Abstract
A topological insulator is an unusual quantum state of matter, characterized by the appearance, at its edges or on its surface, of a gapless metallic state that is protected by timereversal symmetry^{1,2}. The discovery of topological insulators has stimulated the search for other topological states protected by other symmetries^{3,4,5,6,7}, such as the recently predicted^{8} topological crystalline insulator (TCI) in which the metallic surface states are protected by the mirror symmetry of the crystal. Here we present experimental evidence for the TCI phase in tin telluride (SnTe), which has been predicted to be a TCI (ref. 9). Our angleresolved photoemission spectra show the signature of a metallic Diraccone surface band, with its Dirac point slightly away from the edge of the surface Brillouin zone in SnTe. Such a gapless surface state is absent in a cousin material, lead telluride, in line with the theoretical prediction.
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The surface state of threedimensional (3D) topological insulators is characterized by a spin nondegenerate Diraccone energy dispersion protected by timereversal symmetry. In topological insulators, the timereversal symmetry plays a key role in characterizing the topological properties such as the quantum spin Hall effect, the dissipationless spin current and the magnetoelectric effect^{10,11,12,13}. In contrast, in TCIs, the metallic surface states are protected by the mirror symmetry (reflection symmetry) of the crystal^{8}. The TCIs are characterized by a new topological invariant called the mirror Chern number, instead of the Z_{2} invariant in topological insulators. Intuitively, the existence of mirror symmetry allows one to divide the Hilbert space into left and right, and considering only one of them can single out a nontrivial topology that is otherwise cancelled and undetected. Therefore, even when an insulator is trivial in the topological insulator sense, it can still be nontrivial in the TCI sense when it possesses a mirror symmetry and its mirror Chern number is nonzero^{8,9}. Indeed, it was recently shown^{9} that such a situation is realized in an insulating crystal having the rocksalt structure (in which the {001}, {110} and {111} surfaces have mirror symmetry with respect to the (110) mirror plane, see Fig. 1a) when a band inversion occurs at the highsymmetry L points of the bulk Brillouin zone; intriguingly, it was further predicted^{9}, on the basis of tightbinding calculations, that a narrowgap IV–VI semiconductor SnTe is such a TCI, whereas the isostructural PbTe is not. It is thus of particular importance to experimentally examine the possibility of the TCI phase in these semiconductors, to establish the concept of this new topological state of matter and possibly to find topological phenomena beyond the framework of known topological materials.
In our angleresolved photoemission spectroscopy (ARPES) experiment, we paid particular attention to the momentum space around the point of the surface Brillouin zone corresponding to a projection of the L point of the bulk Brillouin zone where a direct bulk bandgap resides^{14,15,16} and the appearance of topological surface states is predicted^{9}; note that the (110) mirror plane is projected to the highsymmetry line in the surface Brillouin zone (Fig. 1a). Our extensive ARPES measurements of the occupied states suggest that the bulkband maximum is indeed located around the point (see Supplementary Fig. S1). As shown in Fig. 1b, the ARPES intensity at the Fermi level (E_{F}) measured with the photon energy h ν = 21.2 eV on the (001) surface exhibits a bright intensity pattern centred around the point and is elongated along the direction. The band dispersion along two selected cuts (red arrows in Fig. 1b) exhibits a linearly dispersive feature crossing E_{F}, as shown in Fig. 1c,d. The top of this Diraclike band is located not at the point but at a point slightly away from it (called here the point), as one can infer from the band dispersion along the cut (Fig. 1e,f) showing the band maxima on both sides of the point ( and for the first and second surface Brillouin zones, respectively). Such a characteristic Mshaped dispersion is not expected from the bulkband calculations at any k_{z} (wave vector perpendicular to the surface) values^{14,15,16}, but is predicted for the surface band^{9} (Supplementary Information), suggesting that the observed Diraclike band originates from the surface states.
To further examine whether the Diraclike band is of surface or bulk origin, we have carried out an ARPES measurement along the cut crossing the point for various photon energies. As one immediately recognizes in Fig. 1g–j, the energy position of the band is stationary with respect to the h ν variation. In fact, when we plot the extracted dispersions for different photon energies in the same panel, they overlap each other within the experimental uncertainties of ∼ 0.05 eV (near E_{F}) to ∼ 0.1 eV (at higher binding energy, E_{B}), demonstrating the surface origin of the Diraclike band. Note that the broadening of the spectra on the righthand side of the branch at higher E_{B} evident in Fig. 1h–j is probably due to a mixture of the bulk state whose energy position changes with h ν, although the bulk state is obviously very broad and we could not clearly resolve its dispersion.
We note that, because asgrown crystals of SnTe tend to show a heavily holedoped nature^{16,17,18}, a key to the present observation of the Diraclike band was to reduce hole carriers in the crystal by minimizing Sn vacancies during the growth procedure. In fact, the Diraclike surface state was not resolved in the previous ARPES study^{16}, mainly owing to the heavily holedoped nature of the sample (chemical potential was located ∼ 0.5 eV lower when compared with our data). Furthermore, a downward band bending, possibly due to a loss of Te atoms on cleaving, was obviously taking place near the surface (Supplementary Information), which further worked in our favour.
As shown in Fig. 1k, the ARPES data at T = 130 K divided by the Fermi–Dirac distribution function indicate that the left and righthand side dispersion branches actually merge into a single peak above E_{F}. The Diracpoint energy is estimated to be 0.05 eV above E_{F} from a linear extrapolation of the two dispersion branches (Fig. 1m) that were determined from the peak positions in the momentum distribution curves; furthermore, the Dirac band velocities extracted from the dispersions are 4.5 and 3.0 eV Å, for the left and righthand side branches, respectively. One can see in Fig. 1m that the band dispersion exhibits no discernible change with temperature (compare the 30 K and 130 K data for h ν = 92 eV).
One may argue that in SnTe the wellknown rhombohedral distortion^{19} would break the mirror symmetry with respect to the (110) plane and destroy the signature of the Diraccone surface states. However, one can safely exclude this possibility in the present experiment, because the rhombohedral phase transition temperature is known to be strongly dependent on the carrier density^{19} and in our samples the transition occurs well below 30 K (the temperature of our ARPES measurements), which is corroborated by the absence of a kink in the temperature dependence of the resistivity (see Supplementary Fig. S6). In addition, the (001) surface of the cubic structure has two mirror planes, and the rhombohedral distortion breaks the mirror symmetry of only one of those two mirror planes. This means that two of the original four Dirac cones remain gapless in the rhombohedral phase; furthermore, as the rhombohedral distortion in SnTe is weak (it induces only 1.6% displacement of the atomic positions^{19}), the expected result is an opening of a small gap at the Dirac point in the other two Dirac cones. Therefore, the small rhombohedral distortion, even when it happens, will not significantly change the surface state spectrum.
To further elucidate the topology of the Dirac cone in detail, we have determined the whole band dispersion in the 2D momentum space. By selecting a specific photon energy (h ν = 92 eV), owing to the matrixelement effects, we found it possible to pick up the dispersion of a single Dirac cone centred at the point ( Dirac cone) while suppressing the intensity of the Dirac cone. Figure 2a–e shows the nearE_{F} ARPES intensity measured along several cuts (A–E) around the point. Along cut A (Fig. 2a), the surface band has its top at an E_{B} of 0.45 eV. On moving from cut A to E, the band maximum (white arrow) approaches E_{F} (cuts A–B), passes E_{F} (cut C), and then disperses back again towards higher E_{B} (cuts D–E). This result establishes the coneshaped dispersion of the Diraclike band in the 2D momentum space as in threedimensional topological insulators^{1,2} and graphene^{20}. In passing, we have surveyed electronic states throughout the Brillouin zone and found no evidence for other metallic surface states (Supplementary Fig. S1) and thus conclude that the surface electronic states consist of four Dirac cones in the first surface Brillouin zone. This indicates that this material is not a topological insulator but is a TCI owing to an even number of bandinversion points^{9} that is reflected in the number of Dirac cones.
As shown in the ARPESintensity contour plots in Fig. 2g for several E_{B} slices, the Dirac cone in SnTe is anisotropic and slightly elongated along the direction, and its topology shows a Lifshitz transition as a function of band filling: namely, at E_{B} = 0.15 eV the crosssection is closed and is elongated towards , but it becomes open at E_{B} = 0.30 eV, suggesting that it is reconnected with the Dirac cone on the other side of (see Supplementary Fig. S5); at E_{B}≥0.45 eV, the bulk band creates strong intensities and partly smears the surface state. This Lifshitz transition is interesting, because it would accompany a marked change in the Diraccarrier properties and provide another ingredient in the physics of topological insulators. The observed evolution in the 2D band dispersion presenting a double Diraccone structure is schematically depicted in Fig. 2h. Although SnTe samples are always ptype, one can access the upper part of this double cone by using scanning tunnelling microscopy or fieldeffecttransistor devices.
To see how unique SnTe is among isostructural IV–VI semiconductors, we have performed an ARPES measurement of PbTe and directly compared the nearE_{F} electronic states around the point, as shown in Fig. 3a,b. The PbTe single crystals used here were specially tuned to be only weakly electron doped and were of very high quality, with an electron mobility of 60,000 cm^{2} V^{−1} s^{−1} (Supplementary Information). Intriguingly, the spectral feature of PbTe shows no evidence for the metallic Diraclike band, and exhibits only a broad feature originated from the top of the bulk valence band^{21}, suggesting that this material is an ordinary (trivial) insulator. Note that this broad feature is intrinsic and is not due to a bad crystallinity, because deeper bands show clear dispersions (Supplementary Information). This naturally suggests that a topological phase transition takes place in a solidsolution system Pb_{1−x}Sn_{x}Te (Fig. 3c). This conclusion agrees with the tightbinding calculation^{9} that predicted that the valence bands at four L points in SnTe are inverted relative to PbTe, resulting in different mirror Chern numbers (2 versus 0). One can thus infer that the bulk bandgap closes at a critical x value, x_{c}, accompanied by a parity change of the valenceband wavefunction and an emergence/disappearance of the Diraccone surface state. Therefore, the present results have established the TCI phase in SnTe, which is in contrast to the trivial nature of isostructural PbTe. Our results unambiguously demonstrate the validity of the concept of TCIs and suggests the existence of many more kinds of topological material.
Methods
Highquality single crystals of SnTe and PbTe were grown by a modified Bridgeman method in sealed evacuated quartzglass tubes from highpurity elements (Sn (99.99%), Pb (99.998%), Te (99.999%)). To obtain SnTe crystals with minimal Sn vacancy, a starting ratio of Sn/Te = 51:49 was chosen and, after melting the elements at high temperature, the tube was slowly cooled to 770 °C (which is only 20 °C below the melting point) and quenched into cold water; the carrier density estimated from the Hall coefficient was 2×10^{20} cm^{−3}, which is lower than usual^{17,18}. PbTe crystals were grown with a starting composition of Pb/Te = 1.005:1 by slowly cooling the melt from 980 °C to 700 °C at 2°C h^{−1} and holding at 700 °C for 12 h; the carrier density in the resulting crystals was very low at 1.7×10^{17} cm^{−3}. Both SnTe and PbTe single crystals are single domain and show good crystallinity in Xray Laue analysis, and their detailed transport properties are described in the Supplementary Information. ARPES measurements were performed with the MBSA1 and VGScienta SES2002 electron analysers with a highintensity helium discharge lamp at Tohoku University and also with tunable synchrotron lights at the beamline BL28A at the Photon Factory (KEK). To excite photoelectrons, we used the He Iα resonance line (h ν = 21.218 eV) and the circularly polarized lights of 50–100 eV at Tohoku University and the Photon Factory, respectively. The energy and angular resolutions were set at 10–30 meV and 0.2°, respectively. Samples were cleaved in situ along the (001) crystal plane in an ultrahigh vacuum of 1×10^{−10} torr at room temperature. A shiny mirrorlike surface was obtained after cleaving the samples, confirming their high quality. The Fermi level of the samples was referenced to that of a gold film evaporated onto the sample holder.
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Acknowledgements
We thank L. Fu for stimulating discussions. We also thank M. Komatsu, M. Nomura, E. Ieki, T. Takahashi, N. Inami, H. Kumigashira and K. Ono for their assistance in ARPES measurements, and T. Ueyama and K. Eto for their assistance in crystal growth. This work was supported by JSPS (NEXT Program and KAKENHI 23224010), JSTCREST, MEXT of Japan (Innovative Area Topological Quantum Phenomena), AFOSR (AOARD 124038) and KEKPF (proposal number: 2012S2001).
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Y.T., T.S., K.N., S.S. and T.T. performed ARPES measurements. Z.R., K.S. and Y.A. carried out the growth of the single crystals and their characterizations. Y.T., T.S. and Y.A. conceived the experiments and wrote the manuscript.
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Tanaka, Y., Ren, Z., Sato, T. et al. Experimental realization of a topological crystalline insulator in SnTe. Nature Phys 8, 800–803 (2012). https://doi.org/10.1038/nphys2442
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DOI: https://doi.org/10.1038/nphys2442
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