of the isovalently substituted iron-based superconductor BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$, a material that qualifies as an archetypical clean superconductor, containing only sparse strong point-like pins [in the sense of C.J. van der Beek {\em et al.}, Phys. Rev. B {\bf 66}, 024523 (2002)]. Widely varying critical current values for nominally similar compositions show that flux pinning is of extrinsic origin. Vortex configurations, imaged using the Bitter decoration method, show less density fluctuations than those pre…
An unexpected insensitivity of the Fermi surface to impurity scattering is found in Ru substituted BaFe$_2$As$_2$ from first-principles theory, offering a natural explanation of the unusual resilience of transport and superconductivity to a high level of disordered substitution in this material. This robustness is shown to originate from a coherent interference of correlated on-site and inter-site impurity scattering, similar in spirit to the microscopic mechanism of superdiffusion in one dimension. Our result also demonstrates a strong substitution dependence of the Fermi surface and carrier …
We elucidate the termination surface of cleaved single crystals of the BaFe_(2-x)Co_(x)As_(2) and Fe_(y)Se_(1-x)Te_(x) families of the high temperature iron based superconductors. By combining scanning tunneling microscopic data with low energy electron diffraction we prove that the termination layer of the Ba122 systems is a remnant of the Ba layer, which exhibits a complex diversity of ordered and disordered structures. The observed surface topographies and their accompanying superstructure reflections in electron diffraction depend on the cleavage temperature. In stark contrast, Fe_(y)Se_(1…
We show that recent measurements of the magnetic field dependence of the magnetization, specific heat and resistivity of overdoped $T_c \sim 17K$ $Tl_{2}Ba_{2}CuO_{6+δ}$ in the vicinity of the superconducting $H_{c2}$ imply that the vortex viscosity is anomalously small and that the material studied is inhomogeneous with small, a few hundred $Å$, regions in which the local $T_{c}$ is much higher than the bulk $T_{c}$. The anomalously small vortex viscosity can be derived from a microscopic model in which the quasiparticle lifetime varies dramatically around the Fermi surface, being small every…
The upper critical field ($H_{c2}$) in superconducting BaFe$_{2-x}$Ni$_{x}$As$_2$ single crystals has been determined by magnetotransport measurements down to 0.6 K over the whole superconducting dome with $0.065 \leqslant x \leqslant 0.22$, both for the inter-plane ($H \parallel c$, $H_{c2}^{c}$) and in-plane ($H \parallel ab$, $H_{c2}^{ab}$) field directions in static magnetic fields up to 16 T and pulsed magnetic fields up to 60 T. The temperature dependence of $H_{c2}^{ab}$ follows the Werthamer-Helfand-Hohenberg (WHH) model incorporating orbital and spin paramagnetic effects, while $H_{c2…
The magnetic properties of the Zn-substituted overdoped high-$T_c$ superconductor La$_{2-x}$Sr$_{x}$Cu$_{1-y}$Zn$_{y}$O$_{4}$ have been studied by magnetization measurements and neutron scattering. Magnetization measurements reveal that for Zn-free samples with $x \geq 0.22$ a Curie term is induced in the temperature dependence of the magnetic susceptibility implying the existence of local paramagnetic moments. The induced Curie constant corresponds to a moment of 0.5 $μ_B$ per additional Sr$^{2+}$ ion that exceeds $x=0.22$. Zn-substitution in the overdoped \lsco also induces a Curie term that…
Efforts to understand the microscopic origin of superconductivity in the cuprates are dependent on knowledge of the normal state. The Hall number in the low temperature, high field limit $n_{\rm H}(0)$ has a particular significance because within conventional transport theory it is simply related to the number of charge carriers, and so its evolution with doping gives crucial information about the nature of the charge transport. Here we report a study of the high field Hall coefficient of the single-layer cuprates Tl$_2$Ba$_2$CuO$_{6+δ}$ (Tl2201) and (Pb/La) doped Bi$_2$Sr$_2$CuO$_{6+δ}$ (Bi22…
We report a comprehensive study of the spin ladder compound BaFe$_2$S$_{2.5}$Se$_{0.5}$ using neutron diffraction, inelastic neutron scattering, high pressure synchrotron diffraction, and high pressure transport techniques. We find that BaFe$_2$S$_{2.5}$Se$_{0.5}$ possesses the same $Cmcm$ structure and stripe antiferromagnetic order as does BaFe$_2$S$_3$, but with a reduced N{é}el temperature of $T_N=98$ K compared to 120 K for the undoped system, and a slightly increased ordered moment of 1.40$μ_B$ per iron. The low-energy spin excitations in BaFe$_2$S$_{2.5}$Se$_{0.5}$ are likewise similar …
The magnetic properties in the parent compounds are often intimately related to the microscopic mechanism of superconductivity. Here we report the first direct measurements on the electronic structure of a parent compound of the newly discovered iron-based superconductor, BaFe$_2$As$_2$, which provides a foundation for further studies. We show that the energy of the spin density wave (SDW) in BaFe$_2$As$_2$ is lowered through exotic exchange splitting of the band structure, rather than Fermi surface nesting of itinerant electrons. This clearly demonstrates that a metallic SDW state could be so…
The London penetration depth was measured in single crystals of self-doped Na$_{1-δ}$FeAs (from under - to optimal - doping, $T_c$ from 14 to 27 K) and electron-doped Na(Fe$_{1-x}$Co$_{x}$)As with $x$ ranging from undoped, $x=0$ to overdoped $x= 0.1$. In all samples, the low - temperature variation of the penetration depth exhibits a power-law dependence, $Δλ(T) = AT^n$, with the exponent that varies in a dome - like fashion from $n \sim 1.1$ in the underdoped, reaching a maximum of $n \sim 1.9$ in the optimally doped and decreasing again to $n \sim 1.3$ on the overdoped side. While the anisot…
We report a fine tuned doping study of strongly overdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ single crystals using electronic Raman scattering. Combined with theoretical calculations, we show that the doping, at which the normal state pseudogap closes, coincides with a Lifshitz quantum phase transition where the active hole-like Fermi surface becomes electron-like. This conclusion suggests that the microscopic cause of the pseudogap is sensitive to the Fermi surface topology. Furthermore, we find that the superconducting transition temperature is unaffected by this transition, demonstrating that th…
Large high-quality single crystals of hole-doped iron-based superconductor (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ were grown over a broad composition range $0.22 \leq x \leq 1$ by inverted temperature gradient method. We found that high soaking temperature, fast cooling rate, and adjusted temperature window of the growth are necessary to obtain single crystals of heavily K doped crystals (0.65$\leq x \leq$ 0.92) with narrow compositional distributions as revealed by sharp superconducting transitions in magnetization measurements and close to 100% superconducting volume fraction. The crystals were exten…
Microscopic, structural, transport and thermodynamic measurements of single crystalline Ba(Fe1-xTMx)2As2 (TM = Ni and Cu) series, as well as two mixed TM = Cu / Co series, are reported. All the transport and thermodynamic measurements indicate that the structural and magnetic phase transitions at 134 K in pure BaFe2As2 are monotonically suppressed and increasingly separated in a similar manner by these dopants. In the Ba(Fe1-xNix)2As2 (x =< 0.072), superconductivity, with Tc up to 19 K, is stabilized for 0.024 =< x =< 0.072. In the Ba(Fe1-xCux)2As2 (x =< 0.356) series, although the structural …
We report a doping, magnetic field and low-temperature dependent study of the specific heat of the iron-arsenide Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ at under (x=0.045), optimal (x=0.08) and overdoped (x=0.103 and 0.105) regimes. By subtracting the lattice specific heat the temperature and magnetic field dependence of the electronic specific heat has been studied. The temperature and field dependencies of the superconducting part of $C_{p}$ exhibit similar behavior for all doping concentrations. The temperature variation of the electronic specific heat as well as its field dependence cannot be…
We report comprehensive resistivity measurements of single crystalline samples of the Ba(Fe(1-x)Co(x))2As2 high Tc superconductor under hydrostatic pressure up to 2.75 GPa and over a broad concentration range, 0 < x < 0.099. We show that application of pressure progressively suppresses the SDW transition temperature, T_SDW, in the underdoped regime. There is no sign of pressure-induced superconductivity in the undoped BaFe2As2 down to 1.8 K, but applied pressure dramatically enhances Tc in the underdoped regime. The effect of pressure on Tc is very small in the optimally and overdoped regimes.…
We have used Resonant Inelastic X-ray Scattering (RIXS) and dynamical susceptibility calculations to study the magnetic excitations in NaFe$_{1-x}$Co$_x$As (x = 0, 0.03, and 0.08). Despite a relatively low ordered magnetic moment, collective magnetic modes are observed in parent compounds (x = 0) and persist in optimally (x = 0.03) and overdoped (x = 0.08) samples. Their magnetic bandwidths are unaffected by doping within the range investigated. High energy magnetic excitations in iron pnictides are robust against doping, and present irrespectively of the ordered magnetic moment. Nevertheless,…
To study the microscopic electronic and magnetic interactions in the substoichiometric iron chalcogenide FeSe$_{1-x}$ which is observed to superconduct at x~1/8 up to $T_c$=27 K, we use first principles methods to study the Se vacancy in this nearly magnetic FeSe system. The vacancy forms a ferrimagnetic cluster of eight Fe atoms, which for the ordered x=1/8 alloy leads to half metallic conduction. Similar magnetic clusters are obtained for FeTe$_{1-x}$ and for BaFe$_2$As$_2$ with an As vacancy, although neither of these are half metallic. Based on fixed spin density results, we suggest the lo…
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…
Microscopic Origin of Pressure-Enhanced and Robust Superconductivity in Infinite-Layer La$_{0.8}$Sr$_{0.2}$NiO$_2$
Center for High Pressure Science and Technology Advanced Research（高压力科学与技术前沿研究中心）；Renmin University of China（中国人民大学）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
We use a renormalized mean field theory to investigate the superconducting properties of underdoped cuprates embedded with overdoped or metallic regions that carry excess dopants. The overdoped regions are considered, within two different models, first as stripes of mesoscopic size larger than the coherence length and then as point impurities. In the former case we compute the temperature dependent superfluid stiffness by solving Bogoliubov de Gennes equations within the slave boson mean field theory. We average over stripes of different orientations to obtain an isotropic result. To compute t…
Scanning tunneling spectroscopy (STS) studies reveal long-range spatial homogeneity and predominantly $d_{x^2-y^2}$-pairing spectral characteristics in under- and optimally doped $\rm YBa_2Cu_3O_{7-δ}$ superconductors, whereas STS on $\rm YBa_2(Cu_{0.9934}Zn_{0.0026}Mg_{0.004})_3O_{6.9}$ exhibits {\it microscopic} spatial modulations and strong scattering near the Zn or Mg impurity sites, together with global suppression of the pairing potential. In contrast, in overdoped $\rm (Y_{0.7}Ca_{0.3})Ba_2Cu_3O_{7-δ}$, $(d_{x^2-y^2}+s)$-pairing symmetry is found, suggesting significant changes in the …
We consider an inhomogeneous anisotropic gap superconductor in the vicinity of the quantum critical point, where the transition temperature is suppressed to zero by disorder. Starting with the BCS Hamiltonian, we derive the Ginzburg-Landau action for the superconducting order parameter. It is shown that the critical theory corresponds to the marginal case in two dimensions and is formally equivalent to the theory of an antiferromagnetic quantum critical point, which is a quantum critical theory with the dynamic critical exponent, z=2. This allows us to use a parquet method to calculate the non…
The momentum dependence of the nematic order parameter is an important ingredient in the microscopic description of iron-based high-temperature superconductors. While recent reports on FeSe indicate that the nematic order parameter changes sign between electron and hole bands, detailed knowledge is still missing for other compounds. Combining angle-resolved photoemission spectroscopy (ARPES) with uniaxial strain tuning, we measure the nematic band splitting in both FeSe and BaFe$_2$As$_2$ without interference from either twinning or magnetic order. We find that the nematic order parameter exhi…
Combining (1) the universal correlations between $T_{c}$ and $n_{s}/m^{*}$ (superconducting carrier density / effective mass) and (2) the pseudo-gap behavior in the underdoped region, we obtain a picture to describe superconductivity in cuprate systems in evolution from Bose-Einstein to BCS condensation. Overdoped and Zn-substituted cuprate systems show signatures of reduced superfluid density in a microscopic phase separation. Scaling of $T_{c}$ to the superfluid volume density $n_{s}$ in all these cases indicate importance of Bose condensation.
The superfluid density and superconducting gaps of superconducting RbFe_{2}As_{2} have been determined as a function of temperature, magnetic field and hydrostatic pressure by susceptibility and muon-spin spectroscopy measurements. From the data, fundamental microscopic parameters of the superconducting state like the London penetration depth λ, the gap values Δ, the upper critical field B_{c2}, and the Ginzburg-Landau parameter κhave been obtained. In accordance with earlier measurements the ratio of the superfluid density n_{s} \propto λ^{-2} to the superconducting transition temperature T_{…
Extensive muon spin relaxation measurements have been performed to determine the magnetic field penetration depth in high-Tc cuprate superconductors with simple hole doping, Zn-doping, overdoping, and formation of static SDW nano islands. System dependence of $n_{s}/m^{*}$ (superconducting carrier density / effective mass) reveals universal correlations between Tc and $n_{s}/m^{*}$ in all these cases with / without perturbation. Evidence for spontaneous and microscopic phase separation was obtained in the cases with strong perturbation, i.e., Zn-doping. overdoping and SDW nano-islands. The len…
In this work we revisit the phase diagram of Co-doped LaFeAsO using single crystals and thermodynamic methods. From magnetic susceptibility studies we track the doping evolution of the antiferromagnetic phase, revealing a continuous suppression of $T_\mathrm{N}$ up to 5$\%$ Co doping. In order to study the evolution of the so-called nematic phase, the temperature dependence of the lengths changes along the $a$ and $b$ orthorhombic directions, $ΔL/L_0$, was determined by high-resolution capacitance dilatometry. The results clearly show a gradual reduction of the orthorhombic distortion $δ$ and …
We present a Ginzburg-Landau theory for a two-band superconductor with emphasis on MgB$_{2}$. Experiments are proposed which lead to identification of the possible scenarios: whether both $σ$- and $π$-bands superconduct or $σ$% -alone. According to the second scenario a microscopic theory of superconducting MgB$_{2}$ is proposed based on the strongly interacting $% σ$-electrons and non-correlated $π$-electrons of boron ions. The kinematic and Coulomb interactions of $σ$% -electrons provide the superconducting state with an anisotropic gap of $s$% *-wave symmetry. The critical temperature $T_{c…
We show that the competition between magnetism and superconductivity can be used to determine the pairing state in the iron arsenides. To this end we demonstrate that the itinerant antiferromagnetic phase (AFM) and the unconventional $s^{+-}$ sign-changing superconducting state (SC) are near the borderline of microscopic coexistence and macroscopic phase separation, explaining the experimentally observed competition of both ordered states. In contrast, conventional $s^{++}$ pairing is not able to coexist with magnetism. Expanding the microscopic free energy of the system with competing orders …
Electron-boson spectral density functions (EBSDFs) can be obtained from measured spectra using various spectroscopic techniques, including optical spectroscopy. EBSDFs, known as glue functions, have a magnetic origin. Here, we investigated EBSDFs obtained from the measured optical spectra of hole-doped cuprates with wide doping levels, from underdoped to overdoped cuprates. The average frequency of an EBSDF provides the timescale for the spin fluctuations to form Cooper pairs. This timescale is directly associated with retarded interactions between electrons. Using this timescale and Fermi vel…
To find out a primary determing factor of $T_{c}$ and a pairing mechanism in high-$T_{c}$ cuprates, we combine the muon spin relaxation results on $n_{s}/m^{*}$ (superconducting carrier density / effective mass), accumulated over the last 15 years, with the results from neutron and Raman scattering, STM, specific heat, Nernst effect and ARPES measurements. We identify the neutron magnetic resonance mode as an analogue of roton minimum in the superfluid $^{4}$He, and argue that $n_{s}/m^{*}$ and the resonance mode energy $\hbarω_{res}$ play a primary role in determining $T_{c}$ in the underdope…
Several decades after the discovery of superconductivity in bismuthates, the strength of their electron-phonon coupling and its evolution with doping remain puzzling. To clarify these issues, polycrystalline hole-doped Ba$_{1-x}$K$_{x}$BiO$_3$ ($0.1 \le x \le 0.6$) samples were systematically synthesized and their bulk- and microscopic superconducting properties were investigated by means of magnetic susceptibility and muon-spin rotation/relaxation ($μ$SR), respectively. The phase diagram of Ba$_{1-x}$K$_{x}$BiO$_3$ was reliably extended up to $x = 0.6$, which is still found to be a bulk super…
Various angle-dependent measurements in hole-doped cuprates suggested that Non-Fermi liquid (NFL) and Fermi-liquid (FL) self-energies coexist in the Brillouin zone. Moreover, it is also found that NFL self-energies survive up to the overdoped region where the resistivity features a global FL-behavior. To address this problem, here we compute the momentum dependent self-energy from a single band Hubbard model. The self-energy is calculated self-consistently by using a momentum-dependent density-fluctuation (MRDF) method. One of our main result is that the computed self-energy exhibits a NFL-lik…
