Coherent current transport in wide ballistic Josephson junctions

We present an experimental and theoretical investigation of coherent current transport in wide ballistic superconductor-two dimensional electron gas-superconductor junctions. It is found experimentally that upon increasing the junction length, the subharmonic gap structure in the current-voltage characteristics is shifted to lower voltages, and the excess current at voltages much larger than the superconducting gap decreases. Applying a theory of coherent multiple Andreev reflection, we show that these observations can be explained in terms of transport through Andreev resonances.

Figure 1

(Left) Average normal transparency $D=R_N∕R_{\mathrm{Sh}}$ as a function of $n_s$ for samples of lengths $L=105\mathrm{nm}$ and $160\mathrm{nm}$. (Right) $I_c{R}_N$ product as a function of $T$ for the same samples. The thin lines are the theory, with $I_c{R}_N\left(T=0\right)$ scaled for best fit by 1.65 $\left(L=105\mathrm{nm}\right)$ and 2.4 $\left(L=160\mathrm{nm}\right)$ and $\hslash v_F∕E_A=0.54{\xi }_0$ (see text). Inset: A schematic cut through the junction, displaying the kink in the 2DEG.

Figure 2

(Left) Measured differential resistances $dV∕dI$ (upper) and (numerically differentiated) $d^{2}I∕d{V}^2$ (lower) as a function of $V$ for $T=1.8\mathrm{K}$. The junction lengths are from bottom to top, $L=105,115,145,160$, and $200\mathrm{nm}$. The traces have been successively shifted for clarity. (Right) Positions of the minima $V_{\min }$ of the $d^{2}I∕d{V}^2$ (lower left) for the SGS $n=1$ $(◁)$, $n=2$ $(●)$, $n=3$ $(◇)$, $n=4$ [$(▷)$, only two minima clearly visible], and $n=5$ $(엯)$. Dashed lines are given by Eq. (1), with an additional length $\hslash v_F∕E_A=0.6{\xi }_0$.

Figure 3

(Left) Plot of the numerically calculated $dI∕dV$ as function of $eV∕\Delta$ and $L∕{\xi }_0$ for $R=0.16$ and $kT⪡\Delta$; light areas correspond to peaks, dark to dips. $\left(\hslash v_F∕E_A=0\right)$. (Right) A contour plot of the third derivative $d{I}^3∕d{V}^3$ around zero, giving the extremal points of $d{I}^2∕d{V}^2$ in the intersections of the dark and white areas. The minima in Eq. (1) are indicated by dashed lines.

Figure 4

(Top) Excess current at $T=1.8\mathrm{K}$ for the five experimentally investigated junctions. (Bottom) Numerically calculated excess current as a function of length $L$, for $R=0.16$ and $k_{B}T⪡\Delta$.