STM Imaging of Impurity Resonances on ${\mathrm{Bi}}_2{\mathrm{Se}}_3$

In this Letter we present detailed study of the density of states near defects in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. In particular, we present data on the commonly found triangular defects in this system. While we do not find any measurable quasiparticle scattering interference effects, we do find localized resonances, which can be well fitted by theory [R. R. Biswas and A. V. Balatsky, Phys. Rev. B 81, 233405(R) (2010)] once the potential is taken to be extended to properly account for the observed defects. The data together with the fits confirm that while the local density of states around the Dirac point of the electronic spectrum at the surface is significantly disrupted near the impurity by the creation of low-energy resonance state, the Dirac point is not locally destroyed. We discuss our results in terms of the expected protected surface state of topological insulators.

Figure 1

$1600\times 1000{\AA }^2$ topograph of the surface of undoped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. Most impurities are triangular (typical one marked), pointing in the same direction, and are a consequence of subsurface Se vacancies [10, 11]. The inset shows a three dimensional rendering of a triangular defect. The image was taken at bias voltage $V_b=+300\mathrm{mV}$ and $I_s=25\mathrm{pA}$.

Figure 2

A topograph (a), and selected energy maps emphasizing two triangular impurities with different intensity, while both are the same size, bright triangle corresponds to a stronger protrusion than the faint one. LDOS at different energies are shown in panels (b), (c), and (d). [Points 1, 2, and 3 in (c) mark the center of defect, side resonance, and background, respectively.] Data were taken using $V_b=+100\mathrm{mV}$ and $I_s=80\mathrm{pA}$. Colored bars’ scale is normalized by the LDOS at zero bias at the location of point 3.

Figure 3

A topograph (a), and selected energy maps emphasizing an extended impurity in Sb-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. LDOS at different energies are shown in panels (b), (c), and (d). (Points 1, 2, and 3 mark the center of the defect, the edge of its extent, and background, respectively.) Data were taken using $V_b=400\mathrm{mV}$ and $I_s=70\mathrm{pA}$. Colored bars’ scale is normalized by the LDOS at zero bias at the location of point 3.

Figure 4

Emergence of a resonance near the Dirac point for two different impurities; (a) triangular defects corresponding to the bright and faint of Fig. 2, with the difference LDOS for both defects shown in (b); (c) extended defect in Sb-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ (Fig. 3), and the difference LDOS shown in (d). Dashed lines mark the location of the Dirac point which is identified as the position of DOS minimum.

Figure 5

Theoretical fits to resonance amplitudes. (a) Raw LDOS difference data for a bright triangle where (1) represents the middle of the triangle and (2) represents the side peaks [see Fig. 2c]. The averaged data are marked with Av; (b) averaged data from (a), fitted to theory (see text) with $V_0=3.17\mathrm{eV}$, $R=15\AA$; (c) fit to extended defect on an Sb-doped sample, at center of defect [point (1) in Fig. 3] with $V_0=0.71\mathrm{eV}$, $R=64\AA$; (d) same parameters as for (c), but away from center of defect [point (2) in Fig. 3] (see text). Dashed lines mark the location of the Dirac point.

Figure 6

LDOS as a function of distance from the center of the impurity. The dashed line is a fit to $1/r$ for the dark points (after $\sim 65\AA$) and the dash-dotted line is a fit to $1/r^2$. The inset shows the contours of decay of the LDOS around the impurity center (●) at 65, 100, and 150 Å.