Tuning the Influence of Microscopic Decoherence on the Superconducting Proximity Effect in a Graphene Andreev Interferometer

We discuss transport measurements through graphene Andreev interferometers exhibiting reentrance of the superconducting proximity effect. We observe that at high gate voltage ($V_{\mathrm{BG}}$) the energy dependence of the Andreev conductance oscillations exhibits a scaling in agreement with theoretical expectations, which breaks down at low $V_{\mathrm{BG}}$, when the Fermi energy approaches the charge neutrality point. The phenomenon is a manifestation of single particle dephasing that increasingly limits the propagation of superconducting correlations away from the superconductor-graphene interface. Our work addresses the interplay between microscopic decoherence and superconductivity, and shows that graphene provides a useful experimental platform to investigate unexplored regimes and phenomena in the superconducting proximity effect.

Figure 1

(a) False color scanning electron micrograph of one of our devices; graphene and the superconducting electrodes are colored in yellow and purple, respectively (contacts 1 and 2 are joined by a $\simeq 12\mu {\mathrm{m}}^2$ superconducting loop. The scale bar corresponds to $1\mu \mathrm{m}$). (b) Resistance per square of the T-shaped graphene ribbon (outlined by dashes) versus $V_{\mathrm{BG}}$. (c) Four-probe conductance $G_{3,2|4,1}$, periodically modulated by the flux threading the loop (measured at $T=250\mathrm{mK}$ with an applied bias $V_{\mathrm{SD}}=40\mu \mathrm{V}$).

Figure 2

(a) Magnetoconductance (background subtracted), averaged over $N=1$, 5, and 25 $V_{\mathrm{BG}}$ values around 50 V ($V_{\mathrm{SD}}=40\mu \mathrm{V}$; the curves are offset for clarity). (b) Thouless energy $E_T$ extracted from the $V_{\mathrm{BG}}$ dependent resistance of the device. (c) Amplitude of the large-field ($200\mathrm{G}<B<500\mathrm{G}$) sample-specific conductance oscillations. (d) Ensemble-averaged (thick line) versus individual $dI/dV$ curves (thin lines) measured around $V_{\mathrm{BG}}=60\mathrm{V}$at $T=250\mathrm{mK}$. (e) Sample-specific oscillation amplitude versus the number of averaged experimental curves.

Figure 3

(a) EA conductance oscillations at $V_{\mathrm{BG}}=60\mathrm{V}$ and $T=250\mathrm{mK}$, for $V_{\mathrm{SD}}$ varying from 0 (bottom curve) to 0.5 mV (top; curves offset for clarity). (b) Bias dependence of the amplitude of the first and second harmonics of the oscillations shown in (a). (c) Temperature dependence of the harmonics of the zero-bias EA oscillations.

Figure 4

(a) Bias-dependent amplitude of the EA oscillations (first harmonic) for $-10\mathrm{G}<B<10\mathrm{G}$, measured at $T=250\mathrm{mK}$ and $12.5\mathrm{V}<V_{\mathrm{BG}}<60\mathrm{V}$. (b) Same data as in (a), plotted in dimensionless units: the curves measured for $V_{\mathrm{BG}}=60$, 50, and 40 V exhibit a perfect scaling, which breaks down starting from $V_{\mathrm{BG}}=30\mathrm{V}$. Inset: calculated conductance of a diffusive NS junction for decreasing values of $L_{\varphi }/L$ ($\infty$, black curve, 0.6, 0.4, 0.3, 0.2, orange curve), using the linearized Usadel equations, as in Ref. [8].

Figure 5

(a)–(c) Ensemble-averaged $dI/dV$ curves between 265 mK (blue) and 3.5 K (red), for different values of $V_{\mathrm{BG}}$ (60, 20, and 12.5 V, respectively). With approaching charge neutrality, the conductance enhancement due to Andreev reflection visible in (a) is suppressed (b), and eventually completely disappears (c).