Extended Data Fig. 2: Measuring and validating terahertz near-fields in an STM junction over gold.
a, Differential rectified charge map, ΔQTHz(τCC,ESF,pk) representing possible terahertz voltage waveforms (see Fig. 1 for setup). The data were recorded in constant-current mode with Vd.c. = 10 mV and Id.c. = 100 pA over Au(111). b, Rectified charge induced by the strong-field terahertz pulse with increasing incident peak field strength (QTHz–ESF,pk). The measurement (black curve) was performed at constant height with Vd.c. = 0 V, and the tip height set by V0 = 10 mV, I0 = 100 pA. A polynomial fit to QTHz–ESF,pk (red dashed curve) acts as input to the terahertz scanning tunnelling spectroscopy inversion algorithm9, along with a test voltage waveform (dashed black line in a). c, Extracted differential conductance (dI/dV, green curve) and extracted current-voltage characteristic (I–V, orange curve) sampled by the terahertz voltage pulse. d, Simulation of ΔQTHz(τCC,VSF,pk) based on the extracted I–V (c), the test waveform temporal profile (dashed black line in a), and a weak-field amplitude set to 3% of the strong-field maximum. e, QTHz–ESF,pk curves as a function of d.c. bias acquired at constant height with the tip retracted by an additional 200 pm from the setpoint V0 = 10 mV, I0 = 100 pA. f, Shifted QTHz–ESF,pk curves from e based on the conversion that 21 V/cm corresponds to 1.0 V ± 0.1 V. The arrows indicate the direction of the applied shift. g, Weak-field voltage waveform, VWF(t), across the STM junction (blue curve and dashed black line in a). The red curve (dashed black line in d) shows the waveform shape determined from the simulation in d, confirming that the selected test waveform at ESF,pk = +150 V/cm (dashed black line in a) is an accurate representation of the weak-field voltage transient at the tip apex. h, Simulated map of current pulses generated by the strong-field voltage waveform applied to the extracted I–V characteristic, confirming that a unipolar current pulse was used for the waveform sampling (dashed black line). Inset: plot of the black (ESF,pk = 150 V/cm) and green (ESF,pk = –170 V/cm) dashed lines. i, THz pulse cross-correlation measurement (blue curve) for ESF,pk = –170 V/cm (dashed green line in a). The waveform is notably different from g. However, by applying the field profile of the test waveform in g to the extracted I–V in c (with appropriate polarity and field strength, ESF,pk = –170 V/cm), we calculate a matching distorted waveform (red curve in i and dashed green line in d), indicating that the misleading shape of the waveform is captured by our model.
