Anomalies in the temperature evolution of Dirac states in the topological crystalline insulator SnTe

Discovery of topologically protected surface states, believed to be immune to weak disorder and thermal effects, opened up a new avenue to reveal exotic fundamental science and advanced technology. While time-reversal symmetry plays the key role in most such materials, the bulk crystalline symmetries such as mirror symmetry preserve the topological properties of topological crystalline insulators (TCIs). It is apparent that any structural change may alter the topological properties of TCIs. To investigate this relatively unexplored landscape, we study the temperature evolution of Dirac fermion states in an archetypical mirror-symmetry protected TCI, SnTe, employing high-resolution angle-resolved photoemission spectroscopy and density functional theory studies. Experimental results reveal a perplexing scenario: the bulk bands observed at 22 K move nearer to the Fermi level at 60 K and again shift back to higher binding energies at 120 K. The slope of the surface Dirac bands at 22 K becomes smaller at 60 K and changes back to a larger value at 120 K. Our results from the first-principles calculations suggest that these anomalies can be attributed to the evolution of the hybridization physics with complex structural changes induced by temperature. In addition, we discover drastically reduced intensity of the Dirac states at the Fermi level at high temperatures may be due to complex evolution of anharmonicity, strain, etc. These results address the robustness of the topologically protected surface states due to thermal effects and emphasize the importance of covalency and anharmonicity in the topological properties of such emerging quantum materials.

Figure 1

(a) Crystal structure of SnTe. (b) Laue diffraction pattern, taken on the (100) surface. (c) Powder x-ray diffraction pattern at 300 K. (d) Resistivity, $\rho$ (line), and $d\rho /dT$ (symbols). (e) Specific heat, $C_v$ (line), and $C_v/T$ (symbols).

Figure 2

(a) Orbital-resolved band structure of SnTe. Sn $5p$ and Te $5p$ states compositions are shown in red and blue, respectively. (b) Sn $5s$ (pink), Sn $5p$ (red), Te $5s$ (green), and Te $5p$ (blue) PDOS. (c) Band structure of (001) surface of SnTe showing a Dirac cone close to $\overline{X}$ point. (d) Constant energy contours at 35 meV below the Fermi level.

Figure 3

Fermi surface at (a) 22 K, (b) 60 K, and (c) 120 K. (d) A sketch of the reciprocal lattice and the surface Brillouin zone. The ARPES data obtained from a horizontal cut across the Fermi pocket (blue line) at (e) 22 K, (f) 60 K, and (g) 120 K. The corresponding momentum distribution curves (MDCs) at (i) 22 K, (j) 60 K, and (k) 120 K. Dashed lines are guides to eye. The symbols are the peak positions derived by fitting the MDCs. (h) Traces of the energy bands (symbols) at different temperatures obtained by fitting the MDCs. (l) Energy distribution curves (EDCs) obtained by momentum integration within the green box shown in (a)–(c).

Figure 4

Energy distribution curves (EDCs) at (a) 22 K, (b) 60 K, and (c) 120 K. Dashed lines are guides to the eye. (d) EDCs at $\mathrm{\Lambda }$ point at 22 K (open circles), 60 K (closed circles), and 120 K (line). Solid black line is a smooth curve of the 22 K data. (e) Band structure calculated using the lattice constant $a=6.2\AA$ and (f) the corresponding Sn $5s$, Sn $5p$, Te $5s$, and Te $5p$ PDOS. Band structure for (g) $a=6.5\AA$ and (h) $a=6.7\AA$. (i) Total energy as a function of $a$(Å). The shaded region shows the inverted band structure region.

Figure 5

Energy band dispersions calculated for the lattice constants (a) $a=6.327\AA$ and (b) $a$ = 6.2 Å. Red lines represent the surface bands.