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Atomic-scale terahertz time-domain spectroscopy

Abstract

Lightwave-driven terahertz scanning tunnelling microscopy (THz-STM) is capable of exploring ultrafast dynamics across a wide range of materials with ångström resolution (10−10 m). In contrast to scanning near-field optical microscopy, where photons scattered by the tip apex are analysed to access the local dielectric function on the nanoscale, THz-STM uses a strong-field single-cycle terahertz pulse to drive an ultrafast current across a tunnel junction, thereby probing the local density of electronic states. Yet, the terahertz field in a THz-STM junction may also be spectrally modified by the local electromagnetic response of the sample. Here we demonstrate atomic-scale terahertz time-domain spectroscopy by combining waveform sampling with terahertz scanning tunnelling spectroscopy to study a single gallium arsenide surface defect, which exhibits a strongly localized terahertz resonance and resembles the elusive DX centre. These results are based on a generally applicable and self-consistent approach for terahertz near-field waveform acquisition in a tunnel junction that can distinguish local sample properties from effects due to terahertz pulse coupling, enabling comprehensive near-field microscopy on the atomic scale.

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Fig. 1: Terahertz waveform shaping and cross-correlation near-field sampling in an atomic tunnel junction.
Fig. 2: Reference for atomic-resolution terahertz time-domain spectroscopy.
Fig. 3: Terahertz time-domain spectroscopy of an atomic defect on a gallium arsenide surface.
Fig. 4: Terahertz time-domain pico-spectroscopy.

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Data availability

Raw data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

The algorithm for subcycle terahertz scanning tunnelling spectroscopy and the simulation of terahertz pulse cross-correlation measurements were implemented using custom-made Python functions, which will be made open-source upon publication of this work. The code will be available on the GitHub repository (https://github.com/NanoTHzCoding/THz_STS_Algorithm). The codes and simulation files that support the plots and data analysis within this paper are available from the corresponding authors on reasonable request.

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Acknowledgements

We thank R. Loloee and R. Bennett for technical support along with M. Grayson and B. Schuler for valuable discussions. This project was supported financially by the Office of Naval Research (grants nos. N00014-21-2537 and N00014-21-1-2682), the Army Research Office (grant no. W911NF2110153), the Air Force Office of Scientific Research (grant no. FA9550-22-1-0547) and the Cowen Family Endowment.

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V.J., K.C.-H., M.H. and T.L.C. designed and constructed the experimental set-up. The experiments were carried out by V.J., M.H., S.A. and S.E.A., with support from K.C.-H. and T.L.C. The modelling was performed by S.A., with support from S.E.A., M.H., V.J. and T.L.C. M.H., S.E.A. and V.J. prepared the samples and tips. V.J., S.A., M.H. and T.L.C. wrote the paper with contributions from all authors. T.L.C. supervised the project.

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Correspondence to V. Jelic or T. L. Cocker.

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Nature Photonics thanks Mengkun Liu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Validating terahertz near-fields in an atomic tunnel junction.

a, Asymmetric terahertz pulses with an incident field strength of ESF,pk and near-field voltage of VSF,pk are constructed by varying the terahertz pulse interferometer delay time (τφ) after inverting the polarity of one interferometer arm with respect to the other. b, The measurements required for waveform validation at a particular τφ are a THz-CC field profile (ΔQTHz as a function of τCC) and a QTHz–VSF,pk curve. c, The THz-STS inversion algorithm uses both measurements to extract the current–voltage characteristic for the tunnel junction that is used to re-rectify the measured terahertz field profile. This produces a simulated current pulse and simulated cross-correlation waveform. If the simulated current pulse is unipolar and the measured and the simulated cross-correlation waveforms match, then the measured field profile is consistent with the model and verified to be accurate.

Extended Data Fig. 2 Measuring and validating terahertz near-fields in an STM junction over gold.

a, Differential rectified charge map, ΔQTHzCC,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 (QTHzESF,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 QTHzESF,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 ΔQTHzCC,VSF,pk) based on the extracted IV (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, QTHzESF,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 QTHzESF,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 IV 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 IV 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.

Source data

Extended Data Fig. 3 Imposing a unipolar strong-field-induced current pulse with a d.c. bias voltage offset and qualitative waveform verification using terahertz pulse autocorrelations.

a,b, Terahertz pulse autocorrelations at VSF,pk = +13 V (red line) and VSF,pk = –13 V (blue line) with Vd.c. = 0 V, z = z0 (a) and Vd.c. = ±8 V, z = z0 + 0.9 nm (b). The left inset in a shows a set of shifted and unshifted QTHzESF,pk curves for the voltage calibration with this tip apex, acquired at Vd.c. = +5 V (orange circles) and Vd.c. = +8 V (purple line) and a tip height of z = z0 + 1.2 nm. The right insets in a and b are a zoom into the central region of the autocorrelation (dashed black line). c, THz-CC waveform measured at Vd.c. = 0 V, VSF,pk = +13 V and VWF,pk = –0.40 V. d, THz-CC waveforms measured at VWF,pk = +0.40 V (light blue line) and VWF,pk = +0.08 V (dark blue circles) with Vd.c. = 0 V and VSF,pk = +13 V. e,f, THz-CC waveforms measured with a d.c. bias of Vd.c. = ±2 V (red and blue lines) and Vd.c. = ±8 V (red and blue circles) applied during the measurement. The d.c. bias polarity was matched to the polarity of VTHz,pk: +9 V (light red line), +13 V (dark red circles), –10 V (light blue line) and –13 V (dark blue circles). The weak-field terahertz amplitude was –0.40 V for e and +0.40 V for f. All measurements were performed at constant height with the feedback disengaged at V0 = 20 mV, I0 = 200 pA on Au(111).

Source data

Extended Data Fig. 4 Validating terahertz near-fields on GaAs(110).

ac, QTHz–ESF,pk curves (left) and THz-CC waveforms (right) for the same tip positions as in Fig. 3. The measurements were all acquired at Vd.c. = 1.2 V and Id.c. = 100 pA, while the waveforms were acquired at ESF,pk = 170 V/cm (a), ESF,pk = 110 V/cm (b), and ESF,pk = 40 V/cm (c). The y-axis in c is shown in reverse due to an inverted phase for the terahertz pulse waveform over the resonator defect.

Source data

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 (zz0 = 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 (zVd.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.

Source data

Extended Data Fig. 6 Waveform repeatability in atomic-scale THz-TDS.

a, STM topography images of Au(111) before (top left) and after (bottom left) atomic-scale THz-TDS on the GaAs(110) surface (right). Top left: Vd.c. = 1 V; Id.c. = 100 pA; height range 25 pm; image size 20 nm × 20 nm; scan speed 120 nm/s. Bottom left: Vd.c. = 0.1 V; Id.c. = 100 pA; height range 25 pm; image size 20 nm × 20 nm; scan speed 300 nm/s. Right: Vd.c. = 1.2 V; Id.c. = 100 pA; height range 200 pm; image size 7 nm × 14 nm; scan speed 33 nm/s. b,c, THz-CC waveforms (b) and spectra (c) acquired on Au(111) before (black cross in a; 2 averages; black curves) and after (orange star in a; 5 averages; orange curves) atomic-scale THz-TDS on GaAs(110). d, An average of ten THz-CC spectra acquired on pristine GaAs(110) (red circle in a) at Vd.c. = 1.2 V, Id.c. = 50 pA, ESF,pk = 150 V/cm, EWF,pk = –8 V/cm. e, An average of two THz-CC spectra acquired at the green plus in a (200 pm away from resonator defect) at Vd.c. = 1.2 V, Id.c. = 100 pA, ESF,pk = 110 V/cm, EWF,pk = –8 V/cm. f, An average of four THz-CC spectra acquired on the terahertz resonator defect (white cross in a) acquired at Vd.c. = 1.2 V, Id.c. = 100 pA, ESF,pk = 40 V/cm, EWF,pk = –8 V/cm. The data in cf are shown as mean values ± s.d. of multiple scans.

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Extended Data Fig. 7 Characterizing the bistable terahertz resonator defect in GaAs(110).

a, Three-dimensional (3D) view of a constant height scan at Vd.c. = 1.2 V and ESF,pk = 50 V/cm (image size 7 nm × 7 nm). The 3D texture is represented by log10[Id.c.(x,y)] using a colormap that ranges from 10 pA (brown) to 500 pA (gold). The simultaneously recorded rectified charge, QTHz(x,y), is superimposed with a colormap that ranges from 20 e/pulse (blue) to 5 e/pulse (transparent). b, Conventional STM current–voltage (IV) characteristics acquired on the bistable defect at z = z0 (red curve) and z = z0 + 400 pm (black curve). The height, z0, was set by Vd.c. = 1.2 V and Id.c. = 100 pA on the defect. The red and black dotted lines are guides to the eye for the voltage at which the silicon dopant moves 400 pm to an adjacent vacant gallium lattice site. c, Scatter plot showing the current and voltage at which the bistable defect jumped back and forth between the two lattice sites. Defect motion was induced by IV curve sweeps (ESF,pk = 0 V/cm) and each point in c was determined based on the position of the discontinuous step in an I-V curve. d, STM (top) and simultaneously recorded THz-STM (bottom) images acquired in sequence (14). IV curves were performed between scans at the position of highest QTHz in the preceding scan to move the defect between the two adjacent lattice sites (Images: Vd.c. = 1.2 V, Id.c. = 100 pA, ESF,pk = 50 V/cm). e,f, STM image (e) and simultaneously acquired THz-STM image (f) witnessing a defect hop that occurs at the dashed red line (Vd.c. = 1.2 V, Id.c. = 100 pA, ESF,pk = 75 V/cm).

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Extended Data Fig. 8 Terahertz pulse weak-field voltage calibration.

a,b, Voltage calibration performed for the weak-field waveform on Au(111), VWF(t), following a similar procedure to Extended Data Fig. 2f. A pair of QTHz–ESF,pk curves (a) acquired at τCC = 0 ps (solid red line) and τCC = –6 ps (solid black line) are used to calibrate the weak-field voltage by translating the red curve along the x-axis by 6.3 V/cm (b), equivalent to 0.30 V. The measurements were performed on Au(111) at constant height with Vd.c. = 0 V and a 100 pm tip approach from the initial tip–sample separation set by V0 = 2 mV, I0 = 300 pA.

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Extended Data Fig. 9 Amplitude scaling of the weak-field terahertz pulse.

a,b, Normalized weak-field waveforms, VWF(t), acquired at VSF,pk = 10 V (a) and VSF,pk = +10 V (b) for weak-field peak terahertz voltages of VWF,pk = ±0.30 V (black line), VWF,pk = ±0.24 V (red line), VWF,pk = ±0.18 V (blue line), VWF,pk = ±0.12 V (green line), and VWF,pk = ±0.09 V (purple line). The measurements were performed on Au(111) at constant current with Vd.c. = 10 mV, Id.c. = 200 pA. c,d, ΔQTHz–VWF,pk curves acquired at τCC = 0 fs (orange line) and τCC = –530 fs (purple line) for a negative-dominant terahertz polarity at VSF,pk = –10 V (c) and a positive-dominant terahertz polarity at VSF,pk = +10 V (d). The insets within c and d show the corresponding verified weak-field terahertz waveforms measured with THz-CC. The weak-field waveform has an inverted polarity with respect to the strong-field waveform due to the experimental geometry (see Fig. 1). The orange and purple circles within the insets indicate the temporal locations of the corresponding measurements. The measurements were performed on Au(111) at constant height with Vd.c. = 0 V and the tip–sample separation set by V0 = 10 mV, I0 = 300 pA. The dashed black lines are linear fits to the data.

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Extended Data Fig. 10 Tunnel gap spectroscopy on Au(111) with STM and THz-STM.

a,b, Conventional (a) and terahertz-pulse-driven (b) approach curves acquired with the feedback loop disengaged at the tip height, z0, set by V0 = 10 mV, I0 = 300 pA. The apparent barrier height is calculated using ϕ = ħ2/(8 m)·(d ln(I)/dz)2 following an exponential fit, where m is the electron mass, ħ is the reduced Planck constant, and I is the d.c. current (a) or rectified charge (b). The value of ϕ in electronvolts is shown beside each measurement. The measurements in a were acquired with VSF,pk = 0 V, while the measurements in b were acquired with Vd.c. = 0 V.

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Supplementary information

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Supplementary Discussions 1–5 and Figs. 1–5.

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Jelic, V., Adams, S., Hassan, M. et al. Atomic-scale terahertz time-domain spectroscopy. Nat. Photon. (2024). https://doi.org/10.1038/s41566-024-01467-2

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