Geometric phase (or Pancharatnam-Berry phase) has many surprising effects. What is this variously named “phase”? To quote Wikipedia, “The Berry phase occurs when [two] parameters are changed simultaneously but very slowly (adiabatically), and eventually brought back to the initial configuration.”  A light-hearted and easily understood introduction can be found in section 1 of ref. . In what follows, I give a few examples of geometric phase effects that are relevant to nano-technology. (A lengthy review of the Berry phase in electronics can be found in .)
- A group at TU Denmark have shown in  that the Berry phase effects associated with electrical current flowing through a conductive molecular bridge may induce mechanical vibration sufficiently strong to rupture the bridge. This phenomenon is unrelated to electromigration, Joule heating, or other well-known effects. It is purely a result of the quantum mechanical phase of the electric waves.
- In an interesting experiment , Kohmura-san and colleagues at RIKEN demonstrate millimeter distance translation of X-rays by bent silicon crystals. The crystal was bent only 80 nm or so to achieve a beam displacement of 1.5 mm. See  for a brief summary.
- The Hasman group at the Technion have constructed optical structures showing technologically applicable geometric phase behavior. In  and  they display nano-lithographically defined gratings and apertures which can act as optical switches, among other things.
Try the little demonstration in . It will serve as a reminder to keep your eyes open to the geometric phase.
 Wikipedia article, http://en.wikipedia.org/wiki/Berry’s_phase
 Robert W. Batterman, “Falling Cats, Parallel Parking, and Polarized Light”, http://philsci-archive.pitt.edu/archive/00000794/00/falling-cats.pdf
 Di Xiao, et al., “Berry Phase Effects on Electronic Properties”, Rev. Mod. Phys. 82 (2010) 1959-2007, http://rmp.aps.org/abstract/RMP/v82/i3/p1959_1
 Jing-Tao Lu, et al., “Blowing the Fuse: Berry’s Phase and Runaway Vibrations in Molecular Conductors”, Nano Letters 10 (2010) 1657-63, http://pubs.acs.org/doi/abs/10.1021/nl904233u
 Yoshiki Kohmura, et al., “Berry-Phase Translation of X Rays by a Deformed Crystal”, Phys. Rev. Lett. 104 (2010) 244801, http://prl.aps.org/abstract/PRL/v104/i24/e244801
 Adams, “Geometric phase kicks x rays down a new path”, http://physics.aps.org/articles/v3/50
 Erez Hasman, et al., “Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures”, Optics Communications 209 (2002) 45-54, DOI: 10.1016/S0030-4018(02)01598-5, http://www.sciencedirect.com/science/article/B6TVF-4645DRF-1/2/6f0b7ca5cf17b751e48bbf1cf1e77d03
 Yuri Gorodetski, “Observation of Optical Spin Symmetry Breaking in Nanoapertures”, Nano Lett., Vol. 9, No. 8, 2009, http://pubs.acs.org/doi/abs/10.1021/nl901437d