How stable are topological properties in bismuth?

By Tom Sharp on April 12, 2017

In a recent Journal of Physics: Condensed Matter paper, Maciej Bieniek, Tomasz Woźniak and Paweł Potasz investigate atomically thin bismuth nanostructures in the context of stability of their topological properties. Read on to find out more in the authors’ own words.

Nowadays, topological effects in condensed matter physics are a topic of interest for many researchers due to their promising applications in spintronics, quantum information processing, and related fields. Two-dimensional crystals are another emerging field, which allow for novel explorations in optics and electronics. One of the materials connecting these two fields is bismuth, a material known for many years, which was recently successfully experimentally confirmed to support a topological insulator state when in layers a single atom thick. We find that, despite many studies, some aspects of topological protection in this material were still unclear.

(a) The side and top view of the bismuth (1 1 1) structure with parameters obtained from the DFT calculations. (b) The energy band structure of the Bi (1 1 1) bilayer along the M- Γ-K direction obtained within the DFT (red lines) and TB methods (black circles) with the SOC λ =1.8 eV. (c) The evolution of energies at the Γ point as a function of the SOC parameter λ using the TB method. A topological phase transition is observed for λ₁ =0.982 eV. The second band crossing between the valence bands is seen for λ₂ =1.471 eV. (d) The TB orbital composition for three different values of SOC parameter (λ =0.8,1.3,1.8 eV); the radius of red (blue) dots represents the p_x+p_y (p_z) orbital contribution to the bands. Taken from J. Phys. Cond. Mat 155501 © IOP Publishing 2017.

In our recent work, we evaluate the applicability of the previously known tight-binding (TB) model to bismuth by comparing it with ab-initio studies. We find, by varying the value of spin-orbit coupling (SOC) parameter, that for a critical value of SOC the system becomes topologically trivial. Combining TB with DFT we show that the topological edge states are weakly affected by the effect of ribbon geometry relaxation. An interaction with a substrate is also considered for narrow ribbons on top of bulk bismuth. Robustness of quantized conductance is also studied in detail for various nanostructure sizes and parameters. We believe that these results may be interesting for both theoretical and experimental communities, especially in clarifying transport physics in this important material.

About the Authors

Maciej Bieniek currently works at Wrocław University of Science and Technology, Poland and University of Ottawa, Canada on his PhD. His main research interests are electronic, optical and transport properties of various novel topological materials, including both strictly 2-dimensional systems like bismuth and MoS₂and effectively 2D electron gases like in HgCdTe heterostructures or on the surfaces of 3D topological crystalline insulators (SnTe).

Tomasz Woźniak obtained his MSc in Technical Physic at Wrocław University of Science and Technology, Poland. Currently within the “Diamond Grant” program supported by the Polish Ministry of Science and Higher Education he is conducting numerical research in the field of layered crystals, which is the topic of his PhD thesis.

Paweł Potasz received his PhD from the Institute of Physics, Wroclaw University of Science and Technology in 2012 for his work on the electronic and optical properties of graphene nanostructures. His research interests are concentrated around electronic properties of low-dimensional systems, correlated phases and topological effects. Currently, he is an adjunct at the Department of Theoretical Physics, Faculty of Fundamental Problems of Technology at Wroclaw University of Science and Technology.

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