Transconductance Fluctuations as a Probe for Interaction-Induced Quantum Hall States in Graphene

Transport measurements normally provide a macroscopic, averaged view of the sample so that disorder prevents the observation of fragile interaction-induced states. Here, we demonstrate that transconductance fluctuations in a graphene field effect transistor reflect charge localization phenomena on the nanometer scale due to the formation of a dot network which forms near incompressible quantum states. These fluctuations give access to fragile broken symmetry and fractional quantum Hall states even though these states remain hidden in conventional magnetotransport quantities.

Figure 1

(a) Two-terminal conductance as a function of density at fields from 1 to 15 T in 1 T steps. (b),(c) Comparison of conductance (b) and transconductance (c) curves measured at $B=15\mathrm{T}$. Both measurements were done with a dc-voltage bias of $V_{\mathrm{ds}}=500\mu \mathrm{V}$. Insets show the schematics of the measurements.

Figure 2

(a) Color rendition of the transconductance in the ($n$, $B$)-plane. (b),(c) Correlation function $C$ obtained by analyzing the data in the windows shown in (a). The details of this analysis method are shown in Fig. 3.

Figure 3

(a) Schematic illustration of the formation of QDs and the development of the compressible spikes in the ($n$, $B$)-plane. (b) Schematic illustration of the numerical analysis to obtain the spectra shown in Fig. 2. (c) Differential conductance and stability diagram measured at 1.4 K and 14 T. Inset shows an energy diagram along the sample on the left and a schematic of the network of compressible QDs with extended edge states on the right.