Possible flat band bending of the Bi1.5Sb0.5Te1.7Se1.3 crystal cleaved in an ambient air probed by terahertz emission spectroscopy

We investigate an evolution of the surface electronic state of the Bi1.5Sb0.5Te1.7Se1.3 single crystal, which is one of the most bulk insulating topological insulators, by examining terahertz light emitted from the sample surface upon the illumination of the near-infrared femtosecond laser pulses. We find that the surface state with a flat band bending can appear in the course of the natural maturation process of the surface state in an ambient air. Furthermore, we demonstrate that the evolution of the surface electronic state can be accelerated, decelerated, or even stopped by controlling environmental conditions to contain different amount of H2O, in particular.

ρxx is saturated and shows a reduction with a further decrease of T which is attributed to the bulk insulating and surface metallic state of BSTS. The Hall resistance RH shown in Fig. S1(b) undergoes a strong T-dependence; it has a positive value at room temperature and a large negative value at T<50 K which are attributed to the change of major charge carrier upon the temperature variation. Note that these behaviors are consistent with the recent report by Taskin et al. 1 . A reflectivity spectrum in the infrared region (Fig. S1(c)) exhibits clear signatures of a free carrier response and the gap excitation which appear as a reflectivity edge at p * /2~190 cm -1 and a hump structure at B/2~2500 cm -1 , respectively. Using the carrier density (~2.210 18 cm -3 ) estimated from RH and the plasma frequency p * (and also with the dielectric constant ∞~2 4 just below the gap energy), we determine the effective mass of the free carriers as 0.31m0 (m0: bare electron mass), which is in good agreement with previous results 2 . Based on these results, we sketch the electronic structure of BSTS in Fig. S1(d). Since the activation energy obtained from ρxx is much lower than the optical gap, we introduce the impurity band inside of the band gap. As it is located near the valence band maximum, it also explains the temperature-dependent change of the majority carrier type 1 . Therefore, BSTS is a bulk-insulating TI with the Fermi energy EF located in the energy band gap.

Discussion about the possible THz generation mechanism
We check the possibility of the optical rectification as a possibility of THz generation mechanism of BSTS by examining azimuth-dependent THz emission responses. Figure S2 displays time(t)domain electric field profiles of emitted THz waves obtained with a full variation of the sample azimuth . Note that the results are obtained long after the sample cleavage. Here, both incident laser pulses and emitted THz waves are set to be p-polarized. Actually, THz light emitted through the optical rectification should reflect the symmetry property of the sample surface, i.e., 3m point group. Hence, the peak-to-peak amplitude of the emitted THz wave E THz peak-peak would have a three-fold or six-fold symmetry in its azimuth dependences as demonstrated in the second harmonic generation 3 . As displayed in Fig. S2(b), the observed azimuth-dependence is fully isotropic, and hence we exclude the nonlinear optical rectification from the possible candidates of THz generation mechanisms in BSTS.  In the main text, we argue that the band bending-induced charge acceleration is the primary origin of the THz emission just after the cleavage as well as in the saturation state. Then the comparison with the result for InAs can provide us with valuable information about the band bending direction. For InAs, a dominant THz emission mechanism is the photo-Dember effect due to the larger mobility of electrons, and hence the corresponding E THz (t) should have the same phase of E THz (t) arising from the upward band bending 4 . Figure S3, however, exhibits that E THz (t) from InAs and Bi1.5Sb0.5Te1.7Se1.3 have opposite phases, and this clearly demonstrates the downward band bending for the BSTS compound just after the sample cleavage.

Adsorption probabilities for gas molecules in the ambient air
The adsorption process is usually determined by three factors. First, the coverage of an adsorbate molecule on the surface is proportional to the partial pressure of the corresponding gas molecule. Second, the van der Waals interaction between the adsorbate and the given surface is a determining factor of the physical adsorption probability, and it is proportional to the polarizability and dipole moment of the molecules. Third, the chemical reactivity of the gas molecule can be the other important factor which determines the chemical adsorption probability. It should be noted that the physisorption contributes to the surface coverage much weakly compared to the chemisorption particularly at relatively high temperature, but it can play an important role in the adsorption process as it may act as precursors to the chemisorption.
Table S1 displays such information for representative gas molecules contained in the ambient air. As a parameter to represent the chemical reactivity, we list the electron affinity and ionization energy of the molecules whereas the ionization energies for all the molecules are similarly large. For N2, although it is a major gas molecule in the ambient air, it is unpolarized and chemically inert. Accordingly, the only attraction between the N2 molecule and the surface arises from van der Waals Supplementary Figure S3. Comparison between E THz (t) from InAs and Bi1.5Sb0.5Te1.7Se1.3 (BSTS). Here, the result for BSTS is obtained just after the sample cleavage in the ambient air (Case I).
forces, and hence its adsorption to the surface is minimal. Actually, Brahlek et al. reported that the N2 atmosphere has the same effect with the vacuum for Bi2Se3 thin films 5 . Note that the same analogy can be applied to the Ar gas. Although O2 is also a non-polar molecule, we can consider its contribution to the adsorption since both the partial pressure and the electron affinity are large. CO2 itself is expected to have the low adsorption rate as its partial pressure is small, the dipole moment is negligible, and also it is chemically stable. For CO, it may allow both physorption and chemisorption since it has relatively large values of polarizability, dipole moment, and electron affinity. Nevertheless, we do not consider its contribution seriously as it has a very tiny partial pressure in air. For reference, we mention that Yashina et al. and Bando et al. found no response of the carbonate-related species from the x-ray photoelectron spectroscopy experiment for Bi2Te3 within 8 hours and 24 hours 6,7 , respectively, after the samples are cleaved in the ambient air.
In the ambient air, we have to consider the contribution of H2O molecules as well; its partial pressure is about 8219 and 6476 ppmv for the relative humidity of 33 % and 26 % at room temperature, respectively. Also, it is a polar molecule. In particular, it can be easily dissociated into OH and O, and the dissorbate OH is a very reactive radical. Hence, H2O can have a much higher effect on the adsorption process than other molecules. Consequently, we take account of O2 and H2O molecules as major adsorbates in the ambient air which can interact with the cleaved BSTS surface.
Supplementary Figure S4. Series of the Te 3d, O 1s, and C 1s core level spectra for BSTS surface in 30 hours after cleaving in the ambient air.  Figure S4 displays core level photoemission spectra of Te 3d, O 1s, and C 1s states for the BSTS sample which was taken at the beamline 4D of Pohang Light Source-II (PLS-II). Before the measurement under the ultrahigh vacuum condition (~8×10 -10 Torr), the sample is cleaved and aged in the ambient air for 30 hours. The adsorption of the oxygen can be clearly observed for Te 3d peaks where a peak corresponding to Te-O bonding is observed together with the other peaks from the original chemical bonding 20 . Accordingly, O 1s peak appears broadly and asymmetrically, and shows a clear signature of the chemical adsorption of oxygen onto the BSTS surface 5 . C 1s peak also appears around 284.3 eV which corresponds to the response of the carbon itself 21 . Actually, we found no signature of the chemical bonding of the carbon with other ions in BSTS, and a weak spectral intensity of the carbon peak, i.e., less than 5 % of the total peak intensity in a wideband spectrum. We therefore conclude that the O and OH are adsorbed, but carbon has a minimal contribution to the adsorption.