Reversal of Nonlocal Vortex Motion in the Regime of Strong Nonequilibrium

We investigate nonlocal vortex motion in weakly pinning $a$-NbGe nanostructures, which is driven by a transport current $I$ and remotely detected as a nonlocal voltage $V_{\mathrm{nl}}$. At a high $I$ of a given polarity, $V_{\mathrm{nl}}$ changes sign dramatically. This is followed by $V_{\mathrm{nl}}$ becoming even in $I$, with the opposite sign at low and high temperatures $T$. These findings can be explained by a Nernst-like effect resulting from local electron overheating (low $T$), and a magnetization enhancement due to a nonequilibrium quasiparticle distribution that leads to a gap enhancement near the vortex core (high $T$).

Figure 1

Typical local (black lines; the green [light gray] lines represent the normal-state voltage) and nonlocal (red [medium gray] and blue [dark gray] symbols) $V(I)$ curves. (a) $T=0.75\mathrm{K}=0.26T_c$ (at $B_{\mathrm{ext}}=3.0\mathrm{T}$, $b=0.64$), and (b) $T=2.50\mathrm{K}=0.85T_c$ (at $B_{\mathrm{ext}}=0.50\mathrm{T}$, $b=0.50$). Inset to (a): Sample geometry; $L=2\mu \mathrm{m}$, $W=250\mathrm{nm}$. Inset to (b): Saturation voltages of $|V_{\mathrm{nl}}|$, plotted against $b$, for low (red [medium gray]) and high (blue [dark gray]) $T$.

Figure 2

(a) Measured $V_{\mathrm{nl}}$ at $T\ll T_c$: antisymmetric (red) and symmetric (black) part of the nonlocal signal at $T=0.75\mathrm{K}$ and $B_{\mathrm{ext}}=3.0\mathrm{T}$. (b) Effective electron temperature $T^{*}(I)$, where the black line stems from an analysis of $V_{\mathrm{l}}(I)$, and the red line from noise measurements in the normal state [8]. Inset: Sketch of the temperature profile along the channel.

Figure 3

Measured $V_{\mathrm{nl}}^{+}(I)$ (a), and $V_{\mathrm{nl}}^{-}(I)$ (b) at $T=2.50\mathrm{K}=0.85T_c$ and $b=0.45$ (black), 0.50 (red), 0.55 (green) and 0.60 (blue). (c) Calculated $j_s/j_{\mathrm{GL}}$ and $|\Delta |/{\Delta }_0$ (inset) vs $r/\xi (u=0)$ for different $u/u_{\mathrm{LO}}$. (d) Calculated $(M_{\mathrm{neq}}-M_{\mathrm{eq}})/M_{\mathrm{eq}}$ against $u/u_{\mathrm{LO}}$ at different $b$ (as indicated).