Topological metal behavior in GeBi${}_2$Te${}_4$ single crystals

The metallic character of the GeBi${}_2$Te${}_4$ single crystals is probed using a combination of structural and physical properties measurements, together with density functional theory (DFT) calculations. The structural study shows distorted Ge coordination polyhedra, mainly of the Ge octahedra. This has a major impact on the band structure, resulting in bulk metallic behavior of GeBi${}_2$Te${}_4$, as indicated by DFT calculations. Such calculations place GeBi${}_2$Te${}_4$ in a class of a few known nontrivial topological metals, and explains why an observed Dirac point lies below the Fermi energy at about −0.12 eV. A topological picture of GeBi${}_2$Te${}_4$ is confirmed by the observation of surface state modulations by scanning tunneling microscopy.

Figure 1

Rietveld refinement profile for the room temperature SXPD data for GeBi${}_2$Te${}_4$. The difference between the measured data (red) and Rietveld fit (black) is shown as a blue line; the calculated Bragg positions are indicated by vertical markers. The secondary phase (asterisk) corresponds to 6.7 wt$\%$ of Bi.

Figure 2

(a) Experimental room temperature crystal structure of GeBi${}_2$Te${}_4$ based on the Rietveld analysis of the room temperature synchrotron x-ray diffraction data. Details of the atomic arrangement in the (b) calculated and (c) experimental structural models for GeBi${}_2$Te${}_4$.

Figure 3

(a) Temperature dependence of the electrical resistivity of two GeBi${}_2$Te${}_4$ single crystals. (b) Calculated DOS of bulk of experimental GeBi${}_2$Te${}_4$ with contributions from all atoms.

Figure 4

Band structure plots of the bulk of experimental GeBi${}_2$Te${}_4$ for varying spin orbital coupling strength (λ): (a) in the absence of spin-orbit coupling, (b) 70$\%$, (c) 85$\%$, (d) 100$\%$ of the physical spin-orbit coupling. The inset in panel (d) depicts a zoomed-in band dispersion near the Fermi level ($E_F$), showing the Dirac cone of surface bands at about −0.12 eV below Fermi energy ($E_F$).

Figure 5

(a) Vacuum slab containing five atomic blocks, each composed of seven atomic layers, with the [001] surface terminated between the Te1-Te1 bond. (b), (c) Calculated band structure of the slab geometry with atomic coordinates using (b) calculated and (c) experimental GeBi${}_2$Te${}_4$ structural models.

Figure 6

A 75×75-nm image of the GeBi${}_2$Te${}_4$ surface showing the local DOS modulation. Inset shows atomic resolution of the surface.

Figure 7

Calculated 2D-FFT of the real space. The image size of 75 nm was chosen to bring the atomic points to the edge of the 2D-FFT image. The six atomic lattice points due to the close-packed structure are visible along the outer edge of the image (green circles), while the scattering signature is visible closer to the dc peak.

Figure 8

A 75×75-nm image of the GeBi${}_2$Te${}_4$ surface showing the local DOS modulation.