Temperature Dependence Of Penetration Depth Research Articles

THE PENETRATION DEPTH OF H3S SUPERCONDUCTOR BY SEMICLASSICAL APPROACH

The penetration depth is a magnetic field mechanism by which an external magnetic field penetrates into superconductors’ surfaces and is related to the Meissner effect. The penetration depth property was studied by the semiclassical approach to identify other properties of superconductors. In this study, we investigated the penetration depth of the H3S superconductor under external pressure. The H3S superconductor is high Tc, s-wave isotropic, and high pressure prepared superconductors. We derive an analytical equation for the near-zero temperature penetration depth with pressure effect parameters. The derived equations were then numerically calculated and predicted the experimental data on H­3S superconductor penetration depth. We discovered that the temperature dependent penetration depth under pressure of H­3S superconductor is reasonable at Tc(χ = 473, ε0 = 91,Qp = 0.1) = 200.832 K. , as well as is the influence of the directly parameter on Tc(χ,ε0,Qp), Δ(0,χ,ε0,Qp), and λ(T,χ,ε0,Qp)/λ(0,χ,ε0,Qp), with Qp>0.1 does not corresponding theory

Optical properties of superconducting pressurized LaH10

Recently superconductivity has been discovered at around 200~K in a hydrogen sulfide system and around 260~K in a lanthanum hydride system, both under pressures of about 200 GPa. These record-breaking transition temperatures bring within reach the long-term goal of obtaining room temperature superconductivity. We have used first-principle calculations based on density functional theory (DFT) along with Migdal-Eliashberg theory to investigate the electron-phonon mechanism for superconductivity in the $Fm\bar{3}m$ phase proposed for the LaH$_{10}$ superconductor. We show that the very high transition temperature $T_c$ results from a highly optimized electron-phonon interaction that favors coupling to high frequency hydrogen phonons. Various superconducting properties are calculated, such as the energy gap, the isotope effect, the specific heat jump at $T_c$, the thermodynamic critical field and the temperature-dependent penetration depth. However, our main emphasis is on the finite frequency optical properties, measurement of which may allow for an independent determination of $T_c$ and also a confirmation of the mechanism for superconductivity.

Power-Law Temperature Dependence of the Penetration Depth in a Topological Superconductor Due to Surface States.

We study the temperature dependence of the magnetic penetration depth in a 3D topological superconductor (TSC), incorporating the paramagnetic current due to the surface states. A TSC is predicted to host a gapless 2D surface Majorana fluid. In addition to the bulk-dominated London response, we identify a T^{3} power-law-in-temperature contribution from the surface, valid in the low-temperature limit. Our system is fully gapped in the bulk, and should be compared to bulk nodal superconductivity, which also exhibits power-law behavior. Power-law temperature dependence of the penetration depth can be one indicator of topological superconductivity.

Determination of London penetration depth from ac susceptibility measurements of a square superconducting thin film

A technique is developed for determining the London penetration depth by ac susceptibility measurements of a square film. It is based on the numerical calculation of the Meissner susceptibility of square superconducting films as a function of the Pearl length and the critical-state susceptibility of thin disks previously derived analytically. With this technique, intrinsic superconducting properties may be studied for each film together with critical-current density. The application of the technique to an actual YBa2Cu3O7−δ film allows us to obtain its temperature dependent penetration depth and depairing current density.

Possible nodal superconducting gap in Fe1+y(Te1−xSex) single crystals from ultralow temperature penetration depth measurements

Using a radio frequency tunnel diode oscillator technique, we measured the temperature dependence of the in-plane London penetration depth $\Delta\lambda_{ab}(T)$ in Fe$_{1+y}$(Te$_{1-x}$Se$_{x})$ single crystals, down to temperatures as low as 50 mK. A significant number of samples, with nominal Se concentration $x$=0.36, 0.40, 0.43 and 0.45 respectively, were studied and in many cases we found that $\Delta\lambda_{ab}(T)$ shows an upturn below 0.7 K, indicative of a paramagnetic type contribution. After subtracting the magnetic background, the low temperature behavior of penetration depth is best described by a power law with exponent $n\approx2$ and with no systematic dependence on the Se concentration. Most importantly, in the limit of T$\rightarrow$0, in some samples we observed a narrow region of linear temperature dependence of penetration depth, suggestive of nodes in the superconducting gap of Fe$_{1+y}$(Te$_{1-x}$Se$_{x})$.

Temperature dependence of penetration depth in electron-doped cuprate superconductors

Within the framework of the kinetic energy driven superconducting mechanism, the temperature dependence of the magnetic field penetration depth in the electron-doped cuprate superconductors is studied. It is shown that the magnetic field penetration depth shows a crossover from the linear temperature dependence at low temperatures to a nonlinear one at the extremely low temperatures, in qualitative agreement with the experimental results.

Fully gapped superconductivity and strong electron correlations in the [formula omitted]-pyrochlore [formula omitted

To elucidate the superconducting gap structure and the influence of rattling motion on quasiparticle dynamics in the superconducting state of KOs 2 O 6 , thermal conductivity and microwave surface impedance were measured at low temperatures. The magnetic field dependence of thermal conductivity at the lowest temperature and the temperature dependence of penetration depth strongly indicate a fully gapped superconductivity in KOs 2 O 6 . The quasiparticle scattering time is strongly enhanced in the superconducting state, indicating a strong electron–electron inelastic scattering in the normal state. These results highlight that KOs 2 O 6 is unique among superconductors, which is characterized by the coexistence of fully gapped superconductivity and strong electron correlations.

Full-gap superconductivity with strong electron correlations in the [formula omitted]-pyrochlore KOs 2O 6

To elucidate the superconducting gap structure and the influence of rattling motion on quasiparticle dynamics in the superconducting state of KOs 2O 6, the thermal conductivity and microwave surface impedance were measured at low temperatures. The magnetic field dependence of thermal conductivity and temperature dependence of penetration depth demonstrate full-gap superconductivity in KOs 2O 6. The quasiparticle scattering time is strongly enhanced in the superconducting state, indicating a strong electron inelastic scattering in the normal state. These results highlight that KOs 2O 6 is unique among superconductors with strong electron correlations.

Evidence fors-wave superconductivity in noncentrosymmetricRe3Wfrom magnetic penetration depth measurements

We report measurements of the temperature dependence of the magnetic penetration depth $\ensuremath{\lambda}(T)$ in noncentrosymmetric superconductor ${\mathrm{Re}}_{3}\mathrm{W}$. We employed two experimental techniques: extraction of $\ensuremath{\lambda}(T)$ from magnetic dc susceptibility, measured on a powder sample, and the rf tunnel diode resonator technique, where a bulk polycrystalline sample was used. The results of both techniques agree: the temperature dependence of the penetration depth can be well described by weak-coupling, dirty-limit, $s$-wave BCS theory where we obtain $\ensuremath{\Delta}(0)∕{k}_{B}{T}_{C}=1.76\ifmmode\pm\else\textpm\fi{}0.05$. No evidence for unconventional pairing resulting from the absence of the inversion symmetry is found.

Thermodynamic and transport investigation ofCeCoIn5−xSnx

Measurements of specific heat, magnetic susceptibility, electrical resistivity, and penetration depth have been performed on $\mathrm{Ce}\mathrm{Co}{\mathrm{In}}_{5\ensuremath{-}x}{\mathrm{Sn}}_{x}$ $(0\ensuremath{\leqslant}x\ensuremath{\leqslant}0.24)$ single crystals. The suppression of superconductivity and the decrease of the specific heat jump at ${T}_{c}$, $\ensuremath{\Delta}C∕{T}_{c}$, with increasing Sn concentration, and the power-law temperature dependence of penetration depth are consistent with impurity scattering calculated within the Abrikosov-Gorkov formalism indicating $d$-wave superconductivity in $\mathrm{Ce}\mathrm{Co}{\mathrm{In}}_{5\ensuremath{-}x}{\mathrm{Sn}}_{x}$. The non-Fermi liquid behavior [$C∕T\ensuremath{\sim}\ensuremath{-}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}T$ and $\ensuremath{\rho}(T)\ensuremath{\sim}T$] observed in the normal state in zero magnetic field is quite robust against Sn substitution (and a variety of other tuning parameters), suggesting quantum criticality involving itinerant $f$-electrons in this system.

Penetration depth and Hc2 anisotropy of MgB 2 by [formula omitted]B NMR

11 B nuclear magnetic resonance (NMR) measurements have been performed to investigate vortex states of polycrystalline MgB 2. The spectrum below T c shows a composite structure with a narrow symmetric peak at an unshifted position and a broad asymmetric peak with a large diamagnetic shift. We identify that the broad peak originates from the vortex state whereas the narrow peak comes from crystallites in the normal state. This behavior can be understood as the NMR powder spectrum with significant anisotropy of an upper critical field H c2. From temperature dependence of the broad fraction, we find the anisotropy of H c2 is ∼4.7. We also determine the temperature-dependent penetration depth from the linewidth of the broad peak.

Magnetic Field Dependence of Penetration Depth of Optimally Doped Bi2Sr2CaCu2O8+? Single Crystal

The behavior of the in-plane penetration depth λ(T) extracted from the reversible magnetization in different magnetic fields for Bi2Sr2CaCu2O8+δ single crystal is investigated. It is found that the temperature dependence of penetration depth in different fields follows a quadratic function between 40 and 60 K. The magnetic field dependence of penetration depth at different temperatures obeys a power law. The observed temperature dependence of λ(T) in different fields is similar to the predicted behaviors of the nonlocal-nonlinear London theory.

Low-temperature magnetic penetration depth in d-wave superconductors: Zero-energy bound state and impurity effects

We report a theoretical study on the deviations of the Meissner penetration depth $\ensuremath{\lambda}(T)$ 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 ${T}_{m0}\ensuremath{\sim}\sqrt{{\ensuremath{\xi}}_{0}/{\ensuremath{\lambda}}_{0}}{T}_{c}$ 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 is not sufficiently large. A phase transition to a state with a spontaneous surface supercurrent is investigated and its critical temperature determined in the absence of a subdominant channel activated at low temperatures near the surface. Nonlinear corrections from Andreev low-energy bound states to the penetration length are obtained and shown, on account of their broadening, to be small in the Meissner state of strong type-II superconductors.

Strong-coupling effects on the temperature dependence of penetration depth inYBa2Cu3O7−δthin films nearTc

We present accurate experimental data on the temperature dependence of the penetration depth \ensuremath{\lambda} in $c$-axis-oriented ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ thin films close to ${T}_{c}.$ The samples were grown in situ on ${\mathrm{LaAlO}}_{3}$ (100) single-crystal substrates. The penetration depth measurements are performed by an inverted microstrip method, using resonators of different geometries. Near ${T}_{c}$ we compare the three-dimensional (3D) $\mathrm{XY}$ critical regime and the Ginzburg-Landau (GL) behavior. Our data show that the GL approach follows the observed temperature dependence closer than the 3D $\mathrm{XY}$ model. The experimental results are discussed in the light of recent models describing the effect of strong coupling on the $\ensuremath{\lambda}(T)$ behavior near ${T}_{c}$ for an $s$-wave and a $d$-wave high-temperature superconductor.

Magnetic levitation force and penetration depth in type-II superconductors.

The superconducting levitation force F acting on a magnet placed above a type-II superconductor in both Meissner and mixed states is calculated as a function of temperature, based upon the London model. A simple relationship between the levitation force and the London penetration depth \ensuremath{\lambda} is found. In particular, in the limit of a/\ensuremath{\lambda}\ensuremath{\gg}1, where a is the separation between the magnet and the superconductor, F varies linearly with \ensuremath{\lambda}, regardless of the shape of the magnet. The temperature dependences of \ensuremath{\lambda} and F are examined for various superconducting pairing states, including s-wave, d-wave, and s+id states. It is found that, at low temperatures, both \ensuremath{\lambda} and F show an exponential temperature dependence for s-wave, linear-T for d-wave, and ${\mathit{T}}^{2}$ dependence in a wide low-temperature range for the s+id state with a dominant d-wave component. The magnetic force microscope (MFM) is proposed to accurately measure the temperature-dependent levitation force. It is shown that the microscopic size of the MFM tip enables one to obtain the intrinsic temperature-dependent penetration depth of a single grain, in spite of the overall quality of the superconducting sample.

STM study of anisotropic superconducting gap of Bi-based oxides

The electron tunneling study was done on both Bi 2Sr 2CaCu 2O 8 and Bi 2Sr 2CaCu 2−xNi xO 8 with use of STM and temperature dependence of the magnetic field penetration depth was also investigated. The tunneling conductance obtained at the lateral surface of single crystal of Bi 2Sr 2CaCu 2O 8 indicates the finite gap on the whole Fermi surface, while the considerable anisotropy is found. The temperature dependence of the penetration depth is of the thermal activation type. These results indicate symmetry of the pair wave function is the predominant s-wave mixed with the d-wave. For Bi 2Sr 2CaCu 2−xNi xO 8, any clear gap structure was not found in the tunneling conductance at the cleaved surface. The penetration depth exhibits the T 2 temperature dependence.

Upper critical field, penetration depth, and GL parameter of Tl-2223 single crystals

A Tl 2Ca 2Ba 2Cu 3O 10 single crystal of platelet shape with T c=121.5 K was investigated by SQUID magnetometry. Zero field cooled (=ZFC) and field cooled (=FC) measurements were carried out in different fields with the applied field parallel to the crystallographic c-axis. Taking the fluctuations of the vortices in Josephson-coupled layered superconductors into account, the temperature dependent penetration depth λ ab, the Ginzburg Landau parameter κ, and the upper critical field H c2 are calculated from the reversible ZFC/FC magnetization data. The H c2-data (Hc) can be fitted linearly at higher temperatures. The temperature dependent penetration depth does not follow the empirical law λ( T)=λ(0)/(1−( T/T c ) 4) 1 2 .

Penetration depth measurements for Nd 1.85Ce 0.15CuO 4 and NbCN thin films using a kinetic inductance technique

The absolute value and the temperature dependence of the magnetic penetration depth λ( T) have been measured for high-quality NbCN and Nd 1.85Ce 0.15CuO 4 (NCCO) thin films. A kinetic inductance technique was used to measure the screening of a thin superconducting film where the film thickness d was less than or of the order of the London penetration depth. In this limit the kinetic inductance L k is proportional to λ 2( T)/ d. The kinetic inductance was measured on unpatterned films using a two-coil mutual inductance technique. It was found that the temperature dependence of the penetration depth for NbCN and NCCO at low temperatures is exponential as expected, confirming earlier reports. We also describe how λ(0) can be extracted from the kinetic inductance data.

The temperature dependence of resonant frequency shift in microwave cavity for high T c superconductors

The dispersive detection of an electron-spin resonance spectrometer is far more sensitive than the conventional absorptive detection. It has been successfully exploited to verify the superconducting state for the recently developed high T c superconductors by the observation of resonant frequency shift in a TE 102 microwave cavity. We attribute the increase of resonant frequency as temperature decreases to be due to the Meissner effect for T < T c and the skin-depth effect for T > T c . The temperature dependence of penetration depth λ( T) following the Casimir-Gorter relation is not adequate to account for the frequency drift at T below T c , while it can be elucidated more fully by the heavy-Fermion pairing mechanism.

Optical properties of doped fullerenes in the superconducting state

The infrared optical conductivity of Rb 3C 60 and K 3C 60 and the temperature-dependent penetration depth of K 3C 60 are calculated within a model for the pairing interaction which includes the possibility of coupling to both intra- and intermolecular phonons. It is found that excellent agreement with experimental data only occurs for coupling to high frequency intramolecular phonons, with an impurity scattering rate in the near-to-dirty limit. Strong coupling to low frequency modes is incompatible with the optical data.