Abstract. 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 bound states, nonlinear Meissner effects, magnetic impurities, magnetic ordering, proximity effects and vortex motion. We also discuss how penetration depth measurements as a function of orientation can be used to explore superconductors with more than one gap and with anisotropic gaps. Details relevant to the analysis of penetration depth data in anisotropic samples are also discussed.Keywords: penetration depth, unconventional superconductivity, pairing symmetry IntroductionThe early suggestion that high temperature superconductors might exhibit unconventional, d-wave pairing, [24,11,154,8] has lead to a wide variety of new experimental probes with sensitivity sufficient to test this hypothesis. The pioneering work of Hardy and coworkers demonstrated that high resolution measurements of the London penetration depth could detect the presence of nodal quasiparticles characteristic of a d-wave pairing state [87]. Since that time, a large number of new superconductors have been discovered, many of which exhibit nontrivial departures from BCS behavior. As we show in this review, penetration depth measurements can be used to examine not only nodal quasiparticles but two-gap superconductivity, anisotropy of the energy gap, Andreev surface states, nonlinear Meissner effect, interplane transport, proximity coupled diamagnetism, vortex matter and the coexistence of magnetism and superconductivity, to name several problems of current interest.

In a superconductor, the ratio of the carrier density, n, to their effective mass, m * , is a fundamental property directly reflecting the length scale of the superfluid flow, the London penetration depth, λL. In two dimensional systems, this ratio n/m * (∼ 1/λ 2 L ) determines the effective Fermi temperature, TF . We report a sharp peak in the x-dependence of λL at zero temperature in clean samples of BaFe2(As1−xPx)2 at the optimum composition x = 0.30, where the superconducting transition temperature Tc reaches a maximum of 30 K. This structure may arise from quantum fluctuations associated with a quantum critical point (QCP). The ratio of Tc/TF at x = 0.30 is enhanced, implying a possible crossover towards the Bose-Einstein condensate limit driven by quantum criticality.In two families of high temperature superconductors, cuprates and iron-pnictides, superconductivity emerges in close proximity to an antiferromagnetically ordered state, and the critical temperature T c has a dome shaped dependence on doping or pressure [1][2][3]. What happens inside this superconducting dome is still a matter of debate [3][4][5]. In particular, elucidating whether a quantum critical point (QCP) is hidden inside it (Figs. 1A and B) may be key to understanding high-T c superconductivity [4,5]. A QCP marks the position of a quantum phase transition (QPT), a zero temperature phase transition driven by quantum fluctuations [7].The London penetration depth λ L is a property that may be measured at low temperature in the superconducting state to probe the electronic structure of the material, and look for signatures of a QCP. The absolute value of λ L in the zero-temperature limit immediately gives the superfluid density λ −2which is a direct probe of the superconducting state; here m * i and n i are the effective mass and concentration of the superconducting carriers in band i, respectively [8]. Measurements on high-quality crystals are necessary because impurities and inhomogeneity may otherwise wipe out the signatures of the QPT. Another advantage of this approach is that it does not require the application of a strong magnetic field, which may induce a different QCP or shift the zero-field QCP [9].BaFe 2 (As 1−x P x ) 2 is a particularly suitable system for penetration depth measurements as, in contrast to most other Fe-based superconductors, very clean [10] and homogeneous crystals of the whole composition series can be grown [11]. In this system, the isovalent substitution of P for As in the parent compound BaFe 2 As 2 offers an elegant way to suppress magnetism and induce superconductivity [11]. Non-Fermi liquid properties are apparent in the normal state above the superconducting dome ( Fig. 2A) [11,12] and de Haas-van Alphen (dHvA) oscillations [10] have been observed over a wide x range including the superconducting compositions, giving detailed information on the electronic structure. Because P and As are isoelectric, the system remains compensated for all values of x (i.e., volumes of the electron and hole Fermi surfaces...

The distribution of magnetic induction in Meissner state with finite London penetration depth is analyzed for platelet samples of rectangular cross-section in a perpendicular magnetic field. The exact 2D numerical solution of the London equation is extended analytically to the realistic 3D case. Data obtained on Nb cylinders and foils as well as single crystals of YBCO and BSCCO are in a good agreement with the model. The results are particularly relevant for magnetic susceptibility, rf and microwave resonator measurements of the magnetic penetration depth in high-Tc superconductors.

We present high precision measurements of the penetration depth of single crystals of κ−(ET)2Cu[N(CN)2]Br and κ−(ET)2Cu(NCS)2 at temperatures down to 0.4 K. We find that, at low temperatures, the in-plane penetration depth (λ ) varies as a fractional power law, λ ∼ T 3 2 . Whilst this may be taken as evidence for novel pair excitation processes, we show that the data are also consistent with a quasilinear variation of the superfluid density, as is expected for a d-wave superconductor with impurities or a small residual gap. Our data for the interplane penetration depth show similar features and give a direct measurement of the absolute value, λ ⊥ (0) = 100 ± 20 µm.PACS numbers: 74.70. Kn, 74.25.Nf Compounds of the family κ−(ET) 2 X have the highest transition temperatures of all organic superconductors known to date [1]. They have recently attracted considerable attention because of their similarity to the high T c cuprates and the possibility that they may also have a non-conventional paring state [2]. The two materials studied here, κ−(ET) 2 Cu[N(CN) 2 ]Br (T c ∼ 11.6 K) and κ−(ET) 2 Cu(NCS) 2 (T c ∼ 9.6 K), are highly anisotropic, layered, extreme type II superconductors. As in the cuprates, the superconducting phase in these materials is in close proximity to an antiferromagnetic phase. Both antiferromagnetic spin fluctuations and a pseudogap have been detected in NMR measurements in the normal state [3]. Neither the underlying pairing mechanism nor the symmetry of the order parameter has been conclusively established. Although NMR [4,5], specific heat [6] and thermal conductivity [7] measurements all suggest a non-conventional pairing state, results of penetration depth measurements have been inconsistent, with evidence for both conventional [8,9] and non-conventional [10][11][12] behavior. However, none of these penetration depth measurements have been performed over a temperature range (T /T c ) and a precision, comparable to those in the cuprates [13]. In this Letter, we present measurements of both the in-plane λ , and the interplane, λ ⊥ , penetration depths in κ−(ET) 2 Cu[N(CN) 2 ]Br and κ−(ET) 2 Cu(NCS) 2 at temperatures down to 0.4 K.Our measurements were performed on single crystals of κ−(ET) 2 Cu[N(CN) 2 ]Br and κ−(ET) 2 Cu(NCS) 2 which were grown at Argonne National Laboratory. Details of the growth procedures have been given elsewhere [14]. Penetration depth measurements were performed using a 13 MHz tunnel diode oscillator [15] mounted on a 3 He refrigerator. The low noise level [ ∆F F0 ≃ 10 −9 ], and low drift of the oscillator allows us to obtain high resolution data with a very small temperature spacing interval. The samples were attached, with a small amount of vacuum grease, to a sapphire rod which fitted inside the copper sense coil. The sense coil was calibrated using spheres of Aluminum. The sample temperature was measured with a calibrated Cernox thermometer attached to the other end of the sapphire rod. The samples were cooled slowly (0.1-1.0 K/min) to avoid introducing disorder [1...

A method is presented to measure the absolute value of the London penetration depth, λ(T=0), from the frequency shift of a resonator. The technique involves coating a high-Tc superconductor with film of low-Tc material of known thickness and penetration depth. The method is applied to obtain λ(YBa2Cu3O7−δ)≈1460±150 Å, λ(Bi2Sr2CaCu2O8+δ)≈2690±150 Å and λ(Pr1.85Ce0.15CuO4−δ)≈2790±150 Å. λ(YBa2Cu3O7−δ) from this method is very close to that obtained by several other techniques. For both Bi2Sr2CaCu2O8+δ and Pr1.85Ce0.15CuO4−δ the values exceed those obtained by other methods.