Multi-mode Fabry-P\'erot Interferences in SiO$_2$-supported Single Layer Graphene, in Large Aspect Ratio 2-terminal Devices

The Fabry-P\'erot (F-P) interference of charge carriers in graphene occur in 2-dimensional cavities defined between $pn$ interfaces. Typically, $pn$ interfaces form by local doping of metallic contacts, and serve as partially reflecting mirrors for ballistic charge carriers. Here, we report on observed F-P resonances in very large aspect ratio devices. For all devices studied, the inter-lead distance is $L \approx 0.2$ $\mathrm{\mu}$m, and the graphene channel widths range from $W \approx 5$ to $17$ $\mathrm{\mu}$m, resulting in aspect ratios up to $W/L \approx 74$. In maps of conductance versus source-drain and gate voltages, we observe long-range tapestry patterns, extending over the gate voltage range from $V_{\mathrm{g}} = -60$ V to $20$ V. These features onset at a temperature of $T \approx 20$ K. Upon lowering the temperature, an additional mode appears around $T \approx 3$ K, and remains fairly unchanged down to $T \approx 30$ mK. From the lowest energy features, we estimate the phase coherence length to be on the order of $1$ to $2$ $\mathrm{\mu}$m. Using FFT, we have identified two modes: the fundamental longitudinal, and one of the transverse modes, which we propose is a result of smaller cavities formed by the disorder-induced charge puddles.