"More is Different"

-Philip Warren Anderson

One Electron

87 Electrons

By Jan Ainali (Own work) [CC BY 3.0 (http://creativecommons.org/licenses/by/3.0)], via Wikimedia Commons

Published online 03 February 2015

doi:10.1038/nphys3251  (2015) Year published: 99–100 Pages: 11,​ Volume: Nature Physics

Dy2Ti2O7​, Ho2Ti2O7

Real Crystals

 

Crystal Structure

Same as Water Ice!

Excitation = Magnetic Monopole

0=\sum_{i\in\text{tet}} S_i
0=itetSi0=\sum_{i\in\text{tet}} S_i

Ice Rule:

  • Semiconductors
  • Topological Insulators
  • Quantum Hall Effect
  • Majorana Particles
  • Fractional Particles
  • Non-abelian particles

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