Supplementary information

Sub-cycle transient scanning tunneling spectroscopy with visualization ofenhanced terahertz near-field

Shoji Yoshida1, Hideki Hirori2, Takehiro Tachizaki3, Katsumasa Yoshioka4, Yusuke Arashida4,Zi-Han Wang1, Yasuyuki Sanari2, Osamu Takeuchi1, Yoshihiko Kanemitsu2, and Hidemi Shigekawa1

1

Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8573, Japan2

Institute for Chemical Research, Kyoto University, Uji, Kyoto, 611-0011

3

Department of Optical and Imaging Science and Technology, Tokai University, Hiratsuka-shi, Kanagawa,259-1292, Japan4Department of Physics, Graduate School of Engineering, Yokohama National University, Yokohama, 2408501, Japan1

Figure S1. Schematic illustration of the experimental setup combining the THz laser system andSTM. a, BS: beam splitter, DS: delay stage, PD: photodetector, PL: polarizer, WP: Wollaston
prism, EOS: electro-optic sampling, TPX: polymethylpentene lens. HWP: half-wave plate. EOS
utilizes the fact that when a THz pulse and a shorter IR pulse irradiate a crystal such as CdTe, thepolarization plane of the IR light rotates by an amount depending on the intensity of thesimultaneously existing THz electric field. Namely, the THz electric field waveform can beobtained by measuring the angle of the rotation of IR light while varying the delay time td between
both pulses. The THz pulse was generated by irradiating the LiNbO3 crystal with IR pulse light(1034 nm, 300 fs, 1 MHz), which was almost a single cycle with a first peak of 1 ps width, asshown in Fig. 2g. The probe light used for photoemission measurement was generated byconverting IR light into a second harmonic wave (517 nm) with a BBO crystal. The relationshipbetween the incident light and the sample is shown in the lower right figure. Both the optical pulses
were focused onto the STM tunnel junction by TPX lens placed in the UHV chamber. The focal
length is 100 mm and the incident angle was 45°. The spot size of the IR light was 10 μm and its
position (on the probe) was scanned in steps of 45 μm with a piezo mirror. The base pressure of
the STM chamber was 1x10-7 Pa and the current noise level was 4 fA/√(Hz). b, Two types of STMtips.

2Figure S2. Dependence of THz waveform at tip apex on electric field strength. a, Change in theTHz near-field waveform at the tip apex (ITHz). The intensity of the THz near field changed
according to the change with the intensity of the incident THz electric field. b, Dependence of themaximum (zero-delay) peak value of the waveform in a on the electric field strength, showing alinear relationship. c, Normalized electric field in a. Corresponding waveforms in a and c are
shown in the same color. A similar waveform was observed regardless of the incident electric fieldstrength.

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Figure S3. Frequency dependence of the THz electric field modulated by the two types of nanotips.
a, Optical micrograph of tip 1. b, c, Maps of electric field strength for frequencies of 0.3 and 0.7
THz, respectively. d, Optical micrograph of tip 2. e, f, Maps of electric-field strength forfrequencies of 0.3 and 0.7 THz, respectively. g, h, Fourier spectra of the electric-field strength
obtained at A, B, and C for tips 1 and 2, respectively. The measurement conditions were the sameas those for Fig. 2. All Fourier spectra of the near field differ strongly from that of the incident
THz electric field. When the incident THz waveform has components centered around 1 THz, thenear-field waveform is shifted to the lower-frequency side (redshift) and becomes centered around
0.5 THz. The change in the bandwidth can be explained to some extent by the dipole. Highfrequency components are reduced by the factor of 1/f (f: frequency), which was experimentallyconfirmed by NSOM1. To investigate the details of the electric field distribution around the metal
tip, we performed finite different time domain (FDTD) calculation and the results are shown inFig. S4. The experimental results were reproduced well.

4Figure S4. FDTD Simulations of near field. a, Calculation configuration consisting of the W tip(tip 1) and graphite sample, and the spatial distribution of the electric field at the Fouriercomponent of 0.7 THz. b, Waveforms simulated at A, B, and C shown in a. c, Frequency
dependence of the THz electric fields obtained from the waveforms in b. In the calculation, thecomplex dielectric function for the metal tip and graphite sample is given by =∞+i/0,, where
ε∞ =1, 0 is the vacuum permittivity, and the conductivity σ for the tungsten tip and graphite sample
are 52.8 nΩ∙m and 0.4 μΩ∙m, respectively. The incident angle of THz pulse is 45 degrees against
the metal tip.

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Figure S5. Measurement results for HOPG. a. Tip-enhanced near-field waveform obtained byphotoelectron measurement. b. Spectrum obtained in tunnel regime obtained for α = π (VS = 2 mV,IT = 2 pA, IIR = 3.8 mJ/cm2, frep = 1 MHz). A similar THz near-field profile was also measured on
the HOPG sample; however, ITHz was very low compared to that for Bi2Se3 and the signal was
faintly observed only for td =0, which is considered to be caused by the weak excitation of hotelectrons in HOPG. Namely, the optical transition in HOPG with the energy of the IR pulse used
is limited to the π-π* transition near the K point, whereas various optical transitions are possible
in Bi2Se3, as known from the results of photoelectron emission spectroscopy. The signal level of
HOPG in this experiment was already extremely low (0.05 e-/pulse), which is close to the detection
limit of our system at present. Further improvement is necessary to investigate weak signals suchas those from HOPG, and the use of a light source with an even higher repetition rate is considered
to be a possible technique6

Figure S6. Relationship between tip-enhanced near field strength and THz intensity obtained byphotoelectron measurement. A linear relationship similar to that in Fig. S2b was obtained.

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Figure S7. Tunnel spectrum of Bi2Se3 (VS = 2 V, IT = 2 pA).

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rFigure S8. Tip-sample distance dependence of the near-field waveform at the tip apex.
a. Optical photograph of tip 1 used in the experiment. b. Tip-sample distance dependence of thenear-field waveform at the tip apex (experiment). The nanotip was retracted from 1μm with stepsof 36 μm, and the same measurements as in Fig. 2 were performed for each step. c. Tip-sample
distance dependence of the near-field waveform at the tip apex in which the electric fieldwaveforms at 1μm was subtracted from the data in b. d. Configuration used for the simulation. d
represents the distance between the tip and sample, which was set to 100 μm here. e. Tip-sample

9distance dependence of the near-field waveform at the tip apex (simulation). The nanotip was
retracted from 20μm with steps of 40 μm Tip-sample distance dependence of the near-field
waveform at the tip apex. f. Tip-sample distance dependence of the near-field waveform at the tipapex in which the electric field waveforms at 20 μm was subtracted from the data in e. Tip-sample
distance dependence of the near-field waveform at the tip apex in which the electric field
waveforms at 1μm was subtracted from the data in d. In c and f, some diagonal lines were
exaggerated as shown by the red and black triangles and the dashed lines. Their positions areslightly different between the experiment and the simulation due to the slight difference in thewaveform shown in b and e. Since the phase shift which produced the slopes corresponds to √2d/c(d : tip-sample distance, c : the speed of light), the observed diagonal lines are considered to be thechange in the delay of the arrival time of the light reflected from the sample, which is in good
agreement with the effect predicted by the simulation for the STM setup in the previous paper2. g.
Map of the strength of the simulated electric field at various frequencies. The effect of the standing
wave exists along the tip, which, however, did not depend on the tip-sample distance, indicatingthat there is no clear resonance effect in this case.
As shown here, the influence of reflection appears at a far place, but the THz waveform at thetip apex hardly changes within the distance of 1 μm.Therefore, it is considered reasonable to use
the THz electric field shown in Fig. 3d for the analysis in the tunnel region in Fig. 3g.

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