Investigation of dimensionality in superconducting NbN thin film samples with different thicknesses and NbTiN meander nanowire samples by measuring the upper critical field

Nazir Mudassar^{1, 2}, Yang Xiaoyan³, Tian Huanfang¹, Song Pengtao^{1, 2}, Wang Zhan^{1, 2}, Xiang Zhongcheng¹, Guo Xueyi¹, Jin Yirong¹, You Lixing³, Zheng Dongning^{1, 2, 4, †}

The temperature dependent parallel and perpendicular upper critical field diagrams. (a) The upper critical field for ultra thin 4 nm film and NbTiN 5 nm nanowire. The H_c2∥(t) shows pronounced 2D behavior and is well fitted with 2D GL Eq. (1) as indicated by the blue dash line. The black open circles and red open squares represent H_c2∥(t) for 4 nm NbN film and NbTiN 5 nm wire, respectively, and the H_c2∥(t) dependence shows a similar behavior. The solid triangles illustrate the H_c2⊥(t) data for NbN 4 nm film. (b), (c) The parallel critical field decreases while the perpendicular upper critical field rises with increasing thickness and the bending curvature moves towards T_c. The H_c2∥(t) is explained with AGL interpolation crossover Eq. (2) and the perpendicular upper critical field data exhibit a linear behavior and are well fitted with Eq. (3). The arrows show t_cr crossover temperature, and H_c2(t) shows crisscross in high thickness samples. The open circles and solid triangles represent parallel and perpendicular field experimental data, respectively, and are fitted using Eqs. (2) and (3) as shown by the red and green solid lines.