Fig. 2: Phase diagram of CrOCl-interfaced BLG in the space of n_tot and D_eff.

a \({\sigma }_{{{{{{{{\rm{xx}}}}}}}}}={R}_{{{{{{{{\rm{xx}}}}}}}}}/({R}_{{{{{{{{\rm{xx}}}}}}}}}^{2}+{R}_{{{{{{{{\rm{xy}}}}}}}}}^{2})\) of Device-S8 plotted in the n_tot-D_eff space, measured at B = 12 T and T = 1.5 K. Here R_xx and R_xy are longitudinal and transverse resistance, respectively. b Line profile of Hall conductance σ_xy at n_tot = 0.2 × 10¹³ cm⁻² along the dashed line in a, in the range of -0.55 V/nm < D_eff < 1.12 V/nm. Here, the effective displacement field is defined as D_eff = (C_tgV_tg − C_bgV_bg)/2ϵ₀ − D₀, where C_tg and C_bg are the top and bottom gate capacitances per area, V_tg and V_bg are the top and bottom gate voltage, and D₀ is the residual displacement field, respectively. Shaded area denotes the region of the charge neutrality. c Schematic image showing the interfacial states near the interface between CrOCl and BLG, with an average distance between these states and BLG defined as d (more details in Methods and Supplementary Note 1). d Simplified electrostatic model with three capacitors with each of their parameters indicated. Here, d_i (i = 1, 2, 3), ε_i (i = 1, 2, 3), and E_i (i = 1, 2, 3), are the distance, dielectric constant, and electrical field of the top (between the top gate and graphene), middle (between graphene and the surface state of CrOCl), and bottom (between bottom gate and the surface state of CrOCl) capacitor, respectively. n_t, n₂, and n_b, denote the carrier concentration induced in the top gate, surface state in CrOCl, and the bottom gate, respectively. I_ds and V_ds denote the source-drain current and voltage, respectively. e Calculated carrier density n_BLG in BLG (step size between each iso-doping line is 2 × 10¹² cm⁻²) at B = 0, using the model described in Supplementary Note 1. f Calculated displacement field D_BLG in BLG, with each iso-D_BLG line stepped by 0.3 V/nm. Phase-boundary of the two distinct phases (i.e., conventional Phase-i, and interfacial coupling Phase-ii) is indicated by the black dashed line. Shaded areas in e, f denote the charge neutrality of the system. g I_ds as a function of 1/T in a semi-log plot. Thermal activation gaps extracted from each curve are labeled, with the solid line being fitted linear slopes.