Figure 2: Mechanism for the waving potential in a graphene sheet.

(a) Charge redistribution of graphene upon adsorption of hydrated Na⁺ (red for regions with charge accumulation and blue for charge depletion). Right bottom inset: Hall voltages as functions of magnetic field for graphene immersed in deionized water and 1 mM NaCl. (b) Schematic EDL and its boundaries by ion adsorption (left) and desorption (right) on the surface of graphene during the insertion and pulling out processes, respectively. Induced potential difference and hole concentration gradient in the graphene sheet are also illustrated. (c) Detected voltage signals of three subsections in graphene sample with four equally spaced electrodes (top inset). The dashed lines mark when the solution surface rises to the corresponding position of the sample in the top inset. The solid red lines are modelling results (Supplementary Note 2). (d) Equivalent circuit for the waving potential. (e) Peak voltage as a function of inserting velocity v of graphene into 0.6 M NaCl solution. The insets zoom in the signals at v=2.25 and 45.1 cm s⁻¹.