Measurement of the nonlinear Meissner effect in superconducting Nb films using a resonant microwave cavity: A probe of unconventional pairing symmetries

Abstract

We report observation of the nonlinear Meissner effect (NLME) in Nb films by measuring the resonance frequency of a planar superconducting cavity as a function of the magnitude and the orientation of a parallel magnetic field. Use of low power rf probing in films thinner than the London penetration depth, significantly increases the field for the vortex penetration onset and enables NLME detection under true equilibrium conditions. The data agree very well with calculations based on the Usadel equations. We propose to use NLME angular spectroscopy to probe unconventional pairing symmetries in superconductors. 74.25.Ha, 74.25.Op, 74.78.Na Meissner effect is one of the fundamental manifestations of the macroscopic phase coherence of a superconducting state. Meissner screening current density J = −en s v s induced by a weak magnetic field is proportional to the velocity v s of the condensate. At higher fields, the superfluid density n s becomes dependent on v s due to pairbreaking effects, resulting in the nonlinear Meissner effect (NLME) [1][2][3][4][5]. NLME has attracted much attention since it probes unconventional pairing symmetries of moving condensates, for example, the dwave pairing in cuprates or multiband superconductivity in pnictides. For a single band isotropic type-II superconductor, the NLME at v s ≪h/mξ 0 is described by,where λ 0 is the London penetration depth, ξ 0 is the coherence length, Q = v s /mh = ∇θ + 2πA/φ 0 , m is the quasiparticle mass, θ is the phase of the order parameter, A is the vector potential, φ 0 is the flux quantum. NLME can manifest itself in a variety of different behaviors, which reveal the underlying pairing symmetry. For instance, Eq. (1) describes a clean d-wave superconductor at high temperatures k B T > p F v s or a d-wave superconductor with impurities, where p F is the Fermi momentum [2-4], while in the clean limit at k B T < p F v s , the nonlinear term in Eq. (1) takes the singular form ≃ a d ξ|Q| [2]. In the s-wave clean limit, the NLME is absent at T ≪ T c where a ∝ exp(−∆/T ) [6], but in the dirty limit a ∼ 1 even for T → 0. In multiband superconductors NLME can probe the onset of nonlinearity due to the appearance of interband phase textures suggested for MgB 2 [7] or the line nodes and interband sign change in the order parameter or mixed s-d pairing symmetries, which have been discussed recently for iron pnictides [8].To date, experiments aiming to observe the NLME in high-T c cuprates and other extreme type-II superconductors have been inconclusive [9-11] mostly because of a very small field region of the Meissner state. Since NLME becomes essential in fields H of the order of the thermodynamic critical field H c = φ 0 /2 √ 2πµ 0 λ 0 ξ 0 [1], penetration of vortices above the lower critical field µ 0 H c1 = (φ 0 /4πλ 2 0 )(ln κ + 0.5) ≪ µ 0 H c imposes the strong restriction H < H c1 , which reduces the nonlinear correction in Eq. (1) Yet even small NLME terms in Eq. (1) result in intermodulation effects [3] under strong ac fields, as observed in YBa 2 Cu ...

Characterization of superconducting nanometric multilayer samples for superconducting rf applications: First evidence of magnetic screening effect

“…Ultimately rf cavities should be tested at 1.3 GHz. Recent results obtained on a 20 GHz Nb strip line resonator show that H C1 is indeed significantly increased in thin films under rf field [33].…”

Thermally activated dynamics of spontaneous perpendicular vortices tuned by parallel magnetic fields in thin superconducting films

“…2 )dx/d averaged over the film thickness, where Q = 2πBx/φ 0 is the gaugeinvariant phase gradient of the order parameter 12 . Thus, n s (B) = [1−(πξdB/φ 0 ) 2 /3] decreases quadratically with B.…”

Improving Superconducting Resonators in Magnetic Fields by Reduced Field Focussing and Engineered Flux Screening

“…One of them is a change of the kinetic inductance (and thus of the total inductance) due to Meissner currents circulating in the superconductor. This effect can be described by nonlinear London equations and leads to a non-hysteretic quadratic shift of the resonance frequency with applied magnetic field [36,38]. The second mechanism is related to the presence of Abrikosov vortices in the superconductor, which not only add losses but also a reactive component [29][30][31]37].…”

“…The sensitivity of superconductors to magnetic fields leads to field-dependent resonance frequency shifts of the resonators and to significantly increased losses due to an additional vortex resistivity [33][34][35]. Hence, many experiments regarding the magnetic field induced property changes of superconducting microwave resonators have been carried out during the last years and different approaches to reduce or minimize them have been investigated [36][37][38][39][40][41][42][43].…”