Destruction of global coherence in long superconducting nanocylinders

Recent experiments on long hollow nanocylinders have reported an anomalous broadening and a multistep character of the resistive transition between normal and superconducting states with increasing magnetic field. Here we show that a first-order phase separation is not the reason for such behavior since it can arise only for a wall thickness that is much larger than in the investigated samples $\left(\sim 30\text{nm}\right)$. On the contrary, it is found that the destruction of global coherence in the transition neighborhood should be triggered by intrinsic long-range inhomogeneities of the cylinder.

Figure 1

(Color online) (a) Distribution of $\xi \left(0\right)$ along an inhomogeneous cylinder with a constant radius $R=75\text{nm}$. Corresponding local critical temperatures $T_c\left(H\right)$ (b) at different positions along the cylinder for a constant wall thickness $t=35\text{nm}$ and (c) at position $z=0.5L$ for different values of wall thickness.

Figure 2

(Color online) Ratio of the resistance $\rho$ to the normal resistance ${\rho }_N$ as a function of the applied magnetic field and the temperature for the cylinder with the distribution of $\xi \left(0\right)$ plotted in Fig. 1a.

Figure 3

(Color online) (a) Proposal for a monotonous $\xi \left(0\right)$ distribution along the cylinder and (b) the corresponding temperature dependences of the resistance (lines) at different field values (from left to right, $H=190$, 184, 175, 165, 155, 145, 115, 95, and 0 G), which fit the experimental data (joined dots) of sample Al-6 from Ref. 8.

Figure 4

(Color online) Coordinate dependences (a) of the zero-temperature coherence length $\xi \left(0\right)$ and (b) of the local transition temperature $T_c\left(H\right)$ at applied field $H=435\text{G}$, used to fit the resistance curves of sample Al-3 from Ref. 8. (c) Distribution of normal and superconducting sections along the cylinder at the temperature $T=0.47\text{K}$.

Figure 5

(Color online) Thick lines: theoretical temperature dependence of the cylinder resistance for applied magnetic field of (from left to right) 456, 449, 445, 440, 435, 430, 425, 420, 415, 410, 405, 400, 347, 295, 246, 197, 145, and 0 G. Joined dots: experimental data from Ref. 8.

Figure 6

(Color online) (a) Proposal for an alternative nonmonotonous $\xi \left(0\right)$ distribution and (b) the corresponding temperature dependences of the resistance (lines) at different field values, which fit the same experimental data (joined dots) as in Fig. 3.