Fig. 7: Absence of an edge state Hall voltage.
From: An epitaxial graphene platform for zero-energy edge state nanoelectronics
a Hall resistance RHall = |R26,15| (in units of R0) versus VG for 0.02 T ≤ B ≤ 9 T shows an anomalous quantum Hall plateau at ≈0.25 R0 for B > 3 T, consistent with a quantum Hall plateau from the dispersing branch N = 0 subband that is shorted by the edge state (see Eqs. 3b, 4). The black dashed lines is the diffusive bulk limit for B = 1 T. b The normalized Hall resistance |RHall/R0B| converges to the diffusive bulk limit for B < 0.5 T and VG > 0.4 V. For VG < 0.4 V and B < 0.1 T it becomes independent of B and saturates at ≈0.2 T−1 and then decreases to 0 independent of B as VG decreases to 0. This behavior is predicted in Eq. 3b (inset); Eq. 3a (inset) does not correspond at all, showing that the edge state does not generate a Hall voltage. c Effective charge density n* = |B/eRHall| . For small B and/or large VG, n* converges to the diffusive limit (thick black dashed line) which is corrected for the quantum capacitance. A significant gap ΔVG = 0.17 V is observed which indicates a band gap which however cannot be quantified by this measurement.
