Fig. 1: Highly tunable Fabry-Pérot interferometer in graphene. | Nature Communications

Fig. 1: Highly tunable Fabry-Pérot interferometer in graphene.

From: Strongly coupled edge states in a graphene quantum Hall interferometer

Fig. 1

a False-color scanning electron microscopy image of a Fabry-Pérot (FP) device identical to the device measured here. The graphite top-gate layer is selectively etched to form 8 separated top-gates (purple). Metal bridges (blue) connect to each graphite top-gate region and two additional bridges (yellow) suspend over the quantum point contacts (QPCs). The lithographic area of the interferometer cavity (area \(A=1.16\mu {{\mbox{m}}}^{2}\)) is defined by the central hexagonal top-gate. Scale bar: \(1{{\rm{\mu }}}{{\rm{m}}}\). b Simplified schematic of the FP tuned so that filling factors \({\nu }_{{{\rm{LG}}}}={\nu }_{{{\rm{MG}}}}{=\nu }_{{{\rm{RG}}}}=2\) and \({\nu }_{{{\rm{SG}}}1}={\nu }_{{{\rm{PG}}}}{=\nu }_{{{\rm{SG}}}2}=0\) illustrating interference of the partitioned outer edge channel (EC) (red) while the inner EC (blue) forms a closed annulus inside the FP. Voltage \({V}_{{{\rm{i}}}}\) applied to the top-gate labeled ‘i’ tunes the local filling factor \({\nu }_{{{\rm{i}}}}\). Voltages \({V}_{{{\rm{QPC}}}1}\) and \({V}_{{{\rm{QPC}}}2}\) applied to the suspended metal bridges selectively gate the QPC constrictions through the etched graphite gaps, tuning the QPC transmissions. We measure the diagonal conductance \({G}_{{{\rm{D}}}}={I}_{{{\rm{d}}}}/({V}_{{{\rm{D}}}}^{+}-{V}_{{{\rm{D}}}}^{-})\), where \({V}_{{{\rm{D}}}}^{\pm }\) and \({I}_{{{\rm{d}}}}\) are measured voltages in \((\pm )\) probes and drained current, respectively. See Supplementary Fig. 1 for the full device details. In addition to magnetic field, we tune the interference phase using voltage \({V}_{{{\rm{MG}}}}\) on the ‘middle gate’ or \({V}_{{{\rm{PG}}}}\) on the ‘plunger gate’. c Conductance as a function of \({V}_{{{\rm{QPC}}}1}\) with \({V}_{{{\rm{QPC}}}2}=7{{\rm{V}}}\) (i.e. \({T}_{{{\rm{QPC}}}2}=2\)) demonstrating QPC1 tunings to interfere outer EC (red dot) and inner EC (blue dot) in \(\nu=2\). See Supplementary Fig. 3 for QPC tuning details and voltages set on the other gates to form the necessary QPC saddle-points to acquire this data. d Same type of plot as (c), but demonstrating QPC2 operation instead of QPC1. e, f Characteristic FP oscillations as a function of \({V}_{{{\rm{PG}}}}\) for the inner EC and outer EC, respectively, at the QPC tunings indicated in (c) and (d). Vertical dashed lines indicate edges of plateaus of filling factor \({\nu }_{{{\rm{PG}}}}\). All data is at fixed magnetic field \(B=6{{\rm{T}}}\).

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