Measurements of the magnetic field penetration depth λin superconductor Mo_3Sb_7 (T_c~2.1 K) were carried out by means of muon-spin-rotation. The absolute values of λ, the Ginzburg-Landau parameter κ, the first H_{c1} and the second H_{c2} critical fields at T=0 are λ(0)=720(100)nm, κ(0)=55(9), μ_0H_{c1}(0)=1.8(3)mT, and μ_0H_{c2}(0)=1.9(2)T. The zero temperature value of the superconducting energy gap Δ(0) was found to be 0.35(1)meV corresponding to the ratio 2Δ(0)/k_BT_c=3.83(10). At low temperatures λ^{-2}(T) saturates and becomes constant below T~0.3T_c, in agreement with what is expected for s-wave BCS superconductors. Our results suggest that Mo_3Sb_7 is a BCS superconductor with the isotropic energy gap
The in-plane magnetic penetration depth λ_{ab} of the iron selenide superconductor with the nominal composition FeSe_0.85 was studied by means of muon-spin rotation. The measurements of λ_{ab}^{-2}(T) are inconsistent with the presence of nodes in the gap as well as with a simple isotropic s-wave type of the order parameter, but can be equally well described within a two-gap (s+s) and an anisotropic s-wave gap picture. This implies that the superconducting energy gap in FeSe_0.85 contains no nodes.
It is shown that the notion of the finite pairing interaction energy range $T_d$ results in a linear temperature dependence of the London magnetic penetration depth $Δλ/ λ(0) = (T/T_d)(2/π)\ln 2$ at low temperature, in the case of the s-wave pairing state.
This topical review summarizes various features of magnetic penetration depth in unconventional superconductors. Precise measurements of the penetration depth as a function of temperature, magnetic field and crystal orientation can provide detailed information about the pairing state. Examples are given of unconventional pairing in hole- and electron-doped cuprates, organic and heavy fermion superconductors. The ability to apply an external magnetic field adds a new dimension to penetration depth measurements. We discuss how field dependent measurements can be used to study surface Andreev bou…
The pressure dependence of the magnetic penetration depth in polycrystalline samples of YBa2Cu3Ox with different oxygen concentrations x = 6.45, 6.6, 6.8, and 6.98 was studied by muon spin rotation (muSR). The pressure dependence of the superfluid density (p_s) as a function of the superconducting transition temperature Tc is found to deviate from the usual Uemura line. The ratio (dTc/dP)/(dp_s/dP) is factor of 2 smaller than that of the Uemura relation. In underdoped samples, the zero temperature superconducting gap and the BCS ratio both increase with increasing external hydrostatic pressure…
The penetration depth of anisotropic two-band s-wave superconductors have been studied by Ginzburg-Landau approach. The anisotropic spherical Fermi surfaces and order parameters with the spherical ellipse or pancake Fermi shape are used for derive penetration depth equation. The numerical calculation of pancake-pancake and pancake-ellipse Fermi sphere shape are fits well with the experiment data of MgB2 and CaAlSi superconductor, consequently. Our model should be the way to increase understanding in the microscopic mechanism of occurrence of the penetration depth in superconductivity state of …
The anisotropy of the London penetration depth is evaluated for two-band superconductors with arbitrary inter- and intra-band scattering times. If one of the bands is clean and the other is dirty in the absence of inter-band scattering, the anisotropy is dominated by the Fermi surface of the clean band and is weakly temperature dependent. The inter-band scattering also suppress the temperature dependence of the anisotropy.
The oxygen-isotope (^16O/^18O) effect (OIE) on the in-plane penetration depth $λ_{ab} (0)$ in underdoped Y_{1-x}Pr_xBa_2Cu_3O_{7-delta} was studied by muon-spin rotation. A pronounced OIE on $λ_{ab}^{-2}(0)$ was observed with a relative isotope shift of $Δλ^{-2}_{ab}/λ^{-2}_{ab}$=-5(2)% for x =0.3 and -9(2)% for x=0.4. It arises mainly from the oxygen-mass dependence of the in-plane effective mass $m_{ab}^{\ast}$. The OIE exponents of T_{c} and of $λ_{ab}^{-2}(0)$ exhibit a relation that appears to be generic for cuprate superconductors.
The temperature and field dependence of the effective magnetic penetration depth in the vortex state of a d-wave superconductor, as measured by muon spin rotation experiments, is calculated using a nonlocal London model. We show that at temperatures below T^* \propto \sqrt{B}, the linear T-dependence of the effective penetration depth crosses over to a T^3-dependence. This could provide an explanation for the low temperature flattening of the effective penetration depth curves observed in a recent muon spin rotation experiment.
Muon spin rotation (mSR) measurements of the in-plane penetration depth lambda_ab have been performed in the electron-doped infinite layer high-Tc superconductor (HTS) Sr0.9La0.1CuO2. Absence of the magnetic rare-earth ions in this compound allowed to measure for the first time the absolute value of lambda_ab(0) in electron-doped HTS using mSR. We found lambda_ab(0)=116(2) nm. The zero-temperature depolarization rate sigma(0)?1/lambda_ab(0)^2=4.6(1) MHz is more than four times higher than expected from the Uemura line. Therefore this electron-doped HTS does not follow the Uemura relation found…
Anisotropy, thermal and quantum fluctuations and their dependence on dopant concentration appear to be present in all cuprate superconductors, interwoven with the microscopic mechanisms responsible for superconductivity. Here we review anisotropy, in-plane and c-axis penetration depths, isotope effect and conductivity measurements to reassess the universal behavior of cuprates as revealed by the doping dependence of these phenomena and of the transition temperature.
The penetration of an $ac$ magnetic signal into a type II superconductor residing in the Shubnikov phase depends on the pinning properties of Abrikosov vortices. Within a phenomenological theory, the so-called Campbell penetration depth $λ_{\rm \scriptscriptstyle C}$ is determined by the curvature $α$ at the bottom of the effective pinning potential. Preparing the sample into a Bean critical state, this curvature vanishes and the Campbell length formally diverges. We make use of the microscopic expression for the pinning force density derived within strong pinning theory and show how flux pene…
A brief discussion is given on the nonlocal effect in multigapped superconductivity. It is pointed out that the effective magnetic penetration depth at lower external fields may be reduced by the nonlocal effect associated with the presence of small energy gap. A crude estimation of the effect in double gap system is provided and compared with the data obtained by muSR in MgB2.
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.
We investigate flux penetration in a disordered type II superconductor by molecular dynamics simulations of interacting vortices. We focus on the effect of different boundary conditions on the scaling laws for flux front propagation. The numerical results can be interpreted using a coarse grained description of the system in terms of a non-linear diffusion equation. We propose a phenomenological equation for the front position that captures the essential behavior of the system and recovers the scaling exponents.
We discuss the Meissner response to a known field source of superconductors having inhomogeneities in their penetration depth. We simplify the general problem by assuming that the perturbations of the fields by the penetration depth inhomogeneities are small. We present expressions for inhomogeneities in several geometries, but concentrate for comparison with experiment on planar defects, perpendicular to the sample surfaces, with superfluid densities different from the rest of the samples. These calculations are relevant for magnetic microscopies, such as Scanning Superconducting Quantum Inte…
We investigate flux front penetration in a disordered type II superconductor by molecular dynamics (MD) simulations of interacting vortices and find scaling laws for the front position and the density profile. The scaling can be understood performing a coarse graining of the system and writing a disordered non-linear diffusion equation. Integrating numerically the equation, we observe a crossover from flat to fractal front penetration as the system parameters are varied. The value of the fractal dimension indicates that the invasion process is described by gradient percolation.
Muon-spin rotation spectroscopy has been used to measure the internal magnetic field distribution in NbSe2 for Hc1 << H < 0.25 Hc2. The deduced profiles of the supercurrent density indicate that the vortex-core radius in the bulk decreases sharply with increasing magnetic field. This effect, which is attributed to increased vortex-vortex interactions, does not agree with the dirty-limit microscopic theory. A simple phenomenological equation in which the core radius depends on the intervortex spacing is used to model this behaviour. In addition, we find for the first time that the in-plane magn…
We present a theoretical description of the London penetration depth of a multi-band superconductor in the case when both superconducting and spin-density wave orders coexist. We focus on clean systems and zero temperature to emphasize the effect of the two competing orders. Our calculation shows that the supefluid density closely follows the evolution of the superconducting order parameter as doping is increased, saturating to a BCS value in the pure superconducting state. Furthermore, we predict a strong anisotropic in-pane penetration depth induced by the spin-density wave order.
We comment on a recent letter by Schopohl and Dolgov (SD) which raised the possibility that a d-wave superconductor might be thermodynamically unstable in the limit $T\to 0$. The point of our comment is that this instability can be inevitably prevented by the non-local effects.
We show that various factors can lead to an isotopic dependence of the penetration depth $δ$. Non-adiabaticity (Jahn-Teller crossing) leads to the isotope effect of the charge carrier concentration $n$ and, consequently, of $δ$ in doped superconductors such as the cuprates. A general equation relating the isotope coefficients of $T_c$ and of $δ$ is presented for London superconductors. We further show that the presence of magnetic impurities or a proximity contact also lead to an isotopic dependence of $δ$; the isotope coefficient turns out to be temperature dependent, $β(T)$, in these cases. …
The magnetization of a planar heterostructure of periodically alternating type-II superconductor and soft-magnet strips exposed to a transverse external magnetic field is studied. An integral equation governing the sheet current distribution in the Meissner state of the superconductor constituents is derived. The field of complete penetration of magnetic flux in the critical state of the superconductor constituents is calculated for different widths of the superconductor and the soft-magnet constituents and a range of values of the relative permeability of the soft-magnet constituents.
We investigate how the geometrical symmetry affects the penetration and arrangement of vortices in mesoscopic superconductors using self-consistent Bogoliubov-de Gennes equations. We find that the entrance of the vortex happens when the current density at the hot spots reaches the depairing current density. Through determining the spatial distribution of hot spots, the geometrical symmetry of the superconducting sample influences the nucleation and entrance of vortices. Our results propose one possible experimental approach to control and manipulate the quantum states of mesoscopic superconduc…
Temperature dependence of the magnetic penetration depth, $λ$(T), was measured in the Meissner state in single crystals B$_{1-x}$K$_{x}$BiO$_{3}$ (x=0.37) using tunnel diode resonator technique. At low temperatures, $0.013 \le T/T_c \le 0.4$, $λ$(T) is exponentially flat, which provides a strong evidence for conventional s-wave BCS behavior. Numerical analysis of the data rules out the possibility of a gap with nodes.
The nonlinear surface impedance of a thin superconducting strip carrying a microwave current has been calculated numerically from first principles based upon flux penetration due to a current-induced critical state. The calculations approach analytic results in the appropriate limit. The technique is useful for design of passive superconducting microwave circuits.
We study the effect of disorder on the London penetration depth in iron-based superconductors. The theory is based on a two-band model with quasi-two-dimensional Fermi surfaces, which allows for the coexistence region in the phase diagram between magnetic and superconducting states in the presence of intraband and interband scattering. Within the quasiclassical approximation we derive and solve Eilenberger's equations, which include a weak external magnetic field, and provide analytical expressions for the penetration depth in the various limiting cases. A complete numerical analysis of the do…
We report on measurements of the temperature dependence of the magnetic penetration depth of a very high quality single crystal of nonmagnetic superconductor LaPt3Si without inversion symmetry. The results are compared with those previously reported for the isostructural antiferromagnetic superconductor CePt3Si. At low temperatures, the penetration depth follows a BCS exponential behavior that implies an isotropic energy gap in LaPt3Si, in contrast to a linear response that indicates line nodes in CePt3Si. These line nodes have been argued to be protected by symmetry or accidentally generated …
We report magnetization measurements under high hydrostatic pressure in the newly discovered pyrochlore superconductor RbOs_2O_6 (T_c\simeq6.3K at p=0). A pronounced and {\it positive} pressure effect (PE) on T_c with dT_c/dp =0.090(1)K/kbar was observed, whereas no PE on the magnetic penetration depth λwas detected. The relative pressure shift of T_c [ dlnT_c/dp \simeq 1.5%/kbar] is comparable with the highest values obtained for highly underdoped high-temperature cuprate superconductors. Our results suggest that RbOs_2O_6 is an adiabatic BCS-type superconductor.
We show that, under certain conditions, the low temperature behavior of the magnetic penetration depth $λ(T)$ of a pure d-wave superconductor is determined by nonlocal electrodynamics and, contrary to the general belief, the deviation $Δλ(T) = λ(T)-λ(0)$ is proportional to T^2 and not T. We predict that the $Δλ(T)\propto T^2$ dependence, due to nonlocality, should be observable experimentally in nominally clean high-T_c superconductors below a crossover temperature $T^* = (ξ_o/λ_o)Δ_o \sim 1 K$. Possible complications due to impurities, surface quality and crystal axes orientation are discusse…
Measurements of the magnetic penetration depth (lambda) in the Fe-based superconductor Ba_(1-x)Rb_xFe_2As_2 (x=0.3, 0.35, 0.4) were carried out using the muon-spin rotation muSR technique. The temperature dependence of lambda is well described by a two-gap s+s-wave scenario with a small gap Delta_1 = 1 - 3 mev and a large gap Delta_2 = 7 - 9 mev. By combining the present data with those obtained for RbFe_2As_2 a decrease of the BCS ratio 2Delta_2/(k_B)(T_c) with increasing Rb content x is observed. On the other hand, the BCS ratio 2Delta_1/(k_B)(T_c) is almost independent of x. In addition, th…
The magnetic penetration depth $λ(T,H,j)$ was measured in the presence of a slowly relaxing supercurrent, $j$. In single crystal $\mathrm{Bi_2Sr_2CaCu_2O_8}$ below approximately 25 K, $λ(T,H,j)$ is strongly hysteretic. We propose that the irreversibility arises from a shift of the vortex position within its pinning well as $j$ changes. The Campbell length depends upon the ratio $j/j_{c}$ where $j_{c}$ is the critical current defined through the Labusch parameter. Similar effects were observed in other cuprates and in an organic superconductor.
We investigate the free energy and the penetration depth of a quasi-two-dimensional d-wave superconductor in the presence of a weak magnetic field by taking account of thermal, nonlocal and nonlinear effects. In an approximation in which the superfluid velocity $v_s$ is assumed to be slowly varying, the free energy is calculated and compared with available results in several limiting cases. It is shown that either nonlocal or nonlinear effects may cut off the linear-$T$ dependence of both the free energy and the penetration depth in all the experimental geometries. At extremely low $T$, the no…
We report measurements of the temperature dependence of the magnetic penetration depth in different quality polycrystalline samples of noncentrosymmetric LaNiC2 down to 0.05 K. This compound has no magnetic phases and breaks time-reversal symmetry. In our highest quality sample we observe a T^2 dependence below 0.4Tc indicative of nodes in the energy gap. We argue that previous results suggesting conventional s-wave behavior may have been affected by magnetic impurities.
Vortex penetration and flux relaxation phenomenon carry the information about the pinning ability, and consequently current-carrying ability, of a type-II superconductor. However, the theoretical descriptions to these phenomena are currently limited to the cases with special initial conditions. A generalization to the recently developed infinite series models is presented here. It is shown that one can convert a vortex penetration process with a non-zero initial internal field into a process with a zero initial internal field by introducing some time parameters. Similarly, one can also convert…
It is shown that attempts to accurately deduce the magnetic penetration depth of overdoped BaFe_{1.82}Co_{0.18}As2 single crystals by transverse-field muon spin rotation (TF-muSR) are thwarted by field-induced magnetic order and strong vortex-lattice disorder. We explain how substantial deviations from the magnetic field distribution of a nearly perfect vortex lattice by one or both of these factors is also significant for other iron-based superconductors, and this introduces considerable uncertainty in the values of the magnetic penetration depth obtained by TF-muSR.
A layered antiferromagnetic superconductor in the mixed state may posses magnetic domains created along the Josephson vortices. This may happen when an external magnetic field is strong enough to flip over magnetic moments, lying in the phase core of the Josephson vortex, from their ground state configuration. The formation of the domain structure of the vortices modifies the surface energy barrier of the superconductor. During this process the entrance of the flux is stopped and a newly created state exhibits perfect shielding. Such behavior should be visible as a plateau on the dependence of…
We show that the clean superconductor with line of gap nodes is not in conflict with the Nernst theorem. The answer to the question in the title of the Schopohl-Dolgov paper in Phys. Rev. Lett. 80 (1998) 4761 (cond-mat/9802264) is yes.
Measurements of the magnetic field penetration depth $λ$ in the ternary boride superconductor Li$_2$Pd$_3$B ($T_c\simeq7.3$ K) have been carried out by means of muon-spin rotation ($μ$SR). The absolute values of $λ$, the Ginzburg-Landau parameter $κ$, and the first $H_{c1}$ and the second $H_{c2}$ critical fields at T=0 obtained from $μ$SR were found to be $λ(0)=252(2)$ nm, $κ(0)=27(1)$, $μ_0H_{c1}(0)=9.5(1)$ mT, and $μ_0H_{c2}(0)=3.66(8)$ T, respectively. The zero-temperature value of the superconducting gap $Δ_0=$1.31(3) meV was found, corresponding to the ratio $2Δ_0/k_BT_c=4.0(1)$. At low …
We investigate the magnetic field distribution near the surface of a magnetic superconductor when a magnetic source is placed close to the superconductor. The magnetic field distribution can be measured by magnetic force microscopy and scanning SQUID microscopy, from which one can extract both the penetration depth $λ_L$ and magnetic susceptibility $χ$. When the magnetic moments are parallel to the surface, one extracts $λ_L/\sqrt{1-4πχ}$. When the moments are perpendicular to the surface, one obtains $λ_L$. By changing the orientation of the crystal, one thus is able to extract both $χ$ and $…
A variety of experiments suggest that in the cuprates, the low-energy superconducting quasiparticles undergo forward scattering from extended impurity potentials. We argue that when such potentials dominate the scattering, the penetration depth may be computed in a simple zero-angle scattering approximation (ZSA), in which the vertex corrections to the Meissner effect may be summed exactly. We find a remarkably simple relationship between the normal fluid density and the quasiparticle density of states of the disordered system which holds for every realization of the disorder. We expect this r…
The notion of a finite pairing interaction energy range via Nam, results in the incomplete condensation in which not all states participate in pairings. Thestates not participating in pairings are shown to yield the lowenergy states responsible for the linear T dependence ofsuperelectron density at low T in a s-wave superconductor. Wepresent extensive quantitative calculations of $λ$(T) forall T ranges, in good agreements with experiments. It is notnecessary to have nodes in the order parameter, to account for thelinear T dependence of $λ$(T) at low T in high Tc superconductors.
The magnetic vortex lattice (VL) of polycrystalline MgB2 has been investigated by transverse-field muon-spin-relaxation (TF-MuSR). The evolution of TF-MuSR depolarization rate, sigma, that is proportional to the second moment of the field distribution of the VL has been studied as a function of temperature and applied magnetic field. The low temperature value s exhibits a pronounced peak near Hext = 75 mT. This behavior is characteristic of strong pinning induced distortions of the VL which put into question the interpretation of the low-field TF-MuSR data in terms of the magnetic penetration …
We report a method to locally measure the penetration depth $λ$ in a superconductor by detecting the diamagnetic response using magnetic force microscopy (MFM). We extract $λ$ by fitting the height dependence of the levitation force in the Meissner state using an analytical model that approximates the MFM tip as a single-domain, truncated conical shell. We demonstrate on two YBa$_2$Cu$_3$O$_{6+x}$ single crystals with two MFM tips that the obtained values agree well with previous results. This approach is not affected by the tip width and can be applied to similar but not identical tips.
We report a theoretical study on the deviations of the Meissner penetration depth $λ(T)$ from its London value in d-wave superconductors at low temperatures. The difference arises from low-energy surface Andreev bound states. The temperature dependent penetration depth is shown to go through a minimum at the temperature $T_{m0}\sim \sqrt{ξ_0/λ_0}T_c$ if the broadening of the bound states is small. The minimum will straighten out when the broadening reaches $T_{m0}$. The impurity scattering sets up the low-temperature anomalies of the penetration depth and destroys them when the mean free path …
It is demonstrated that in the type I and II superconductors with low-transparent twinning planes (TP) the penetration of external parallel magnetic field into the region of the twinning plane can be energetically favorable. In the type I superconductors the twinning planes become similar to Josephson junctions and the magnetic field penetrates into the center of the TP in the form of soft Josephson-like vortices. This leads to increase in the critical magnetic field values. The corresponding phase diagram in the parameter plane "temperature - magnetic field" essentially differs from the one o…
The effect of pressure on the magnetic penetration depth $λ$ was tested in the hole-doped superconductor YBa2Cu3O(7-d) and in the electron-doped one Sr0.9La0.1CuO2 by means of magnetization measurements. Whereas a large change of $λ$ was found in YBa2Cu3O(7-d), confirming the non-adiabatic character of the electron-phonon coupling in hole-doped superconductors, the same quantity is not affected by pressure in the electron-doped Sr0.9La0.1CuO2, suggesting a close similarity of the latter to conventional adiabatic BCS superconductors. The present results imply a remarkable difference between the…
Muon spin spectroscopy measurements have been used to study the superconducting state of FeTe0.5Se0.5. The temperature dependence of the in-plane magnetic penetration depth, lambda_ab(T), is found to be compatible with either a two gap s+s wave or an anisotropic s-wave model. The value for lambda_ab(T) at T=0 K is estimated to be lambda_ab(0)=534(2)nm.
A generalized phenomenological model for the critical state of type-II superconductors with magnetic field parallel to the superconducting plate is proposed. This model considers the global magnetization including both the equilibrium magnetization from surface screening current and the non-equilibrium magnetization from bulk pinning in a self-consistent way. Our model can be used to simulate the magnetization-hysteresis-loops (MHLs) and flux penetrating process of different type-II superconductors, from low- to high-kappa values. Here we take an optimally doped Ba0.6K0.4Fe2As2 single crystal …
We have performed transverse field muon spin rotation measurements of single crystals of Ba(Fe$_{0.93}$Co$_{0.07})_2$As$_2$ with the applied magnetic field along the $\hat{c}$ direction. Fourier transforms of the measured spectra reveal an anisotropic lineshape characteristic of an Abrikosov vortex lattice. We have fit the $μ$SRSR spectra to a microscopic model in terms of the penetration depth $λ$ and the Ginzburg-Landau parameter $κ$. We find that as a function of temperature, the penetration depth varies more rapidly than in standard weak coupled BCS theory. For this reason we first fit the…
We report measurements of the magnetic penetration depth $λ$ in single crystals of CeCoIn$_{5}$ down to $\sim$0.14 K using a tunnel-diode based, self-inductive technique at 28 MHz. While the in-plane penetration depth tends to follow a power law, $λ_{//} \sim {\it T}^{3/2}$, the data are better described as a crossover between linear ({\it T} $\gg $ ${\it T}^\ast $) and quadratic ({\it T} $\ll {\it T}^\ast $) behavior, with ${\it T}^\ast $ the crossover temperature in the strong-coupling limit. The {\it c}-axis penetration depth $λ_{\perp} $ is linear in {\it T}, providing evidence that CeCoIn…
We show that in superconductors that break time reversal symmetry and have anisotropy, such as p+ip materials, all order parameters and magnetic modes are mixed. Excitation of the gap fields produces an excitation of the magnetic field and vice versa. Correspondingly the long-range decay of the magnetic field and order parameter are in general given by the same exponent. Thus one cannot characterize p+ip superconductors by the usual coherence and magnetic field penetration lengths. Instead the system has normal modes that are associated with linear combinations of magnetic fields, moduli of an…
We calculate the change in susceptibility resulting from a thin sheet with reduced penetration depth embedded perpendicular to the surface of an isotropic superconductor, in a geometry applicable to scanning Superconducting QUantum Interference Device (SQUID) microscopy, by numerically solving Maxwell's and London's equations using the finite element method. The predicted stripes in susceptibility agree well in shape with the observations of Kalisky et al. of enhanced susceptibility above twin planes in the underdoped pnictide superconductor Ba(Fe1-xCox)2As2 (Ba-122). By comparing the predicte…
The electromagnetic response of a system with two planes per unit cell involves, in addition to the usual intraband contribution, an added interband term. These transitions affect the temperature dependence and the magnitude of the zero temperature c-axis penetration depth. When the interplane hopping is sufficiently small, the interband transitions dominate the low temperature behaviour of the penetration depth which then does not reflect the linear temperature dependence of the intraband term and in comparison becomes quite flat even for a d-wave gap. It is in this regime that the pseudogap …
Polarized neutron reflectometry (PNR) provides evidence that nonlocal electrodynamics governs the magnetic field penetration in an extreme low-k superconductor. The sample is an indium film with a large elastic mean free path (11 mkm) deposited on a silicon oxide wafer. It is shown that PNR can resolve the difference between the reflected neutron spin asymmetries predicted by the local and nonlocal theories of superconductivity. The experimental data support the nonlocal theory, which predicts a nonmonotonic decay of the magnetic field.
We study the problem of flux penetration into type--I superconductors with high demagnetization factor (slab geometry).Assuming that the interface between the normal and superconducting regions is sharp, that flux diffuses rapidly in the normal regions, and that thermal effects are negligible, we analyze the process by which flux invades the sample as the applied field is increased slowly from zero.We find that flux does not penetrate gradually.Rather there is an instability in the process and the flux penetrates from the boundary in a series of bursts, accompanied by the formation of isolated…
Substantial control of the interlayer spacing in Bi-based high temperature superconductors has been achieved through the intercalation of guest molecules between the superconducting layers. Measurements using implanted muons reveal that the penetration depth increases with increasing layer separation while T_c does not vary appreciably, demonstrating that the bulk superfluid density is not the determining factor controlling T_c. Our results strongly suggest that the superfluid density appearing in the Uemura scaling relation n_s/m* \propto T_c should be interpreted as the two dimensional densi…
Magnetic penetration depth, $λ_{m}$, was measured as a function of temperature and magnetic field in single crystals of low carrier density superconductor YPtBi by using a tunnel-diode oscillator technique. Measurements in zero DC magnetic field yield London penetration depth, $λ_{L}\left(T\right)$, but in the applied field the signal includes the Campbell penetration depth, $λ_{C}\left(T\right)$, which is the characteristic length of the attenuation of small excitation field, $H_{ac}$, into the Abrikosov vortex lattice due to its elasticity. Whereas the magnetic field dependent $λ_C$ exhibit …
The influence of antiferromagnetic order on the mixed state of a superconductor may result in creation of spin-flop domains along vortices. This may happen when an external magnetic field is strong enough to flip over magnetic moments in the vortex core from their ground state configuration. The formation of domain structure causes modification of the surface energy barrier, and creation of the new state in which magnetic flux density is independent of the applied field. The modified surface energy barrier has been calculated for parameters of the antiferromagnetic superconductor DyMo$_{6}$S$_…
Campbell penetration depth in a single crystal of heavy fermion superconductor CeCoIn$_5$
Ames National Laboratory（艾姆斯国家实验室）；Iowa State University（爱荷华州立大学）；Missouri University of Science and Technology（密苏里科技大学）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Shanghai Advanced Research in Physical Sciences (SHARPS)（上海物理科学研究院）；Vinca Institute of Nuclear Sciences, University of Belgrade（贝尔格莱德大学温卡核科学研究所）
