We studied the temperature and magnetic field dependence of vortex dissipation and critical current in the mixed-state of unconventional superconducting alloys Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ ($0.044 \leq x \leq 0.100$) through current-voltage measurements. Our results reveal that all the electric field $E$ vs current density $j$ curves in the Ohmic regime merge to one point ($j_0,E_0$) and that there is a simple relationship between the critical current density $j_c$ and flux-flow resistivity $ρ_{\rm ff}$: $ρ_{\rm ff}/ρ_{\rm n} = (1- j_{c}/j_{0})^{-1}$, where $ρ_{\rm n}=E_0/j_0$ is the normal-state resistivity just above the superconducting transition. In addition, $E_0$ is positive for all five dopings, reflecting the abnormal behavior of the flux-flow resistivity $ρ_{\rm ff}$: it increases with decreasing magnetic field. In contrast, $E_0$ is negative for the conventional superconductor Nb since, as expected, $ρ_{\rm ff}$ decreases with decreasing magnetic field. Furthermore, in the under-doped and over-doped single crystals of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$, the parameter $E_0$ remains temperature independent, while it decreases with increasing temperature for the single crystals around optimal doping ($ 0.060\leq x\leq 0.072 $). This result points to the co-existence of superconductivity with some other phase around optimal doping.
Observation of a Universial Low Temperature Limit of the Free Flux Flow Resistivity in Superclean Bi_2Sr_2CaCu_2O_8 Whiskers
我们报道了洁净Bi $_2$ Sr $_2$ CaCu $_2$ O $_8$单晶中特有的涡旋运动，它揭示了几乎线性的$T$电阻率尾向低温延伸。电阻率被发现，以满足经典的Bardeen-Stephen模型的自由磁通量流动，否则很难观察到在正常的实验条件下，在高- $T_c$铜酸盐。此外，在超净制度，一个普遍的温度无关的磁通流电阻率值，观察到，$ρ_f = 1.4(B-B^*)$。我们解释这种载流子弛豫{ \it独立}行为与涡核内的minigap状态引起的耗散有关。结果与理论计算（N. B. Kopnin和G. E. Volovik，Phys. Rev. Lett. { \bf 79}，1377（1997））。
We numerically investigate the effect of in-plane anisotropic Fermi surface (FS) on the flux-flow resistivity $ρ_{\rm f}$ under rotating magnetic field on the basis of the quasiclassical Green's function method. We demonstrate that one can detect the phase in pairing potential of Cooper pair through the field-angular dependence of $ρ_{\rm f}$ even if the FS has in-plane anisotropy. In addition, we point out one can detect the gap-node directions irrespective of the FS anisotropy by measuring $ρ_{\rm f}$ under rotating field.
The magnetic-field dependencies of the longitudinal and Hall resistance of the electron-doped compounds Nd$_{2-x}$Ce$_x$CuO$_{4+δ}$ in underdoped region with $x$=0.14 and with varying degrees of disorder ($δ$) were investigated. It was established experimentally that the correlation between the longitudinal electrical resistivity and the Hall resistivity can be analyzed on the basis of scaling relationships: $ρ_{xy}$($B$)$\sim$ $ρ^β_{xx}$($B$). For the totality of the investigated single-crystal films of Nd$_{2-x}$Ce$_x$CuO$_{4+δ}$/SrTiO$_3$ the universal value $β$=1.5 $\pm$0.4 is found. The o…
We theoretically investigate the applied magnetic field-angle dependence of the flux-flow resistivity $ρ_{\rm f}(α_{\rm M})$ for an uniaxially anisotropic Fermi surface. $ρ_{\rm f}$ is related to the quasiparticle scattering rate $\varGamma$ inside a vortex core, which reflects the sign change in the superconducting pair potential. We find that $ρ_{\rm f}(α_{\rm M})$ is sensitive to the sign-change in the pair potential and has its maximum when the magnetic field is parallel to the gap-node direction. We propose the measurement of the field-angle dependent oscillation of $ρ_{\rm f}(α_{\rm M})$…
We measured the microwave surface impedances and obtained the superfluid density and flux flow resistivity in single crystals of a phosphor-doped iron-based superconductor SrFe$_2$(As$_{1-x}$P$_{x}$)$_2$ single crystals ($x=0.30$, $T_c=25 \mathrm{K}$). At low temperatures, the superfluid density, $n_s (T)/n_s(0)$, obeys a power law, $n_s (T)/n_s (0)=1-C(T/T_c)^n$, with a fractional exponent of $n=1.5$-1.6. The flux flow resistivity was significantly enhanced at low magnetic fields. These features are consistent with the presences of both a gap with line nodes and nodeless gaps with a deep mini…
We measured the microwave surface impedance of FeSe$_{0.4}$Te$_{0.6}$ single crystals with- and without external magnetic fields. The superfluid density exhibited a quadratic temperature dependence, indicating a strong pair-breaking effect. The flux-flow resistivity behaved as $ρ_f(B\ll B_{\rm c2})/ρ_n=αB/B_{\rm c2}$. The observed $α$ value of $\approx0.66$ was considerably smaller than that of other Fe-based materials ($α\geq1$) and was attributed to a back-flow of superfluids remarkable in disordered superconductors. This is the first-time observation of the back-flow phenomenon caused by an…
The conductivity of vortex lattices in multiband superconductors with high concentration of impurities is calculated based on microscopic kinetic theory. Both the limits of high and low fields are considered, when the magnetic induction is close to or much smaller than the critical field strength $H_{c2}$, respectively. It is shown that in contrast to single-band superconductors the resistive properties are not universal but depend on the pairing constants and ratios of diffusivities in different bands. The low-field magneto-resistance can strongly exceed Bardeen-Stephen estimation in a quanti…
We theoretically investigate the magnetic-field-angle dependence of the flux-flow resistivity $ρ_{\rm f}$ in unconventional superconductors. Two contributions to $ρ_{\rm f}$ are considered: one is the quasiparticle (QP) relaxation time $τ(\bm{k}_{\rm F})$ and the other is $ω_0(\bm{k}_{\rm F})$, which is a counterpart to the interlevel spacing of the QP bound states in the quasiclassical approach. Here, $\bm{k}_{\rm F}$ denotes the position on a Fermi surface. Numerical calculations are conducted for a line-node s-wave and a d-wave pair potential with the same anisotropy of their amplitudes, bu…
The resistivity tensor correlations $ρ_{xy}$($B$)$\sim$ $[ρ_{xx}(B)]^β$ for the mixed state magnetic field dependencies of the resistivity tensor of electron-doped Nd$_{2-x}$Ce$_x$CuO$_{4+δ}$/SrTiO$_3$ single crystal films near the antiferromagnetic (AF) - superconducting (SC) phase transition and with varying degree of disorder ($δ$) were studied. The decrease of $β$ from 1.2$\pm$0.2 at $x$ = 0.14 to 0.6$\pm$0.1 at $x$ = 0.15 points out on the evidence of the change from the anisotropic $s$ - wave to the $d$ - wave pairing symmetry in the external magnetic field at the transition from underdo…
The electrical resistivity of polycrystalline Bi2Sr2Ca2Cu3O10-x (Bi-2223) was measured vs. applied magnetic fields up to 0.45 T, applied currents up to 1 A, and temperature from liquid nitrogen temperature (LN2) to room temperature. In the lowest temperature region, the only truly zero resistivity was observed when the magnetic field was zero; otherwise, a quadratic dependence on the magnetic field occurred. Hysteresis was noted at the higher currents. Current vs. voltage curves in this region revealed a non-ohmic resistivity. In the transition region to the mixed state, indications of negativ…
Measurements of the current-voltage characteristics were performed on Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ single crystals with doping level $0.044 \leq x \leq 0.1$. An unconventional increase in the flux-flow resistivity $ρ_{\rm ff}$ with decreasing magnetic field was observed across this doping range. Such an abnormal field dependence of flux-flow resistivity is in contrast with the linear field dependence of $ρ_{\rm ff}$ in conventional type-II superconductors, but is similar to the behavior recently observed in the heavy-fermion superconductor CeCoIn$_5$. A significantly enhanced $ρ_{\rm ff}$ wa…
Measurements of the high-frequency complex resistivity in superconductors are a tool often used to obtain the vortex parameters, such as the vortex viscosity, the pinning constant and the depinning frequency. In anisotropic superconductors, the extraction of these quantities from the measurements faces new difficulties due to the tensor nature of the electromagnetic problem. The problem is specifically intricate when the magnetic field is tilted with respect to the crystallographic axes. Partial solutions exist in the free-flux-flow (no pinning) and Campbell (pinning dominated) regimes. In thi…
Mixed-state microwave response in superconducting cuprates
本文报道了RE Ba $_{2}$ Cu $_{3}$ O $_{7-δ}$薄膜（RE = Y，Sm）的磁场感生微波复电阻率的测量结果。在48 GHz下通过端壁替换配置中的谐振腔进行测量。的磁场的依赖性进行了研究，通过施加一个中等（0.8 T）的磁场沿c轴。在已知的涡旋动力学模型内分析了YBa $_{2}$ Cu $_{3}$ O $_{7-δ}$和SmBa $_{2}$ Cu $_{3}$ O $_{7-δ}$中测量的涡旋态复电阻率。结果表明，归因于所观察到的响应涡运动单独导致不一致的确定涡参数（如涡粘度和钉扎常数）。相比之下，归因于整个响应场致对断裂导致的数据几乎定量的描述。
We study the superconductor-insulator transition in nanohole ultrathin films in a transverse magnetic field by numerical simulation of a Josephson-junction array model. Geometrical disorder due to the random location of nanoholes in the film corresponds to random flux in the array model. Monte Carlo simulation in the path-integral representation is used to determine the critical behavior and the universal resistivity at the transition as a function of disorder and average number of flux quanta per cell, $f_o$. The resistivity increases with disorder for noninteger $ f_o$ while it decreases for…
Using the self-flux technique we grew superconducting $(K_{1-z}Na_z)_{x}Fe_{2-y}Se_2$ (z = 0.3) single crystals. The EDX mapping revealed the uniform elements distribution on the crystal surface while the XRD measurements indicate that the crystals are compositionally inhomogenous on nanoscale. The physical properties of the as-prepared sample are characterized by electrical resistivity, magnetization and specific heat measurements. Resistivity measurements show the onset of the superconducting transition at 33 K and zero resistivity at 31.7 K. The large upper critical field $H_{c2}$(0) was es…
The magnetic flux penetration into the half-space superconductor sample is studied in the flux flow regime in parallel geometry assuming that an external magnetic field increasing with time in accordance with the power law. Assuming that the flux flow resistivity as a power-law function of the magnetic field induction we found an exact analytical solution for the nonlinear local magnetic flux diffusion equation. The obtained solution describes space-time distribution of the magnetic induction in the sample.
The study of the iron-based superconductor FeSe has blossomed with the availability of high quality single crystals, obtained through flux/vapor-transport growth techniques below the structural transformation temperature of its tetragonal phase, T~450 C. Here, we report on the variation of sample morphology and properties due to small modifications in the growth conditions. A considerable variation of the superconducting transition temperature Tc, from 8.8 K to 3 K, which cannot be correlated with the sample composition, is observed. Instead, we point out a clear correlation between Tc and dis…
The mixed-state Hall effect was examined in a Ba(Fe1-xCox)2As2 epitaxial film with a high critical current density. The transverse resistivity ρxy and the longitudinal resistivity ρxx follow power law scaling ρxy = Aρxxβ. In the temperature-sweep with a fixed field (T sweep), all of the β values are independent of magnetic field up to 9 T, and are lower than 2.0 (around 1.8). In contrast, the β values in the magnetic-field sweep with a fixed temperature (H sweep) change from 1.8 to 2.0 as the temperature increases from 13 to 16 K even in the T/H region that overlaps with the T sweep measuremen…
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 interplay between vortex guiding and the Hall effect in superconducting Nb films with periodically arranged nanogrooves is studied via four-probe measurements in standard and Hall configurations and accompanying theoretical modeling. The nanogrooves are milled by focused ion beam and induce a symmetric pinning potential of the washboard type. The resistivity tensor of the films is determined in the limit of small current densities at temperatures close to the critical temperature for the fundamental matching configuration of the vortex lattice with respect to the pinning nanolandscape. The…
The magnetic-field dependencies of the longitudinal and Hall resistivity of the electron-doped compounds $Nd_{2-x}Ce_xCuO_{4+δ}$ in underdoped region (x=0.14) were investigated. It was established experimentally a strong magnetic field dependence of the Hall conductivity, $σ_{xy}(B)=C-b/B$, in the region of magnetic fields corresponding to a transition from superconducting to resistive state. The observed feature can be explained with the sum of contributions of the quasiparticles and moving Abrikosov vortices into Hall effect in a mixed state of type-II superconductor.
In previous work in undoped MFe2As2, partial drops in the resistivity indicative of traces of superconductivity have been observed in some samples of M=Ba (Tc ~ 20 K, up to 25% drop in resistivity) and M=Ca (Tc ~ 10 K, up to 45 % drop in resistivity.) A complete drop in the resistivity to 0, along with a finite fraction of Meissner flux expulsion, has been observed in M=Sr, Tc = 22 K. Using In-flux grown single crystal samples of undoped BaFe2As2, we find a complete drop in the resistivity to 0 in most samples beginning at Tc(onset) = 22.5 K. However, in contrast to the SrFe2As2 results, there…
We report the results from resistivity and magnetic measurements on polycrystalline Ce oxypnictide (CeFeAsO1-xFx) samples where x spans from 0.13 to 0.25. We find that the orbital limiting field is as high as 150 T and it systematically decreases with increasing doping. The Maki parameter is greater than one across the phase diagram and the large Maki parameter suggests that orbital and Pauli limiting effects contribute to the upper critical field. The broadening of the superconducting transition in the resistivity data was interpreted using the thermally activated flux flow (TAFF) model where…
We report the anisotropy of the upper critical fields mu0Hc2(T) and thermally-activated flux flow (TAFF) behavior of quenched KxFe2-ySe2. Even though the post-annealing and quenching process enhances the superconducting volume fraction, it has a minor effect on the upper critical fields for H//c and H//ab. Analysis of the angular-dependence of resistivity rho_ab(theta,H) indicates that it follows the scaling law based on the anisotropic Ginzburg-Landau (GL) theory and the anisotropy Gamma(T) increases with decreasing temperature with Gamma(T) ~ 3.6 at 27 K. The resistivity of quenched sample e…
We report the effects of Ce substitution on structural, electronic, and magnetic properties of layered bismuth-chalcogenide La1-xCexOBiSSe (x = 0-0.9), which are newly obtained in this study. Metallic conductivity was observed for x > 0.1 because of electron carriers induced by mixed valence of Ce ions, as revealed by bond valence sum calculation and magnetization measurements. Zero resistivity and clear diamagnetic susceptibility were obtained for x = 0.2-0.6, indicating the emergence of bulk superconductivity in these compounds. Dome-shaped superconductivity phase diagram with the highest tr…
We present resistivity, magnetization and specific heat measurements on flux grown single crystals of NiBi3. We find typical behavior of a type-II superconductor, with, however, a sizable magnetic signal in the superconducting phase. There is a hysteretic magnetization characteristic of a ferromagnetic compound. By following the magnetization as a function of temperature, we find a drop at temperatures corresponding to the Curie temperature of ferromagnetic amorphous Ni. Thus, we assign the magnetism in NiBi$_3$ crystals to amorphous Ni impurities.
We have performed an experimental study on the temperature dependence of electrical resistivity $ρ$($T$) and heat capacity $C$($T$) of the Mo$_{1-x}$Re$_x$ $(x = 0.20, 0.25)$ alloy superconductors in different magnetic fields. In the presence of applied magnetic field, the electrical resistivity of these alloys go to zero at a temperature well above the bulk superconducting transition temperature obtained with the help of heat capacity measurements in the same magnetic field. Our study indicates the presence of surface superconducting state in these alloys, where the flux lines are pinned in t…
We present wideband microwave measurements (1-22 GHz) taken on Superconductor/Ferromagnet heterostructures with the Corbino disk technique. We apply the technique to Nb/PdNi/Nb trilayers in the vortex state and we compare the results to data taken with the same technique on a Nb thin film. We show that it is possible to directly extract the genuine flux-flow resistivity from our frequency-dependent measurements without overcoming the (depinning) critical current. The characteristic frequency for vortex relaxation can also be estimated, without resorting to a specific model. We find that the F …
