Fig. 4. Effect of electrostatic gating of the 2DEG on the SPhP band in LaAlO₃/ SrTiO₃.

a Sheet resistance of 2DEG as a function of the gate voltage, measured in situ during the cryogenic s-SNOM experiment. b Nano-FTIR spectra of ${\mathrm{s}}_3/{\mathrm{s}}_{3,\max }$ (normalized to the peak value) collected far away from the metal edge at selected values of the gate voltage $V_G$: 0, −50 and −150 V. c The onset frequency ${\omega }_{\mathrm{onset}}$ extracted using linear fits as shown in b and Supplementary Fig. S7 as a function of the gate voltage. The relative shift of the onset frequency with respect to $V_G\mathit{=}$ 0 V is given on the right axis. d Simulated shift of ${\omega }_{\mathrm{onset}}$ obtained in two ways. First, the real part of the 2DEG permittivity is changing while the imaginary part is kept constant (red symbols). Second, the imaginary part is varied at constant real part (blue symbols). The arrows indicate the change of the real part of the permittivity corresponding to the experimentally observed shift of the onset frequency at 0 V, −50 V and −150 V. All error bars correspond to the standard deviation.