Fig. 4: Electron tripling and pairing.

a, b Schematic of edge channel configurations: interference with the outer channel (a) and the middle channel (b). Inner, middle, and outer edges are represented in black, blue, and red, respectively. Dashed lines denote the partitioned edges. The orange wavy line depicts the middle–--outer edge interaction, and the violet wavy line illustrates the interactions among all three edges. c Gate spectroscopy, derived from the conductance oscillations when partitioning the outer edge channel at V_bg = 2.5 V (ν_B = 2.93) with QPC transmission T₁ = 0.59 and T₂ = 0.5. Sliding FT was performed with a 0.45 V window. The top axis is the filling factor beneath the plunger gate. Frequencies for inner f_i, middle f_m, and outer f_o edges are marked with black, blue and red dashed lines. The orange dashed line (pairing1, f_p1) is the sum of f_m and f_o, and the violet dashed line (tripling, f_t) is the sum of all three channel frequencies. Data were taken at V_DC = 0 V, with a full set of their bias voltage dependence provided in Supplementary Movie 5. Prominent signals between 1 < ν_pg < 2 (above 250 V⁻¹) are associated with electron tripling f_t. Weaker signals at low frequencies (~100 V⁻¹) correspond to f_o and f_p1. In this regime, the inner edge has been already expelled from beneath the plunger gate, while the middle and outer edges remain beneath the plunger gate and are slightly displaced from the graphene crystal edge (supplementary information section VI for details). d, Gate–spectroscopy obtained from outer edge channel interference, with T₁ = 0.78 and T₂ = 0.81, at V_DC = − 55 μV. The orange dashed line here (pairing2, f_p2) corresponds to the sum of f_m and f_i. Full bias voltage–dependent gate spectroscopy is in Supplementary Movie 6. Lobe structures for all the channels are detailed in Supplementary Fig. 3.