$1∕f$ flux flow noise due to a coexistence of qualitatively different vortex states

We investigate the vortex-motion voltage noise in a hybrid structure consisting of a weak-pinning amorphous ${\mathrm{Nb}}_{0.7}{\mathrm{Ge}}_{0.3}$ microbridge on top of which a strong-pinning, longitudinal Nb line with a narrow interruption in the middle is added. The Nb part enforces a branching of the applied current, causing a modulation of the current density within the ${\mathrm{Nb}}_{0.7}{\mathrm{Ge}}_{0.3}$, where vortex motion induces a voltage. When the ${\mathrm{Nb}}_{0.7}{\mathrm{Ge}}_{0.3}$ is sufficiently dissipative, the modulation is strong and the vortex dynamics is spatially dependent. Under these circumstances, the distribution function for normal excitations in vortex cores varies considerably over the sample, which results in a coexistence of distinct vortex states spreading from nearly equilibrium to strongly nonequilibrium ones. This leads to a range of characteristic times for the voltage fluctuations and, consequently, to the frequency $\left(f\right)$ dependence of the noise being of $1∕f$ type. The noise originates in the fluctuations of the vortex-core size around the average set by the nonequilibrium effects in vortex motion.

Figure 1

Photographs of sample G (the $a\text{−}\mathrm{Nb}\mathrm{Ge}$ layout for samples L and P is identical). (a) The whole structure with the bonds for four-point measurements. (b) Expanded view of the microbridge area, with the designation of the materials. The direction of $B$ and the average directions of $J$ and vortex velocity $u$ are indicated.

Figure 2

(a) $R(T,0)$ of the samples showing $T_c=2.8\mathrm{K}$ and $T_c^{\mathrm{Nb}}\approx 6\mathrm{K}$. (b) $R(T=\mathrm{const},B)$ of sample G (solid lines) and sample P (dashed lines) at $T=1.1\mathrm{K}$ $(B_{c2}=3.1\mathrm{T},B_{c2}^{\mathrm{Nb}}\approx 4.3\mathrm{T})$ and $T=2.55\mathrm{K}$ $(B_{c2}=0.7\mathrm{T},B_{c2}^{\mathrm{Nb}}\approx 3.3\mathrm{T})$. The dotted line indicates $R_0=675\Omega$. In both (a) and (b), the right-hand scale displays the $\rho (T,B)$.

Figure 3

A schematic representation of $J$ in sample G (not to scale) when the $a\text{−}\mathrm{Nb}\mathrm{Ge}$ is sufficiently dissipative. The magnitude of $J$ corresponds qualitatively to the gray scale shown.

Figure 4

$⟨V\left(I\right)⟩$ of sample G (solid lines), with $B$ increasing as shown by the arrows, at (a) $T=1.1\mathrm{K}$ and (b) $T=2.55\mathrm{K}$. The dashed lines represent $R_0=675\Omega$. The solid circles mark $⟨V_i\left(I_i\right)⟩$ as defined in the text, the open circles the appearance of ${\Sigma }_V\propto f^{-\nu }$ with $\nu =1$, and the open diamonds the points beyond which $\nu >1$. Insets to (a) and (b): A comparison of selected $⟨V\left(I\right)⟩$ of samples G and P for strongly and weakly nonlinear dependences, with $T$ being the same as in the corresponding main panel and $B$ as indicated.

Figure 5

(a) ${\Sigma }_V\propto {⟨V⟩}^2∕f$ for $T=1.1\mathrm{K}$, $B=1.7\mathrm{T}$, and $I=12–32\mu \mathrm{A}$ $(⟨V⟩=5.3–19\mathrm{mV})$. For the same $T$ and $B$, in (b)–(d) we plot ${\Sigma }_V$ (lower curves, left-hand scales) and $f{\Sigma }_V$ (upper curves, right-hand scales) against $f_1⩽f⩽f_2$. (b) At low $⟨V⟩$, both ${\Sigma }_V\left(f\right)$ and $f{\Sigma }_V\left(f\right)$ are flat; the noise is too small to extract the $f$ dependence of ${\Sigma }_V$. As $⟨V⟩$ increases, ${\Sigma }_V\left(f\right)\propto 1∕f^{\nu }$ can be resolved clearly, with (c) $\nu =1$ in a range of $⟨V⟩$ and (d) $\nu >1$ at larger $⟨V⟩$.

Figure 6

Averaged $f{\Sigma }_V$ vs ${⟨V⟩}^2$ for the spectra of the type shown in Fig. 5c. Irrespective of $T$, the noise decreases with increasing $B$. (a) $T=1.1\mathrm{K}$. At $B=0.6$ and $0.9\mathrm{T}$, the noise is considerably larger than at higher $B$, and it is shown in the upper inset. For $B⩾1.5\mathrm{T}$, the low-$⟨V⟩$ part can be approximated by a linear dependence, with a slope $K$ plotted against $B$ by the symbols in the lower inset and the solid line indicating $K\propto 1∕B$. (b) $T=2.55\mathrm{K}$. $f{\Sigma }_V\propto {⟨V⟩}^2$ at low $⟨V⟩$ is acceptably well defined only for $B=0.5$ and $0.6\mathrm{T}$.