Measurements of London penetration depth are a sensitive tool to study multi-band superconductivity and it has provided several important insights to the behavior of Fe-based superconductors. We first briefly review the "experimentalist - friendly" self-consistent Eilenberger model that relates the measurable superfluid density and structure of superconducting gaps. Then we focus on the \BaFe -derived materials, for which the results are consistent with 1) two distinct superconducting gaps; 2) development of strong in-plane gap anisotropy with the departure from the optimal doping; 3) appearance of gap nodes along the $c-$direction in a highly overdoped regime; 4) significant pair-breaking, presumably due to charge doping; 5) fully gapped (exponential) intrinsic behavior at the optimal doping if scattering is removed (probed in the "self-doped" stoichiometric LiFeAs); 6) competition between magnetically ordered state and superconductivity, which do coexist in the underdoped compounds. Overall, it appears that while there are common trends in the behavior of Fe-based superconductors, the gap structure is non-universal and is sensitive to the doping level. It is plausible that the rich variety of possible gap structures within the general $s_{\pm}$ framework is responsible for the observed behavior.
The London model describes strongly type-2 superconductors as massive vector field theories, where the magnetic field decays exponentially at the length scale of the London penetration length. This also holds for isotropic multi-band extensions, where the presence of multiple bands merely renormalises the London penetration length. We show that, by contrast, the magnetic properties of anisotropic multi-band London models are not this simple, and the anisotropy leads to the inter-band phase differences becoming coupled to the magnetic field. This results in the magnetic field in such systems ha…
The mechanism of formation of dome-like phase diagrams and the features of magnetic field penetration in iron pnictides with hetero- and isovalent doping are considered within the framework of the previously proposed model, which assumes the local character of doping and the cluster structure of resulted superconducting phase. It is shown that the proposed model, despite its simplicity and neglect of the features of the electronic structure, makes it possible not only to accurately calculate the positions of superconducting domes on the phase diagrams of specific HTSC compounds, but also to ex…
We show on a few examples of one-band materials with spheroidal Fermi surfaces and anisotropic order parameters that anisotropies $γ_H$ of the upper critical field and $γ_λ$ of the London penetration depth depend on temperature, the feature commonly attributed to multi-band superconductors. The parameters $γ_H$ and $γ_λ$ may have opposite temperature dependencies or may change in the same direction depending on Fermi surface shape and on character of the gap nodes. For two-band systems, the behavior of anisotropies is affected by the ratios of bands densities of states, Fermi velocities, aniso…
The London penetration depth $λ$ is the basic length scale for electromagnetic behavior in a superconductor. Precise measurements of $λ$ as a function of temperature, field, and impurity scattering have been instrumental in revealing the nature of the order parameter and pairing interactions in a variety of superconductors discovered over the past decades. Here we recount our development of the tunnel-diode resonator technique to measure $λ$ as a function of temperature and field in small single crystal samples. We discuss the principles and applications of this technique to study unconvention…
We have characterized an electron-irradiated Ba1-xKxFe2As2 (x = 0.53) single-crystal using two different experimental techniques: magneto-optic measurements and microwave measurements. The crystal has been measured before as well as after the 2.5 MeV electron irradiation process. After irradiation it was annealed in a number of steps, between 90 deg C and 180 deg C, and measured after each annealing step. Most microwave measurements were performed by means of a copper cavity, taking advantage of the TE011 and TM110 modes, allowing for the determination of the London penetration depths changes …
Unconventional London penetration depth in Ba(Fe0.93Co0.07)2As2 single crystals
在几种Ba（Fe $_{0.93}$ Co $_{0.07}$）$_2$ As $_2$单晶中测量了伦敦穿透深度$λ(T)$。热力学，电磁和结构表征测量证实，这些晶体是优良的品质。所观察到的$λ(T)$的低温变化遵循幂律，$Δλ(T) \sim T^n$与$n=2.4 \pm 0.1$，表明至少在$0.02T_c$以下存在正常准粒子。这与最近对NdFeAsO $_{1-x}$ F $_x$和SmFeAsO $_{1-x}$ F $_x$的单晶的穿透深度测量相反，其指示各向异性但无节点间隙。我们建议，在电子结构的Ba（Fe $_{0.93}$ Co $_{0.07}$）$_2$作为$_2$的三维字符可能会导致各向异性的$s-$波隙与点节点，将解释所观察到的$λ(T)$。
A simple relation is established between the zero-$T$ penetration depth $λ(0)$ and the slope of $λ^{-2}(T)$ near $T_c$, similar to Helfand-Werthamer's relation for $H_{c2}(0)$ and the slope of $H_{c2}(T)$ at $T_c$ for the isotropic s-wave case with non-magnetic scattering.\cite{HW} When the scattering parameter $ρ=\hbar v/2πT_c\ell$ ($v$ is the Fermi velocity and $\ell$ is the mean-free path) varies from 1 to 10, the coefficient of proportionality between $λ^{-2}(0)$ and $T_c (dλ^{-2}/dT)_{T_c}$ changes from 0.43 to 0.38. Combining this relation with the Rutgers thermodynamic identity, one can…
The issue of whether the quantum critical point (QCP) is hidden inside unconventional superconductors is a matter of hot debate. Although a prominent experiment on London penetration depth has demonstrated the existence of the QCP in the isovalent-doped iron-based superconductor BaFe$_2$(As$_{1-x}$P$_x$)$_2$, with the observation of a sharp peak in the penetration depth in the vicinity of the disappearance of magnetic order at zero temperature, the nature of such an emerging QCP remains unclear. Here, we provide a unique picture to understand well the phenomena of the QCP based on the framewor…
The breakdown magnetic field is the key parameter which determines the performance of superconducting radio-frequency cavities. This is the maximum field up to which the Meissner state remains stable and in uniform material, it is approximately given by the thermodynamic field. There are several recent suggestions to use nonuniform structures to enhance the breakdown field. One of possible realizations of such structure is depth profile of the scattering rate which, in the first approximation, modifies the London penetration depth but does not change the thermodynamic field. In this paper, we …
Reply to "Comment on \emph{"Precision global measurements of London penetration depth in Fe(Te$_{0.58}$Se$_{0.42}$)"}"
我们对T. Klein，P. Rodière and C. Marcenat（arXiv：1205.2566），我们的论文，“Precision global measures of London penetration depth in FeTe $_{0.58}$ Se $_{0.42}$“，Phys.Rev.B84，174502（2011）。我们的工作受到Klein \emph{et. al}，“Thermodynamic phase diagram of Fe（Se $_{0.5}$ Te $_{0.5}$）single crystals in fields up to 28 Tesla”，Phys.Rev.B82，184506（2010）的启发。在他们的论文中，Klein等人将从他们的隧道二极管谐振器（TDR）测量中获得的伦敦穿透深度值与从“首次穿透场”计算的伦敦穿透深度值的五倍差异归因于表面粗糙度，尽管他们没有通过实验验证。在我们的论文中，我们研究了故意引入的表面粗糙度的影响，发现它的影响是轻微的，不能负责这种幅度的差异。相反，我们建议，由于我们的回复中概述的几个原因，用霍尔阵列测量的“首次穿透场”的值不能用于提取真正的较低临界场。我们强调，TDR技术的校准过程的准确性已经在一些先前的研究中得到了仔细的验证，我们对$_{0.58}$ Se $_{0.42}$的工作进一步…
We study the effects of anisotropic order parameters on the temperature dependence of London penetration depth anisotropy $γ_λ(T)$. After MgB$_2$, this dependence is commonly attributed to distinct gaps on multi-band Fermi surfaces in superconductors. We have found, however, that the anisotropy parameter may depend on temperature also in one-band materials with anisotropic order parameters $Δ(T,k_F)$, a few such examples are given. We have found also that for different order parameters, the temperature dependence of $Δ(T)/Δ(0)$ can be represented with good accuracy by the interpolation suggest…
Superconducting gap structure was probed in type-II Dirac semimetal PdTe$_2$ by measuring the London penetration depth using tunnel diode resonator technique. At low temperatures, the data for two samples are well described by weak coupling exponential fit yielding $λ(T=0)=230$~nm as the only fit parameter at a fixed $Δ(0)/T_c\approx 1.76$, and the calculated superfluid density is consistent with a fully gapped superconducting state characterized by a single gap scale. Electrical resistivity measurements for in-plane and inter-plane current directions find very low and nearly temperature-indep…
The half-Heusler compounds YPdBi and TbPdBi, while having similar band structure, exhibit different magnetic properties. YPdBi is a diamagnet, while TbPdBi shows antiferromagnetic order below 5.5 K. Both are superconductors with T${_c}\approx$1 K for YPdBi and T${_c}\approx$1.75 K for TbPdBi. Such a contrast in properties between these two compounds opens a question about the effects of band structure or magnetic correlations on superconductivity. Using the combination of a tunnel diode oscillator (TDO) and a commercial dilution refrigerator, we measured temperature dependent magnetic penetrat…
We study the effect of Coulomb repulsion between oxygen holes on the London penetration depth $λ$ based on the concept of spin-polaron nature of Fermi quasiparticles in cuprates superconductors. It is shown that for the generally accepted values of the parameters of the spin-fermion model, taking into account the Coulomb interaction, both the one-site Hubbard $U_p$ and interaction between the holes on next-nearest-neighbor oxygen ions $V_2$, allows one to achieve a much better agreement of the calculated temperature dependencies of the value $λ^{-2}$ with the experimental data in La$_{2-x}$Sr$…
Magnetic susceptibility of non-ellipsoidal samples is a long-standing problem in experimental studies of magnetism and superconductivity. Here the quantitative description of the Meissner-London response (no Abrikosov vortices) of right circular cylinders in an axial magnetic field is given. The three-dimensional adaptive finite-element modeling was used to calculate the total magnetic moment, m, in a wide range of London penetration depth, λ, to sample size ratios. By fitting the numerical data, the closed-form universal magnetic susceptibility is formulated involving only sample dimensions a…
The optimum design of high-sensitivity Superconducting Quantum Interference Devices (SQUIDs) and other devices based on thin HTS films requires accurate inductance modeling. This needs the London penetration depth $λ$ to be well defined, not only at 77 K, but also for any operating temperature, given the increasingly widespread use of miniature low-noise single-stage cryocoolers. Temperature significantly affects all inductances in any active superconducting device and cooling below 77 K can greatly improve device performance, however accurate data for the temperature dependence of inductance …
The London penetration depth in single crystals of Ba(Fe_{1-x}Co_x)_2As_2 at various doping levels
用隧道二极管谐振器技术测量了Ba（Fe $_{1-x}$ Co $_{x}$）$_{2}$ As $_{2}$单晶的伦敦穿透深度$λ(T)$。测量的$x=$ ~0.038、0.047、0.058、0.074和0.10的掺杂水平的范围从欠掺杂到过掺杂浓度。测量结果表明，参与超导性的载流子密度急剧下降，在欠掺杂制度，但作为温度的函数的渗透深度表现出强大的幂律，$Δλ(T)\sim T^{n}$，所有测量的掺杂，与$n$之间的2和2.5。我们讨论了这些结果的影响和可能的解释，这种强大的行为。
London penetration depth in Ba(Fe$_{1-x}$T$_x$)$_2$As$_2$ (T=Co, Ni) superconductors irradiated with heavy ions
用Pb离子辐照Ba（Fe $_{1-x}$ T $_x$）$_2$ As $_2$（T=Co，Ni）单晶，研究了无序对面内伦敦穿透深度$λ(T)$的影响。随着辐照剂量的增加，超导转变温度$T_c$单调下降，而对转变宽度影响不大。在Co和Ni掺杂体系中，我们发现了一个幂律行为，即$Δλ(T) \propto T^n$，其指数$n$随无序度的增加而系统地减小。这一观察，支持的理论分析，最终指向一个无节点的$s^\pm$状态与成对断裂杂质散射（带间）的强度是玻恩和幺正极限之间的中间。
Non-exponential London penetration depth in RFeAsO$_{0.9}$F$_{0.1}$ (R=La,Nd) single crystals
测量了RFeAsO $_{0.9}$ F $_{0.1}$（R=La，Nd）单晶（R-1111）的超导穿透深度$λ(T)$。在Nd-1111中，我们发现$λ(T)$在冷却时出现了一个上升，并将其归因于Nd离子的顺磁性，类似于电子掺杂的铜酸盐Nd-Ce-Cu-O的情况。经过顺磁性校正后，发现伦敦穿透深度变化遵循幂律行为，在低温下为$Δλ_L(T)\propto T^{2}$。在非磁性La-1111晶体中发现了与$λ(T)$相同的$T^2$变化。在整个温度范围内的超流密度和渗透深度各向异性的分析是一致的双间隙超导。在此基础上，结合我们以前的工作，我们得出结论：RFeAsO（1111）和BaFe $_2$ As $_2$（122）族磷属元素化物超导体都具有非常规的双能隙超导性。
Anisotropic properties of single crystals of SrPt$_{3}$P were studied using London penetration depth and electrical resistivity measurements. The upper critical field, $H_{c2}(T)$, was determined from four-probe electrical resistivity measurements for three orthogonal directions of a magnetic field with respect to the crystal. The London penetration depth, $λ(T)$, was determined from the magnetic susceptibility of the Meissner-London state measured using a tunnel-diode resonator technique. Whereas $H_{c2}(T)$ and the normal-state $ρ(T)$ are practically identical for all three magnetic field or…
Temperature-dependent London penetration depth, $λ(T)$, of a high quality optimally-doped $\text{YBa}_{2}\text{Cu}_{3}\text{O}_{7-δ}$ single crystal was measured using tunnel-diode resonator. Controlled artificial disorder was induced at low-temperature of 20~K by 2.5 MeV electron irradiation at accumulating large doses of $3.8\times10^{19}$ and $5.3\times10^{19}$ electrons per $\textrm{cm}^{2}$. The irradiation caused significant suppression of the superconductor's critical temperature, $T_{c}$, from 94.6 K to 90.0 K, and then to 78.7 K, respectively. The low-temperature behavior of $λ\left(T…
