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Topological insulators

A romance with many dimensions

Nature Nanotechnology volume 5, pages 477–479 (2010)Cite this article

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Electric charges on the boundaries of certain insulators are programmed by topology to keep moving forward when they encounter an obstacle, rather than scattering backwards and increasing the resistance of the system. This is just one reason why topological insulators are one of the hottest topics in physics right now.

One of the best role models for 'thinking outside the box' has to be A. Square, the hero of Edwin A. Abbott's novella Flatland. Despite being confined to two dimensions, the hapless Square nevertheless imagines and then experiences worlds truly beyond his own, venturing into both lower and higher dimensions. Flatland is a timeless story embedded in the mathematics of geometry and, at the same time, it is a clever, edgy satire on life in the Victorian era. But often forgotten is the fact that Flatland is, at its core, a romance — the book's full title is Flatland: A Romance of Many Dimensions — between a tireless explorer and forbidden knowledge. In recent years physicists and engineers have plunged head over heels into their own interdimensional love affair. The target of their affections is a new class of materials known as topological insulators. To understand this relatively recent rapture, we need to introduce Square to two new concepts that he did not know about at the time — topology and quantum mechanics.

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Figure 1: Different dimensions.
Figure 2: Topological insulators and band structures.
Figure 3: Inside a topological insulator.

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Authors and Affiliations

  1. Hari C. Manoharan is in the Department of Physics, Stanford University, Stanford, California 94305, USA, and at the Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA. manoharan@stanford.edu,

    Hari C. Manoharan

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Manoharan, H. A romance with many dimensions. Nature Nanotech 5, 477–479 (2010). https://doi.org/10.1038/nnano.2010.138

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