Thin films of the high-temperature superconductor HgBa$_2$CaCu$_2$O$_{6+δ}$ have been prepared on SrTiO$_3$ substrates by pulsed-laser deposition of precursor films and subsequent annealing in mercury-vapor atmosphere. The microstructural properties of such films can vary considerably and have been analyzed by x-ray diffraction and atomic force microscopy. Whereas the resistivity is significantly enhanced in samples with coarse-grained structure, the Hall effect shows little variation. This disparity is discussed based on models for transport properties in granular materials. We find that, despite of the morphological variation, all samples have similar superconducting properties. The critical temperatures $T_c \sim 121.2$ K $\dots 122.0$ K, resistivity, and Hall data indicate that the samples are optimally doped. The analyses of superconducting order parameter fluctuations in zero and finite magnetic fields yield the in-plane $ξ_{ab}(0) \sim 2.3$ nm $\dots 2.8$ nm and out-of-plane $ξ_{c}(0) \sim 0.17$ nm $ \dots 0.24$ nm Ginzburg-Landau coherence lengths at zero temperature. Hall measurements provide estimates of carrier scattering defects in the normal state and vortex pinning properties in the superconducting state inside the grains.
Pure electronic Raman spectra with no phonon structures superimposed to the electronic continuum, are reported, in optimally doped HgBa_{2}CaCu_{2}O_{6+δ} single crystals (T_{c }=126 K). As a consequence, the spectra in the A_{1g }, B_{1g } and B_{2g } symmetries, including the crucial low energy frequency dependence of the electronic scattering, are directly and reliably measured. The B_{2g } and, most strikingly, the B_{1g } spectra exhibit a strong intrinsic linear term, which suggests that the nodes are shifted from the [110] and [1\bar{1}0] directions, a result inconsistent with a pure d_…
Using resonant X-ray diffraction and Raman spectroscopy, we study charge correlations and lattice dynamics in two model cuprates, HgBa$_{2}$CuO$_{4+δ}$ and HgBa$_{2}$CaCu$_{2}$O$_{6+δ}$. We observe a maximum of the characteristic charge order temperature around the same hole concentration ($p \approx 0.09$) in both compounds, and concomitant pronounced anomalies in the lattice dynamics that involve the motion of atoms in and/or adjacent to the CuO$_2$ layers. These anomalies are already present at room temperature, and therefore precede the formation of the static charge correlations, and we a…
We report the transverse relaxation rates 1/$T_2$'s of the $^{63}$Cu nuclear spin-echo envelope for double-layer high-$T_c$ cuprate superconductors HgBa$_{2}$CaCu$_{2}$O$_{6+d}$ from underdoped to overdoped. The relaxation rate 1/$T_{2L}$ of the exponential function (Lorentzian component) shows a peak at 220$-$240 K in the underdoped ($T_c$ = 103 K) and the optimally doped ($T_c$ = 127 K) samples but no peak in the overdoped ($T_c$ = 93 K) sample. The enhancement in 1/$T_{2L}$ suggests development of the zero frequency components of local field fluctuations. Ultraslow fluctuations are hidden i…
It is well established that the hole density in the prototypical superconductor La$_{2-x}$Sr$_x$CuO$_4$ is very inhomogeneous due to Sr-dopant induced disorder. On the other hand, until recently it is widely believed that the hole distribution in HgBa$_2$CuO$_{4+δ}$ and Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ doped by interstitial oxygen is much more uniform. Recent nuclear magnetic resonance measurements indicate, however, that the charge inhomogeneity in HgBa$_2$CuO$_{4+δ}$ is close to that in La$_{2-x}$Sr$_x$CuO$_4$. Calculations performed in the present paper confirm this observation. We also show t…
Triple sign reversal in the mixed-state Hall effect has been observed for the first time in ion-irradiated HgBa_{2}CaCu_{2}O_{6} thin films. The negative dip at the third sign reversal is more pronounced for higher fields, which is opposite to the case of the first sign reversal near T_c in most high-T_c superconductors. These observations can be explained by a recent prediction in which the third sign reversal is attributed to the energy derivative of the density of states and to a temperature-dependent function related to the superconducting energy gap. These contributions prominently appear…
We have succeeded in the synthesis of Re-doped $HgBa_{2}Ca_{n-1}Cu_{n}O_{2(n+1)+δ}$ quickly by a sealed tube technique with a bit of CsCl flux. Powder X-ray diffraction measurement revealed that the single phases of Re-doped $HgBa_{2}CuO_{4+δ}$ (Hg1201), $HgBa_{2}CaCu_{2}O_{6+δ}$ (Hg1212), and $HgBa_{2}Ca_{2}Cu_{3}O_{8+δ}$ (Hg1223) formed in 4 h. The sample grains exhibited plate-like crystals with the sizes of 20$\times$20$\times$1 $μm^{3}$ and the chemical compositions of Hg1201, Hg1212, and Hg1223. The superconducting transitions were observed at 25 K for Hg1201, 122 for Hg1212, and 133 K f…
Superconductivity studied by solving ab initio low-energy effective Hamiltonians for carrier doped CaCuO$_2$, Bi$_2$Sr$_2$CuO$_6$, Bi$_2$Sr$_2$CaCu$_2$O$_8$, and HgBa$_2$CuO$_4$
We make comments on the paper presented by Kim \textit{et al.} [Phys. Rev. B \textbf{61}, 11317 (2000)]. The authors analyzed activation energies of HgBa$_2$Ca$_2$Cu$_3$O$_{8+δ}$ thin films with a scaling relation, and defined four vortex regions for thin films. We find that the definitions of four vortex regions and the scaling relation are questionable when studying their definition of the resistivity range for thermally activated flux flow. Using the empirical activation energy form suggested by Zhang \textit{et al.} [Phys. Rev. B \textbf{71}, 052502 (2005)] for lower resistivity data, we f…
We report the successful synthesis of single-crystalline cuprate superconductors HgBa$_{2}$CaCu$_{2}$O$_{6+δ}$ and HgBa$_{2}$Ca$_{2}$Cu$_{3}$O$_{8+δ}$. These compounds are well-known for their high optimal superconducting critical temperatures of $T_\mathrm{c}$ = 128 K and 134 K at ambient pressure, respectively, and for their challenging synthesis. Using a conventional quartz-tube encapsulation method and a two-layer encapsulation method that utilizes custom-built high-pressure furnaces, we are able to grow single crystals with linear dimensions up to several millimeters parallel to the CuO$_…
The mixed-state Hall resistivity and the longitudinal resistivity in HgBa_{2}CaCu_{2}O_{6}, HgBa_{2}Ca_{2}Cu_{3}O_{8}, and Tl_{2}Ba_{2}CaCu_{2}O_{8} thin films have been investigated as functions of the magnetic field up to 18 T. We observe the universal scaling behavior between ρ_{xy} and ρ_{xx} in the regions of the clean and the moderately clean limit. The scaling exponent βis 1.9 in the clean limit at high field and low temperature whereas βis 1.0 in the moderately clean limit at low field and high temperature, consistent with a theory based on the midgap states in the vortex cores. This f…
The vortex-liquid and vortex-solid phases in single crystals of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ placed in tilted magnetic fields are studied by in-plane resistivity measurements using the Corbino geometry to avoid spurious surface barrier effects. It was found that the anisotropy of the vortex-solid phase increases with temperature and exhibits a maximum at $T\approx 0.97 T_c$. In contrast, the anisotropy of the vortex-liquid rises monotonically across the whole measured temperature range. The observed behavior is discussed in the context of dimensional crossover and thermal fluctuations of vort…
Resistive transitions of an epitaxial Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ thin film were measured in various magnetic fields ($H\parallel c$), ranging from 0 to 22.0 T. Rounded curvatures of low resistivity tails are observed in Arrhenius plot and considered to relate to deviations from plastic barriers. In order to characterize these deviations, an empirical barrier form is developed, which is found to be in good agreement with experimental data and coincide with the plastic barrier form in a limited magnetic field range. Using the plastic barrier predictions and the empirical barrier form, we succ…
A parent insulator of the Bi-based high-$T_c$ superconductor Bi$_2$Sr$_{2-x}$La$_x$CaCu$_2$O$_{8+δ}$ was successfully grown by a traveling solvent floating zone method. The in-plane resistivity $ρ_{ab}$ shows metallic behavior ($dρ_{ab}/dT >$ 0) near room temperature, although the magnitude of the resistivity is far above the Mott limit for metallic conduction. The Hall mobility of the parent insulator does not so much differ from that of an optimally doped sample. These results suggest that the system is not a simple insulator with a well-defined gap, and the hole in the parent insulator is e…
A parent insulator of the Bi-based high-$T_c$ superconductor Bi$_2$Sr$_{2-x}$La$_x$CaCu$_2$O$_{8+δ}$ was successfully grown by a traveling solvent floating zone method. The in-plane resistivity $ρ_{ab}$ shows metallic behavior ($dρ_{ab}/dT >$ 0) near room temperature, although the magnitude of the resistivity is far above the Mott limit for metallic conduction. The Hall mobility of the parent insulator does not so much differ from that of an optimally doped sample. These results suggest that the system is not a simple insulator with a well-defined gap, and the hole in the parent insulator is e…
The Hall conductivities of HgBa_{2}CaCu_{2}O_{6+δ}and HgBa_{2}Ca_{2}Cu_{3}O_{8+δ} thin films are investigated for a magnetic field parallel to the c axis. The mixed-state Hall conductivity for these compounds is well described by σ_{xy}=C_{1}/H+C_{2}+C_{3}H. The prefactor C_1 shows a temperature dependence of the form C_1 = A(1-t)^n near T_c, where t=T/T_c is the reduced temperature. Contrary to the previous results, C_2 also follows a temperature-scaling behavior similar to that of the coefficient C_1. The observed value of n = 1.8 - 2.3 is comparable to the previously observed values for YBa…
To elucidate the pseudogap phase diagram including the overdoped state of high transition temperature (high-$T_c$) cuprates, we must understand the origin of the positive out-of-plane magnetoconductivity (MC) observed in these compounds. For this purpose, the out-of-plane resistivity $ρ_c(T,H)$ of an overdoped Bi$_{1.6}$Pb$_{0.4}$Sr$_{2}$CaCu$_{1.96}$Fe$_{0.04}$O$_{8+δ}$ (Bi-2212) single crystal is measured under pulsed magnetic fields up to 60 T. We show that the superconductive density-of-states (DOS) depletion effect, in addition to the pseudogap effect, clearly appears below the supercondu…
We consider the problem of c-axis transport in double-layered cuprates, in particular with reference to Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ compounds. We exploit the effect of the two barriers on the thermal and tunnel transport. The resulting model is able to describe accurately the normal state c-axis resistivity in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$, from the underdoped side up to the strongly overdoped. We extend the model, without introducing additional parameters, in order to allow for the decrease of the barrier when an external voltage bias is applied. The extended model is found to d…
We present measurements of the magnetic field-induced microwave complex resistivity changes at 47 GHz in Tl$_2$Ba$_2$CaCu$_2$O$_{8+δ}$ (TBCCO) thin films, in the ranges 58 K$<T<T_{c}$ and 0$<μ_{0}H<$0.8 T. The large imaginary part $Δρ_{2}(H)$ points to strong elastic response, but the data are not easily reconciled with a rigid vortex model. We find that, over a wide range of temperatures, all the pairs of curves $Δρ_{1}(H)$ and $Δρ_{2}(H)$ can be collapsed on a pair of scaling curves $Δρ_{1}[H/H^{*}(T)]$, $Δρ_{2}[H/H^{*}(T)]$, with the same scaling field $H^{*}(T)$. We argue that $H^{*}(T)$ i…
We have investigated the pressure dependence of the superconducting transition temperature $T_{c}$ up to 18 GPa of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ single crystals ranging from the highly underdoped through the nearly optimally doped to the highly overdoped level. For all three samples studied, $T_{c}$ is found to increase initially and then saturate at a critical pressure $P_{c}$ but decrease modestly with further compression. Oxygen doping tends to reduce the increase in $T_{c}$ and $P_{c}$. A new high-pressure phase diagram between the saturated $T_{c}$ and $P_{c}$ is then obtained. Theo…
We report peculiar vortex motion in clean Bi$_2$Sr$_2$CaCu$_2$O$_8$ single crystals, which reveals nearly linear-$T$ resistivity tails extending to low temperatures. The resistivity was found to satisfy the classical Bardeen-Stephen model for free flux flow, which is otherwise hard to observe under normal experimental conditions in high-$T_c$ cuprates. Moreover, in the superclean regime, a universal temperature-independent value for the flux flow resistivity was observed, $ρ_f = 1.4(B-B^*)$. We interpret this carrier-relaxation {\it independent} behavior as being related to the dissipation cau…
One of the prime manifestations of an anisotropic electronic state in underdoped cuprates is the in-plane resistivity anisotropy $Δρ\equiv(ρ_{a}-ρ_{b})/ρ_{b}$. Here we use a Boltzmann-equation approach to compute the contribution to $Δρ$ arising from scattering by anisotropic charge and spin fluctuations, which have been recently observed experimentally. While the anisotropy in the charge fluctuations is manifested in the correlation length, the anisotropy in the spin fluctuations emerges only in the structure factor. As a result, we find that spin fluctuations favor $Δρ>0$, whereas charge flu…
We investigate the effect of disorder at various lattice sites outside the CuO$_2$ plane on the superconducting critical temperature $T_c$ of the cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212). The most effective disorder turns out to be that at the Sr site in the neighboring blocks, which contain apical-oxygen atoms. The Sr-site disorder reduces $T_c$ and also produces a residual component ($ρ_0$) in the in-plane resistivity, the magnitude of which is found to be proportional to the magnitude of $T_c$ reduction. We demonstrate that both $T_c$-degradation rate and $ρ_0$ decrease…
We propose and show that the c-axis transport in high-temperature superconductors is controlled by the pseudogap energy and the c-axis resistivity satisfies a universal scaling law in the pseudogap phase. We derived approximately a scaling function for the c-axis resistivity and found that it fits well with the experimental data of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+δ}$, and YBa$_2$Cu$_3$O$_{7-δ}$. Our works reveals the physical origin of the semiconductor-like behavior of the c-axis resistivity and suggests that the c-axis hopping is predominantly coherent.
The thermal conductivity κof Bi-2212 is measured in pure and Zn-doped crystals as a function of temperature and magnetic field. The in-plane resistivity is also measured on the identical samples. Using these data, we make a crude estimate of the impurity-scattering rate Γof the pure and the Zn-doped crystals. Our measurement show that the "plateau" in the κ(H) profile is not observed in the majority of our Bi-2212 crystals, including one of the cleanest crystals available to date. The estimated values of Γfor the pure and Zn-doped samples allow us to compare the κ(H) data with the existing the…
We present measurements of the field induced changes in the 47 GHz complex resistivity, $Δ\tilde ρ(H,T)$, in Tl$_{2}$Ba$_{2}$CaCu$_{2}$O$_{8+x}$ (TBCCO) thin films with $T_{c}\simeq$ 105 K, prepared on CeO$_{2}$ buffered sapphire substrates. At low fields ($μ_{0}H<$10 mT) a very small irreversible feature is present, suggesting a little role of intergranular phenomena. Above that level $Δ\tilde ρ(H,T)$ exhibits a superlinear dependence with the field, as opposed to the expected (at high frequencies) quasilinear behaviour. We observe a crossover between predominantly imaginary to predominantly …
To investigate the relationship between the pseudogap and superconductivity, we measured both the in-plane ($ρ_{ab}$) and out-of-plane ($ρ_c$) resistivity for oxygen-controlled Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ single crystals subject to magnetic fields (parallel to the $c$ axis) of up to 17.5 T. The onset temperature for the superconductive fluctuation, $T_{scf}$, is determined by the large positive in-plane magnetoresistance (MR) and negative out-of-plane MR observed near $T_c$, whereas the pseudogap opening temperature $T^*$ is determined by the semiconductive upturn of the zero-field $ρ_…
The strongly correlated electron fluids in high temperature cuprate superconductors demonstrate an anomalous linear temperature ($T$) dependent resistivity behavior, which persists to a wide temperature range without exhibiting saturation. As cooling down, those electron fluids lose the resistivity and condense into the superfluid. However, the origin of the linear-$T$ resistivity behavior and its relationship to the strongly correlated superconductivity remain a mystery. Here we report a universal relation $dρ/dT=(μ_0k_B/\hbar)λ^2_L$, which bridges the slope of the linear-$T$-dependent resist…
The Fermi-liquid-like (FL) resistivity recently observed in clean HgBa2CuO4 below the pseudogap temperature was related to carriers at the nodal points on the Fermi surface [4]. We show that this necessitates important implications for the electronic spectrum of underdoped (UD) cuprates in whole. Photoemission experiments picture the spectrum as of metallic arcs separated from each other by regions with large energy gaps. We solved the kinetic equation in such model rigorously. The Fermi arcs carriers contribute to FL resistivity, if scattering between the opposite nodal points admits the Umkl…
We report thermodynamic and transport properties, and also theoretical calculations, for Cu-based compound Ca2Cu6P5 and compare with CaCu(2-x)P2. Both materials have layers of edge-sharing copper pnictide tetrahedral CuP4, similar to Fe-As and Fe-Se layers (with FeAs4, FeSe4) in the iron-based superconductors. Despite the presence of this similar transition-metal pnictide layer, we find that both Ca2Cu6P5 and CaCu(2-x)P2 have temperature-independent magnetic susceptibility and show metallic behavior with no evidence of either magnetic ordering or superconductivity down to 1.8 K. CaCu(2-x)P2 is…
We propose a model for explaining the recent results obtained by J. Schon et al (1,2) on transport properties of electrons and holes in one plane of CuO2 in a layered cuprate (CaCuO2) where the carriers are created using a field effect transistor (FET). We use the known band structure of a CuO2 plane showing a van Hove singularity (vHs). When the energy of the hole lies near the vHs a variation of the resistivity linear with temperature (T) is calculated and when the FL lies far from the vHs, a quadratic law is obtained at low temperature and becomes linear at higher T. We find that the transi…
We apply Landau-Ott scaling to the reversible magnetization data of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ published by Y. Wang et al. [\emph{Phys. Rev. Lett. \textbf{95} 247002 (2005)}] and find that the extrapolation of the Landau-Ott upper critical field line vanishes at a critical temperature parameter, T^*_c, a few degrees above the zero resistivity critical temperature, T_c. Only isothermal curves below and near to T_c were used to determine this transition temperature. This temperature is associated to the disappearance of the mixed state instead of a complete suppression of superconductivity in…
Interlayer tunneling resistivity is used to probe the low-energy density-of-states (DOS) depletion due to the pseudogap in the normal state of Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$. Measurements up to 60 T reveal that a field that restores DOS to its ungapped state shows strikingly different temperature and doping dependencies from the characteristic fields of the superconducting state. The pseudogap closing field and the pseudogap temperature $T^{\star}$ evaluated independently are related through a simple Zeeman energy scaling. These findings indicate a predominant role of spins over the orbital eff…
The in-plane resistivity and Hall coefficient have been measured for the single-layer compound Bi$_2$Sr$_2$CuO$_{6+δ}$ for the whole range of doping states. The deviation of the Hall coefficient, $R_H$, from a high-temperature linear behavior and the temperature dependence of the Hall angle are both only weakly dependent upon doping, contrasting with Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+δ}$ and Bi$_2$Sr$_2$CaCuO$_{8+δ}$. This is in contradiction with former proposals that the transverse transport detects the formation of incoherent Cooper pairs in the pseudogap state. Conversely, the analysis of the …
Discriminating superconducting fluctuations from the pseudogap in Bi$_2$Sr$_2$Ca$_{n-1}$Cu$_n$O$_{2n+4+δ} (n = 2,3)$: A magnetotransport study
Hirosaki University（弘前大学）；Kyoto University of Advanced Science (KUAS)（京都先端科学大学）；University of Tokyo（东京大学）；Tohoku University（东北大学）；Kyoto University（京都大学）；Iwate University（岩手大学）
Electronic structure, magnetic correlations, and superconducting pairing in the reduced Ruddlesden-Popper bilayer La$_3$Ni$_2$O$_6$ under pressure: different role of $d_{3z^2-r^2}$ orbital compared with La$_3$Ni$_2$O$_7$
