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Phononic crystals

Entering an acoustic phase

Nature Physics volume 11, pages 215–216 (2015)Cite this article

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Electrons moving in a one-dimensional crystal can acquire a geometrical phase. Sound waves in phononic crystals are now shown to display the same effect — underlining the similarity between conventional solids and acoustic metamaterials.

Imagine yourself one day looking at a Foucault pendulum. Due to the Earth's rotation, 24 hours later the pendulum's plane of oscillation will have rotated by an angle of exactly 360° times the sine of the geographical latitude — an angle known as the geometric phase. So, if you are in Cairo, or any other place at 30° latitude, the oscillation plane would be the same the next day at the same time. Similarly, polarized light evolving over an analogous closed cycle in a Poincaré sphere, where polarization states reside, does not return to its initial state but differs by a geometric phase. Less widely known, though, is that electrons in solids, riding their energy bands along a cyclic path in quasi-momentum space, can also exhibit a geometric phase. For one-dimensional solids, this is known as the Zak phase1. Understanding such phases and related topological properties of Bloch bands has led to a modern, revised (topological) classification of condensed matter.

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Figure 1: One-dimensional systems and the Zak phase.

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  1. Julio T. Barreiro is in the Department of Physics, University of California San Diego at La Jolla, California 92093, USA,

    Julio T. Barreiro

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  1. Julio T. Barreiro
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Correspondence to Julio T. Barreiro.

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Barreiro, J. Entering an acoustic phase. Nature Phys 11, 215–216 (2015). https://doi.org/10.1038/nphys3273

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