Impurity resonance

Chapter 3: STM/STS studies of Topological Insulators

3.8 Impurity resonance

As we mentioned before, although the majority dI/dV-vs.-V spectra look like either V-shaped gapless spectra or U-shape gapped spectra, there were occasionally reproducible minority spectra that were distinctly different from the characteristics of majority spectra. The impurity resonance spectra is one of them. We can think of impurity resonance as a single discrete state in DOS. Hence, the DOS curve looks like a delta function or a single peak.

3.8.1 the appearance of the magnetic impurity resonance curve

Figure 3.21 STS of impurity resonance. (a) I vs. V (b) dI/dV vs. V

In our STS of binary TI/MTI samples, some sharp double peaks showed up. Their I-vs.-V spectra exhibited hysteresis, which indicated their magnetic origin. Therefore, the spectra

appeared as double peaks in the dI/dV-vs.-V. We note that the I-vs.-V spectrum looks like the 𝑅𝑅_{𝑥𝑥𝑦𝑦} 𝑣𝑣𝑣𝑣.𝐵𝐵 data and the dI/dV-vs.-V spectrum looks like the 𝑅𝑅_{𝑥𝑥𝑥𝑥} 𝑣𝑣𝑣𝑣.𝐵𝐵 data (Chapter 4).

It might also be related to the topological magnetoelectric (TME) effect. On the other hand, non-magnetic impurity is the only single peak with its energy right in the middle of double peak magnetic impurity. Interestingly, we also observed some single peak magnetic impurities with their peak position the same as one of the double peaks.

Another notable thing is that the energy between the double peaks of impurity is almost the same no matter the location or even the temperature. These seemingly puzzling results are investigated further in the following.

3.8.2 Spatial distributions of the magnetic impurity resonance

The location of each impurity resonance can be determined easily through the conductance map at one of its peak energy, as shown in Figure 3.22 (b). The locations of double-peak and single-peak resonances can be recognized easily by comparing the conductance map at both peak energy. Those impurities are extremely localized (within 0.1 ~ 0.2 nm range), as shown in the 3D conductance map in Figure 3.22 (c) and dI/dV along the line cut cross the impurity at Figure 3.22 (d).

This extreme localization of magnetic impurity resonances in binary TI/MTI may be attributed to the topological protection of the surface state. In contrast, no impurity resonances were observed in the ternary TI/MTI samples. As elaborated in Chapter 4, the Fermi level in the ternary TI/MTI samples that we studied always involved bulk carriers so that the surface states were not dominant as in the case of binary TI/MTI systems. We conjecture that the significant contributions of bulk bands at all temperatures in the ternary TI/MTI system weakened the topological protection of the surface state, hence the absence of any localized magnetic resonances in the ternary TI/MTI system.

Figure 3.22 (a) Spatial distributions of impurity resonances on the gap map for the (1+6)-5%

binary TI/MTI sample. The up triangle is for a single peak at higher energy. The down triangle is for a single peak at the lower energy. The diamond shape is for a double peak. (b) Conductance map at one of the impurity peak energy -0.28V (c) 3D conductance map near the impurity resonance. (d) dI/dV along the line cut cross the impurity resonance.

Interestingly, when we overlapped the location of the impurities onto the gap map, we found that the impurity mostly appeared at the boundary of the gapped and gapless domains. This finding is reasonable because isolated spins along the domain boundaries were not tightly aligned to the magnetization of the domain, and so could respond to the TME effect exerted from the STM tip. For isolated spin aligned in the in-plane direction, sweeping the voltage could create an effective magnetic field to move the spin along either +z or –z direction, hence the double-peak feature (Figure 3.21(b) and Figure 3.23(b)). On the other hand, for an isolated spin along either +z or –z direction, the TME effect from the STM tip would simply

determine the sign of effective energy associated with the isolated spin, hence a single peak resonance (Figure 3.23(c)).

Figure 3.23 (a) Explanation of the location of impurity. (b) Double peak resonance might be caused by in-plane spin impurity (c) Single peak might be caused by out of plane spin impurity

3.8.3 The number of impurity resonance vs. temperature

In our investigation of a Se-capped (1+6)-10% binary TI/MTI, we found that the tunneling conductance spectroscopic studies revealed a large gap almost everywhere with spotty gapless regions. In this particular sample, many domain boundaries were present, which were accompanied by the frequent appearance of the impurity resonances.

To verify whether our observed impurity resonances were indeed associated with isolated spins along domain boundaries, we analyzed the number of impurity resonance vs.

temperature, as shown in Figure 3.24. At low temperatures, the number of impurity resonances was low small. As the temperature increased, the number of impurities went up sharply near 250 K, which was approximately the 2D Curie temperature we observed. A sudden drop occurs, and then the impurity gradually went up again.

The temperature dependence of the number of impurity resonances is consistent with the finding of isolated spins along the gapped and gapless boundaries because strong thermal fluctuations could allow more spins along the domain boundaries to freely respond to the TME effect of the STM tip, hence a strong increase in the number of impurity resonances near the 2D Curie temperature.

Figure 3.24 The number of impurity resonance vs. temperature

On the other hand, the specific influence of Se-cap is still unknown. It might introduce more gap regions on the sample. Future investigations of Al-capped binary TI to Se-capped binary TI/MTI samples could shed light on the relevance of the Se-capping.

3.8.4 Summary of impurity resonances

Magnetic impurity resonances due to isolated spins only appeared in binary bilayer TI/MTI samples, which may be attributed to the lack of long-range ferromagnetism and the dominance of the surface state for better topological protection. Impurity resonances only appeared between gapped and gapless domain boundaries and were found to be very localized and robust. Therefore, these interesting features may be considered as “topological bits” for potential applications to quantum memory. We may take advantage of the finite

range of magnetic proximity effect in the binary TI/MTI system to design a device with different thicknesses of the top TI-layer to create a controlled gap and gapless regions, which could confine magnetic impurities to the designed boundaries as shown in Figure 3.25. The interaction among the impurities may be tuned by the Fermi level, which is controlled by the back gate.

Ternary TI, on the other hand, lacks any impurity resonance. The transport measurement also demonstrates that weak anti-localization exists above 13K. Below 13K, weak localization appears under the weak magnetic field (<0.5 T). We might be able to see something interesting below this temperature.

Figure 3.25 Possible device to line up the location of impurity and control it by the back gate.