Quantum fluctuations in ultranarrow superconducting aluminum nanowires

Progressive reduction of the effective diameter of a nanowire is applied to trace evolution of the shape of the superconducting transition $R\left(T\right)$ in quasi-one-dimensional aluminum structures. In nanowires with effective diameter $⩽15\mathrm{nm}$ the $R\left(T\right)$ dependences are much wider than predicted by the model of thermally activated phase slips. The effect can be explained by quantum fluctuations of the order parameter. Negative magnetoresistance is observed in the thinnest samples. Experimental results are in reasonable agreement with existing theoretical models. The effect should have a universal validity, indicating a breakdown of the zero-resistance state in a superconductor below a certain scale.

Figure 1

(Color online) (a) Atomic force microscope (AFM) image of a typical $5\text{−}\mu \mathrm{m}$-long aluminum nanowire just after lift-off. (b) AFM images showing evolution of the shape of the same nanowire after several sessions of ion beam sputtering. Bright color above the horizontal plane (initial level of the substrate) corresponds to metal, dark color below to sputtered Si substrate. Note the reduction of the initial surface roughness of the nanowire.

Figure 2

(Color online) Resistance vs temperature for the thinnest samples obtained by progressive reduction of the diameter of the same aluminum nanowire Al-Cu126-3 with length $L=10\mu \mathrm{m}$. The Langer-Ambegaokar-McCumber-Halperin (LAMH) model fitting is shown with dashed lines for 11 and $15\mathrm{nm}$ samples with the best-fit mean free path $\mathcal{l}=3$ and $10\mathrm{nm}$, correspondingly, $T_c=1.46\mathrm{K}$ and critical magnetic field $B_c\left(0\right)=10\mathrm{mT}$. Fitting using a simplified short-wire model (Ref. 11) [Eqs. (2, 3)] is shown with solid lines. For 11-, 12-, 13-, and $15\text{−}\mathrm{nm}$ wires the fitting parameters are $T_c=1.5\mathrm{K}$; $A=0.15$, mean free path $\mathcal{l}=5.4$, $5.8$, $7.3$, $7.5\mathrm{nm}$; and the normal-state resistance $R_N=7200$, 5300, 4200, and $2700\mathrm{k}\Omega$.

Figure 3

(Color online) Resistance vs temperature for a ${\sigma }^{1∕2}=11\mathrm{nm}\pm 2\mathrm{nm}$ sample of aluminum nanowire Al-Cu115 with length $L=10\mu \mathrm{m}$ measured at various dc and ac currents. Inset: resistance vs temperature for three samples obtained by progressive reduction of the diameter of the same nanowire.

Figure 4

(Color online) (a) Resistance vs temperature for three samples of the same wire as in Fig. 2 with progressively reduced cross sections. Solid dots are fittings to power dependence $R\sim T^{2\gamma -2}$. (b) $V\left(I\right)$ dependences of the same samples taken at close temperatures stabilized with accuracy $\pm 0.1\mathrm{mK}$. Solid lines correspond to proportionality $R\left(T\right)\equiv V\left(T\right)∕I\sim I^{2\gamma -2}$. In both figures the only fitting parameter is the quasiparticle resistance $R_{\mathit{qp}}$.

Figure 5

(Color online) Slowly recorded $(\sim 1\mathrm{h})$ resistance vs temperature dependence for the $11\text{−}\mathrm{nm}$ sample from Fig. 2. While sweeping the temperature, a few times the perpendicular magnetic field $B=19.6\mathrm{mT}$ was switched on and off. The top branch corresponds to zero field, while the lower one to field “on.” Inset: resistance vs perpendicular magnetic field for the same sample measured at constant temperature and small ac current.