Spatially resolved Landau level spectroscopy of the topological Dirac cone of bulk-type ${\mathrm{Sb}}_2{\mathrm{Te}}_3\text{(0001)}$: Potential fluctuations and quasiparticle lifetime

Using low-temperature scanning tunneling spectroscopy, we probe the Landau levels of the topologically protected state of ${\mathrm{Sb}}_2{\mathrm{Te}}_3$(0001) after in situ cleavage of a single crystal. Landau levels are visible for magnetic fields $B\ge 2$ T at energies, which confirm the Dirac type dispersion including the zeroth Landau level. We find different Dirac velocities for the lower and the upper part of the Dirac cone in reasonable agreement with previous density functional theory data. The Dirac point deduced from the zeroth Landau level shifts by about 40 meV between different areas of the sample indicating long-range potential fluctuations. The local potentials are correlated to different local defect densities varying slightly stronger than expected from a statistical distribution. Moreover, the width of the Landau level peaks is analyzed. It is found to increase, mostly linearly, with the energy distance to the Fermi level. Consequently, we attribute the peak width to a dominating scattering of the hot quasiparticles by electron-electron interaction.

Figure 1

(a) Large-scale STM image of cleaved ${\mathrm{Sb}}_2{\mathrm{Te}}_3$(0001) ($V=0.9$ V, $I=50$ pA) revealing large terraces of widths up to 50 nm. Inset: Line profile along the blue line of the main image showing the step heights which correspond to the height of one QL ($\approx 1$ nm). (b) Atomically resolved STM image ($V=0.4$ V, $I=1$ nA) recorded in the area marked by the black box in (a). A hexagonally arranged pattern of the top surface Te atoms is observed with an average atomic distance of 0.42 nm. Different types of defects are visible as clover-shaped structures appearing dark and bright.

Figure 2

(a) $dI/dV\left(V\right)$ spectrum recorded on cleaved ${\mathrm{Sb}}_2{\mathrm{Te}}_3$(0001) at $B=6.7$ T showing Landau quantization of the topological surface state ($V_{\mathrm{stab}}=0.3$ V, $I_{\mathrm{stab}}=400$ pA, $V_{\mathrm{mod}}=4$ mV). The spectrum is an average of ten consecutive spectra measured at the same point on an area away from defects. $E_{\mathrm{D}}$ marks the position of the Dirac point located at ${\mathrm{LL}}_0$, the numbers mark the LL index $n$, and the dashed lines mark the peak positions deduced from Lorentzian fits. Inset: $dI/dV\left(V\right)$ spectrum at $B=0$ T measured at the same position as the one in the main image with $E_{\mathrm{D}}$ marking the minimum of the curve ($V_{\mathrm{stab}}=0.3$ V, $I_{\mathrm{stab}}=50$ pA, $V_{\mathrm{mod}}=4$ mV). (b) Landau level energies deduced from Lorentzian fits of the peaks in (a) and plotted against $\mathrm{sgn}(n$)$\sqrt{\left|n\right|B}$. The line is a linear fit resulting in the Dirac velocity $v_{\mathrm{D}}$ as indicated.

Figure 3

(a) STM image ($V$ = 0.9 V, $I$ = 100 pA) revealing typical types of defects at the surface of ${\mathrm{Sb}}_2{\mathrm{Te}}_3$(0001). (b) Zoom into the marked area of (a) showing a closeup view with four different types of defects marked by different colored ellipses, which are labeled according to [54].

Figure 4

(a) $dI/dV\left(V\right)$ spectra recorded at $B=0–7$ T as marked on a different sample area as the LLs from Fig. 2 ($V_{\mathrm{stab}}=0.3$ V, $I_{\mathrm{stab}}=100$ pA, $V_{\mathrm{mod}}=2$ mV). For direct comparison of the spectra, each spectrum (at a distinct field), which is again an average of 10 spectra, is measured on the same point away from the defects. The vertical dotted line indicates the field-independent zeroth Landau level at the Dirac point $E_{\mathrm{D}}$. The spectra are shifted vertically for clarity. Inset: $dI/dV\left(V\right)$ spectrum for a larger energy range measured at $B=0$ T in the same sample area ($V_{\mathrm{stab}}=0.3$ V, $I_{\mathrm{stab}}=100$ pA, $V_{\mathrm{mod}}=2$ mV). (b) Landau level energies deduced from Lorentzian fits of the curves in (a) and plotted versus momentum $k_n$ as deduced from Eq. (2). The dashed lines are linear fits to the lower and upper part, respectively, with resulting Dirac velocities $v_{\mathrm{D}}$ marked. (c) Full width at half maximum for each Landau level, as deduced by a Lorentzian fit function, plotted as a function of energy. Different $B$ fields are indicated. The dashed line is a linear fit forced through $\mathrm{\Delta }E=0$ meV at $E_{\mathrm{F}}$.