Fig. 2: Density-tuned Aharonov-Bohm frequency doubling transition of outer EC.
From: Strongly coupled edge states in a graphene quantum Hall interferometer
a Hall conductance \({G}_{{{\rm{xy}}}}\) in the region gated by \({V}_{{{\rm{LG}}}}\), demonstrating that \({V}_{{{\rm{LG}}}}\) (equivalently, any of the top gates) tunes the filling \(\nu\) underneath it at a fixed magnetic field \(B=6{{\rm{T}}}\). Colored dots indicate the filling (set by equivalent \({V}_{{{\rm{MG}}}}\) voltages) at which interference data are shown in (b–e); vertical dashed lines show the range of \({V}_{{{\rm{MG}}}}\) swept for (f). Top inset: schematic of compressible regions expected in the FP cavity when \({V}_{{{\rm{MG}}}}\) is swept. b–e Conductance \({G}_{{{\rm{D}}}}\) oscillations on the outer EC with \({V}_{{{\rm{PG}}}}\) and \(B\), for each of the indicated \({V}_{{{\rm{MG}}}}\) values. f \({G}_{{{\rm{D}}}}\) oscillations on the outer EC with \({V}_{{{\rm{PG}}}}\) and \({V}_{{{\rm{MG}}}}\), for \({V}_{{{\rm{MG}}}}\) swept continuously over the transition from apparent \(h/e\) to \(h/2e\) oscillations periodicity, at \(B=6{{\rm{T}}}\). \({G}_{{{\rm{D}}}}\) is plotted as a percentage of \(\frac{{e}^{2}}{h}\) deviation from the average value calculated for each fixed \({V}_{{{\rm{MG}}}}\) linecut and subtracted off. Further phase jumps or periodicity changes are not observed past \({V}_{{{\rm{MG}}}} \, \approx \, 1.7{{\rm{V}}}\) (checked up to \(\nu=7\)). QPCs are retuned to maintain transmissions \({T}_{{{\rm{QPC}}}1}={T}_{{{\rm{QPC}}}2}=0.5\) over the dataset while \({\nu }_{{{\rm{LG}}}}{=\nu }_{{{\rm{RG}}}}=2\) and \({\nu }_{{{\rm{SG}}}1}{=\nu }_{{{\rm{SG}}}2}=0\) are fixed.
