Separating the bulk and surface $n$- to $p$-type transition in the topological insulator GeBi${}_{4-x}$Sb${}_x$Te${}_7$

We identify the multilayered compound GeBi${}_4$Te${}_7$ to be a topological insulator with a Dirac point slightly above the valence band maximum, using angle-resolved photoemission spectroscopy (ARPES) measurements. The spin polarization satisfies the time reversal symmetry of the surface states, visible in spin-resolved ARPES. For increasing Sb content in GeBi${}_{4-x}$Sb${}_x$Te${}_7$ we observe a transition from $n$ to $p$ type in bulk sensitive Seebeck coefficient measurements at a doping of $x=0.6$. In surface sensitive ARPES measurements a rigid band shift is observed with Sb doping, accompanied by a movement of the Dirac point towards the Fermi level. Between $x=0.8$ and $x=1$ the Fermi level crosses the band gap, changing the surface transport regime. This difference of the $n$- to $p$-type transition between the surface region and the bulk is caused by band bending effects which are also responsible for a noncoexistence of insulating phases in the bulk and in the near surface region.

Figure 1

(a) Crystal structure of GeBi${}_4$Te${}_7$. (b) Band dispersion along the high symmetry directions $\overline{\Gamma }\overline{K}$ and $\overline{\Gamma }\overline{M}$. (c) Constant energy cuts in the CB region at $E_b=70$ meV and at $E_b=370$ meV in the VB region. (d) Energy distribution curves in $\overline{\Gamma }\overline{M}$ direction. (e) Energy distribution curves at normal emission (bright blue) and at $k=-0.11$ Å${}^{-1}$ (dark blue) in $\overline{\Gamma }\overline{M}$ direction with marked points of interest.

Figure 2

(a) Spin polarization maps in the $k_x$-$k_y$ plane at $E_b=200$ meV of GeBi${}_4$Te${}_7$ for the three spatial components weighted by the total intensity. (b) Polarization along the circle marked in (a) with a radius of $0.07$ Å${}^{-1}$ in the direction of the arrow. The sinusoidal gray lines are guides to the eye.

Figure 3

(a) Band dispersions around normal emission for five different compounds of GeBi${}_{4-x}$Sb${}_x$Te${}_7$ with $x=0$, 0.4, 0.6, 0.8, and 1. (b) Energy distribution curves at $k=0$ Å${}^{-1}$ for the different Sb contents with marked points of interest: min of CB, Dirac point, and VB feature. (c) Energetic position of the Fermi levels with respect to the Dirac point fitted with a sigmoid function. The energetic position of the CB minima, the VB maxima, and the VB at normal emission with respect to the Dirac point fitted with linear functions. The VB and CB region are shaded gray. Errors are of the size of the marks ($\pm 25$ meV) or indicated with error bars. (d) Composition dependence of the Seebeck coefficient of the measured samples at 30 K and 295 K. (e) Shift of the binding energy of the CB minimum, the Dirac point, the VB maximum, and corresponding fitted sigmoid curves (dashed) with respect to the Sb content $x$. The dashed gray line marks the center of the band gap. The VB and CB region are shaded gray. Errors are of the size of the marks ($\pm 25$ meV).

Figure 4

(a) XPS spectra in the region of interest for the different compounds measured with $h\nu =80$ eV. (b) Sb/Bi ratio determined from the measurements; the dashed red line is a straight line fitted to the data. The dashed blue line shows the stoichiometric ratio of the samples.