Introduction

Topological insulators (TIs) are a new class of materials that are unique in their ability to conduct electricity along their surfaces while remaining insulative in their bulk, or interior. As a result of this property, TIs can conduct electricity on their surface without experiencing any energy loss due to resistance. This quirk makes TIs incredibly valuable in the field of electronics development, where minimizing energy loss is crucial. As the demand for highly efficient technologies grows, understanding TIs’ conductive and quantum properties has become increasingly important.

First, this review examines studies on TI conductivity, highlighting ways in which both internal and external factors influence conductivity. Next, the review focuses on evidence of TIs exhibiting the quantum Hall effect, which is a phenomenon that is crucial to quantum device development. Lastly, it discusses recent advancements toward practical applications of modified TIs, describing how they are paving the way for innovations in electronics. Together, these studies provide a foundation for understanding the properties of TIs as well as how they can transform future technology.

Factors Influencing Conductivity

The conductive properties of TIs are a major area of study, as these play arguably the most important role in their electronic applications. While it is already established that TIs are conductors only on their surface, the efficiency of this surface conduction under real-world influences is still being researched. For instance, Huang, et al. (2022) explored how Coulomb impurities, which are naturally occurring areas of charged defects within a material, affect the conductivity of two-dimensional TIs. Through the use of theoretical models, it was discovered that electron puddles created by Coulomb impurities allowed electrons to move more freely throughout the material, resulting in metallic-like behavior (Huang, et al. 2022). These findings show that these impurities affect electron flow and enhance conductivity in TIs. The authors state that their theory has real world implications, such as controlling TI conductivity for more efficient electronics (Huang, et al. 2022).

                  Similarly, in a study done by Nguyen, et al. (2020), the electrical conductivity of TIs was measured with the goal of understanding how external factors influence TIs’ conducting ability. To do this, the researchers applied the Kubo-Greenwood formalism, a mathematical model used to calculate conductivity, on a material called SnTe (001), and observed any conductivity changes in response to electric fields, on-site energy differences, and exchange fields. They concluded that applying electric fields or on-site energy differences increase conductivity, while applying an exchange field decreases conductivity (Nguyen, et al., 2020). A crucial finding that makes this study so important is the discovery that, by manipulating external factors, conductivity is possible even at zero temperature (Nguyen, et al., 2020). This opens doors to the possibility that scientists can eventually completely control how TIs perform under any circumstance, a theory that should be explored further.

Comparing the two studies, they are similar in the sense that they both highlight ways in which factors can be controlled to optimize TI performance. However, before their findings can be applied to the real world, more research needs to be conducted on a wider range of TIs. Because the outcomes of both experiments were highly dependent on the structure of the specific materials being examined (2D and crystalline TIs), they cannot be generalized, which calls for further experimentation. Despite this, it is evident from these studies that the conductive properties of TIs can be manipulated for specific electronic purposes.

Quantum Hall Effect

Another aspect of TIs that has implications for transforming future technologies is its quantum nature. The quantum Hall effect (QHE) is a phenomenon where conductivity in an applied magnetic field has “quantized”, or fixed, values instead of a range of many values. Thus, QHE being observed in a material indicates that the conductivity of that material is stable and that electrons are “locked” into specific pathways. This occurs when electrons move along the edges of the material in paths that resist scattering, minimizing resistance and energy loss. In a study done by Xu, et al. (2014), the presence of QHE was observed in BiSbTeSe₂, a 3D TI, after placing BiSbTeSe₂ under a strong magnetic field and measuring conductivity. Through this experiment, they noted that BiSbTeSe₂ strongly demonstrates the QHE, which indicates that it has the ability maintain quantum states at the surface while insulating their bulk (Xu, et al. 2014). This quality of TIs could help stabilize quantum information, making TIs a strong candidate for quantum computing development.

 Thinking back to the earlier studies focused on electrical conductivity, Xu, et al. (2014) effectively explains the strong link between the concepts of TI conductivity and quantum physics, as it delves into the ins and outs of QHE and surface conduction. QHE being observed in BiSbTeSe₂ is a sign that electrons on the surface of the material can move without losing energy, further confirming the efficiency of TIs. Thus, Xu, et al. (2014) not only showcases the relevance of TIs in discussions around quantum computing devices, but it also strengthens the idea that TIs can be used to create dissipationless electronics (Xu, et al. 2014).

Potential for Future Innovations

While all the previous studies have been focused on understanding the capabilities of TIs, Zhao, et al. (2024) goes one step beyond this and examines the potential of modified TIs. The focus of the study was a TI called Sn-doped Bi1.1Sb0.9STe2, or BSST, and the goal was to observe the conduction performance of BSST under room temperature (Zhao, et al., 2024). The experimental setup was similar to that of Xu, et al.’s (2014) study, as quantum properties were one of the variables being measured. The study found that BSST maintained its surface-conducting properties even in high-temperature conditions, which shows promise for real-world applications without the extreme cooling that TIs traditionally require (Zhao, et al., 2024).

This study’s strength is in demonstrating how modified TIs can demonstrate resilience to environmental factors, particularly temperature. Of course, more research would need to be done on BSST to fully determine its usefulness as a TI, such as ones that examine its performance under high pressure or impurities. However, the results of this paper alone are promising and show that we are taking crucial steps towards being able to manipulate and even create TIs for optimal performance in future technologies. Zhao, et al.’s study offers a glimpse into ways we can unlock TI potential for practical applications.

Conclusion

This review explored the unique properties and uses for TIs by examining their conductive and quantum behaviors, as well as recent strides made to create TIs that can be used in the real world. Collectively, the studies discussed highlight the promise of TIs as versatile materials that can change future technologies for the better by maximizing efficiency while remaining sustainable. Future research on TIs should focus on more experiments to confirm theories, as well as examine different types of TIs (including modified ones) to fully understand their different behaviors. Addressing these gaps will help move TIs toward practical applications that need both quantum stability and energy efficiency, setting the stage for next-generation materials.

References

Huang, Y., Skinner, B., & Shklovskii, B. I. (2022). Conductivity of Two-Dimensional Small Gap Semiconductors and Topological Insulators in Strong Coulomb Disorder. Journal of Experimental and Theoretical Physics, 135(4), 409–425. https://doi.org/10.1134/s1063776122100065

Nguyen, V. C., Hoi, B. D., & Yarmohammadi, M. (2020). Electrical conductivity of statically perturbed topological crystalline insulators. Journal of Physics D: Applied Physics, 53(42), 425301. https://doi.org/10.1088/1361-6463/ab9d9c

‌ Xu, Y., Miotkowski, I., Liu, C., Tian, J., Nam, H., Alidoust, N., Hu, J., Shih, C.-K., Hasan, M. Z., & Chen, Y. P. (2014). Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator. Nature Physics, 10(12), 956–963. https://doi.org/10.1038/nphys3140 Zhao, W., Xing, K., Chen, L., Vu, T., Akhgar, G., He, Y., Bake, A., Wang, X., & Karel, J. (2024). Quantum interference effects in a 3D topological insulator with high-temperature bulk-insulating behavior. Applied Physics Review, 11(1), 011419. https://doi-org.ccny-proxy1.libr.ccny.cuny.edu/10.1063/5.0168129