Extended Data Fig. 5: Terahertz tunnelling spectroscopy of Gundlach oscillations on Au(111).
a, Constant height current–voltage characteristics (Id.c.–Vd.c. curves) acquired at several tip–sample separations (z – z0 = 0.2 nm, 0.4 nm, 0.6 nm, 0.9 nm, and 1.2 nm for magenta, green, blue, red and black solid lines, respectively) and then normalized to the initial tip height4. The initial tip–sample separation, z0, was set by V0 = 10 mV, I0 = 300 pA. The corresponding normalized differential conductance, (dI/dV)/(I/V), is shown with a solid orange line. b, Schematic for a one-dimensional metal-vacuum-metal tunnel junction illustrating the emergence of field emission resonances (FERs; n = 1, 2, 3, 4) at a sufficiently high magnitude d.c. bias, beyond the work function of the tip (ϕt) or sample (ϕs). The square barrier approximation is represented by a solid grey line, while the barrier that incorporates image potential effects is represented by the solid black curve. Fermi levels for the tip and sample are given by εF,t and εF,s, respectively, where eVd.c. = εF,t – εF,s. c, Terahertz-pulse-induced rectified charge (QTHz) versus peak strong-field terahertz voltage (VSF,pk) for the waveform in Supplementary Figure 4 acquired at several different tip heights and Vd.c. = 0 V. The initial tip–sample separation, z0, was set by V0 = 2 mV, I0 = 30 pA. Shading indicates the polarity of QTHz, with red and blue representing positive and negative, respectively. d, Differential rectified charge (|ΔQTHz|) versus peak terahertz voltage (VSF,pk) acquired simultaneously with c. The weak-field terahertz pulse used to modulate the total induced voltage at the tip apex had a peak voltage of |VWF,pk| = 0.35 V and a relative delay of τCC = 0 ps with respect to the largest half-cycle of the strong-field pulse. e, The corresponding normalized differential rectified charge (|ΔQTHz/QTHz|) versus peak terahertz voltage (VSF,pk) for the measurements in c and d. Within e, the curves are vertically offset for clarity. f, Scatter plot of the FER voltage positions in b and e as a function of tip height with grey solid lines representing hyperbolic-like functions (see Supplementary Discussion 1). The absolute voltages of the Gundlach oscillation (FER) peaks for both positive and negative voltages and their respective tip heights for STS and THz-STS are shown in red and blue, respectively. Fit parameters: A = 200 pm\(\sqrt{{\rm{eV}}}\), B = 1500 pm\(\sqrt{{\rm{eV}}}\), ϕ = 3.5 eV and zs = 2.15 nm. g, Conventional STM constant-current distance–voltage spectroscopy (z–Vd.c.). The derivative of the relative tip height, z, with respect to d.c. bias (dz/dVd.c.) is shown with a solid purple line. The differential conductance (dId.c./dVd.c.) was acquired by applying a 10 mV amplitude a.c. modulation while sweeping Vd.c. and retracting the tip height to maintain Id.c. = 300 pA (solid orange line). Inset: relative tip height throughout the measurement. h, THz-STS distance–voltage spectroscopy (ΔQTHz/QTHz versus Vd.c.) acquired at VSF,pk = –7.8 V, VWF,pk = +350 mV and τCC = 0.0 ps, while retracting the tip to maintain Id.c. = 100 pA.
