Sunday 17 November 2013

Determining the quantum geometry of a crystal

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Geometrical phases occur in many places in nature. One of the simplest examples is the Foucault pendulum: a tall pendulum free to swing in any vertical plane. Due to the earth rotation, the actual plane of swing rotates relative to the earth. One observes that every day the plane of rotation changes by a small "geometric" angle, associated to the spherical shape of the earth. In quantum mechanics a similar effect was discovered in 1984 by the British physicist Sir Michael Berry, who identified a geometrical phase in quantum-mechanical problems that is today known as the "Berry's phase". Such quantum-mechanical phases can have a profound effect on material properties and are responsible for a variety of phenomena. Some examples are the dielectric polarization or the quantum Hall effect, with the latter one being used nowadays to define the standard of resistance.



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