Surface superconductivity as the primary cause of broadening of superconducting transition in Nb films at high magnetic fields

We study the origin of broadening of superconducting transition in sputtered Nb films at high magnetic fields. From simultaneous tunneling and transport measurements we conclude that the upper critical field $H_{c2}$ always corresponds to the bottom of transition $R\sim 0$, while the top $R\sim R_n$ occurs close to the critical field for destruction of surface superconductivity $H_{c3}\simeq 1.7H_{c2}$. The two-dimensional nature of superconductivity at $H>H_{c2}$ is confirmed by cusplike angular dependence of magnetoresistance. Our data indicates that surface superconductivity is remarkably robust even in disordered polycrystalline films and, surprisingly, even in perpendicular magnetic fields. We conclude that surface superconductivity, rather than flux-flow phenomenon, inhomogeneity, or superconducting fluctuations, is the primary cause of broadening of superconducting transition in magnetic field.

Figure 1

Resistive transitions of a 150 nm thick Nb film. (a) Temperature dependence of the resistance in zero magnetic field. (b) and (c) Field dependencies of resistances at $T=1.8$ K in fields (b) perpendicular and (c) parallel to the film. Black and red circles mark the upper critical field $H_{c2}$ and the field of the onset of resistive transition, which coincides with the critical field of surface superconductivity $H_{on}\sim H_{c3}$.

Figure 2

Comparison of theoretically calculated [(a)–(c)] and experimentally measured [(d)–(f)] characteristics of Nb/Al-${\mathrm{AlO}}_x$/Nb tunnel junctions. (a) and (d) Temperature dependence of $I-V$ characteristics at zero field. (b) and (e) Field dependence of $I-V$ characteristics for field perpendicular to the junction/films at $T\simeq 2$ K. (c) and (f) The corresponding differential conductances for curves from panels (b) and (e). The field scale in (f) is normalized by the upper critical field $H_{c2}^{\perp }=1.61$ T, which is obtained as a single scaling factor for all the curves at different fields. Data are from Ref. [13].

Figure 3

(a) Differential conductances of a Nb/${\mathrm{AlO}}_x$/Nb junction (in a semilogarithmic scale) for films parallel to the magnetic fields and $T=1.8$ K. (b) and (c) Scaling of the sum-gap peak resistance (b) and voltage (c) as a function of $H/H_{c2}\left(T\right)$ at different temperatures and parallel fields. Dashed and dashed-dotted lines in (b) represent theoretical curves at $T=1.96$ and 4.7 K, respectively. (d) and (e) Black squares represent upper critical fields perpendicular (d) and parallel (e) to the films, obtained from the scaling of magneto-tunneling characteristics. Dashed lines represent the expected third critical field for surface superconductivity $H_{c3}=1.69H_{c2}$. Red circles mark the top onset of the resistive transition. (f) Angular dependence of resistance of Nb electrodes for fields slightly below and above ${\mu }_0{H}_{c2}(\parallel )=2.52$ T. A cusplike feature at $H>H_{c2}$ indicates occurrence of the two-dimensional surface superconductivity.

Figure 4

(a) Bias dependence of $R\left(\mathrm{\Theta }\right)$ at $T=1.8$ K and $H=2.81$ T. (b) Deduced current-voltage characteristics at different angles from the data in panel (a). Dashed line represents the normal state $I-V$. (c) Simulated angular dependence of $R\left(\mathrm{\Theta }\right)$ in the surface superconductivity model, taking into account nonlinearity of $I-V$ characteristics in the vicinity of critical current. Solid lines represent calculated of $R\left(\mathrm{\Theta }\right)$ at different bias. The dashed curve represents the standard flux-flow dependence $H/H_{c3}$.

Figure 5

(a) and (b) Excess conductance vs magnetic field at $T=1.8$ K plotted in (a) a double-logarithmic and (b) a semilogarithmic scale. Quasi-exponential decay $\mathrm{\Delta }S\left(H\right)$ is seen. (c) The high-field part of excess conductance. It reveals a fluctuation contribution, which is positive for parallel but negative for perpendicular field orientation. (d) Analysis of power-law scaling expected for surface superconductivity according to Eq. (4). The dashed line represents a power law with the exponent $\nu =4.8$. (e) AFM image of the studied Nb film.