NSRRC Activity Report 2022

016 NSRRC ACTIVITY REPORT 2022 Å −1 away from the Γ point around the Fermi energy (E F ). The thickness- and strain-dependent topological phase transitions in α-Sn(001) provide fruitful insights into the surface electronic structure of α-Sn and can be generalized to other Dirac materials. The band evolution in a few BLs of α-Sn was initially discussed, focusing on the evolution of a topological surface state (TSS1). Figure 1 displays the ARPES spectra of these few BLs (3-, 6- and 8 BLs) α-Sn samples and the corresponding second-derivative plots along Γ–X. An M-shaped hole band and a V-shaped electron pocket are observed in the 3- and 4-BL samples, and can be attributed to the wavefunction hybridization of the top and bottom surface states. The conduction band minimum was located at an ~0.07 eV binding energy (E B ) and the valence band maximum was at ~0.17 eV E B at Γ. The gap size was approximately 100 meV. The separated hole and electron bands transformed into a linearly dispersive TSS1 as the films grew thicker than 6 BLs. In an 8-BL sample, sharper ARPES spectra with a gapless TSS1 were attained. The TSS1 in the 8-BL sample had the same Fermi velocity as that in a 6-BL one; the DP of TSS1 in the 8-BL sample was ~60 meV higher in E B compared to that in the 6-BL sample. This experimental observation of the critical thickness in the topological phase transition is consistent with our DFT calculations and a recent prediction for free-standing α-Sn(001). During the survey of TSSs in α-Sn, they discovered an extra pair of surface states located outside TSS1 in all α-Sn films thicker than 30 BLs. Figure 2(a) displays the constant energy mappings of 370-BL α-Sn; distinct square-like intensity distributions (yellow arrows) were observed outside the Dirac cone of TSS1 (red dashed lines). A significant difference in the band structures in the Γ–X and Γ–M high-symmetry directions shown in Figs. 2(b)–2(e) is that a large band splitting of RSSs was clearly Fig. 1 : (a) ARPES spectra of 3-, 6-, and 8-BL α-Sn(001) along Γ–X with an incident photon energy of 21.2 eV. (b) Second-derivative plots of (a). [Reproduced from Ref. 1] Fig. 2 : (a) Stack of constant energy contours of 370-BL strained α-Sn(001) thin film with the TSS1 marked by red dashed lines and the RSS marked by yellow arrows. (b) ARPES spectra and (c) DFT results along Γ–X. (d) ARPES spectra and (e) DFT results along Γ–M. (f) k z k // plot (k // along Γ–X) at 0.2 eV E B . (g) Constant energy contour at 0.2 eV E B . (h) ARPES spectra along Γ–M (cut 2) and other parallel cuts (1 and 3) with an incident photon energy of 20 eV; each cut is separated by 0.078 Å −1 with its direction labeled in (g). [Reproduced from Ref. 1]