Determining the absolute value of magnetic penetration depth in small-sized superconducting films

Abstract

In the previous four decades, the two-coil mutual inductance (MI) technique has been widely employed in characterizing magnetic penetration depth, , of superconducting films. However, the conventional methods used to obtain are not applicable to small-sized films with common shapes, which limits the application of the MI technique in superconductivity research. Here, we first employed the fast wavelet collocation (FWC) method to a two-coil system and then proposed the possibility of directly obtaining the absolute of polygonal superconducting films with arbitrary sizes. To verify its accuracy and advantages, we extracted the values of square NbN films with different sizes using the FWC and conventional flux leakage subtraction (FLS) methods. Notably, the FLS method fails for a film, which is attributed to the significant current peak at the film edge. In contrast, the absolute extracted using the FWC method was independent of the film size. Finally, we established the applicability of the FWC method to large coil spacings, which may pave the way for integrating high-accuracy measurements with the ionic liquid gating technique.

Calculation of penetration depth under various numerical models for the reflection-type two-coil mutual inductance technique

“…When an alternating current with angular frequency ω and amplitude I d is applied to the drive coil, an induced voltage V p will be generated across the pickup coil and proportional to the mutual inductance M [24,27,35,36],…”

“…Under this model, both calculation complexity and cost are increased compared to those under the above two models with higher geometrical symmetry. The FWC method has recently been utilized to calculate λ for a quadrangle film in the transmission-type TCMI measurement [27]. Herein we apply it to the analysis of reflection-type TCMI measurement results.…”

“…The value of λ is associated with the superfluid density, ρ s ∝ λ −2 , which is closely related to various fascinating phenomena including Berezinskii-Kosterlitz-Thouless transition, quantum critical point and phase fluctuations [7][8][9][10][11][12][13][14][15][16]. Currently, several useful experimental methods have been developed to achieve λ in superconducting films, such as microwave surface impedance [17][18][19][20], muon-spin relaxation (µSR) [21,22] and two-coil mutual inductance (TCMI) measurements [15,[23][24][25][26][27][28]. The microwave surface impedance measurement requires prior knowledge of its dependence on temperature to determine λ values, and it is difficult to implement continuous measurement with temperature variation using the µSR technique .…”

“…For both types, λ values can be obtained from experimental data only after a proper numerical calculation. So far, various numerical models with different film geometry, i.e., the infinite-, circularand quadrangle-film, have been proposed for the calculation of λ [23,24,27,34,35]. Both the infinite and circular films have been well studied and widely used for both transmissionand reflection-type TCMI techniques partially because of their high geometrical symmetry and thus calculation simplicity [23][24][25][34][35][36][37][38].…”

“…In many experiments, however, film samples are usually grown on a single-crystal wafer cut into a rectangular shape. Therefore, a numerical model of a quadrangle film was proposed recently for the transmission-type TCMI technique and solved by using the so-called fast wavelet collocation (FWC) approach [27]. For the reflection-type TCMI technique, however, the numerical model of a quadrangle film has not yet been reported, although the reflection-type is superior to the transmission-type for in-situ experiments.…”