Symmetry, magnetism and superconductivity in new materials

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This proposal concerns magnetic and superconducting crystals with exotic, symmetry-derived properties. At high temperatures, an ordered, non-magnetic crystal possesses the following symmetries: time reversal (i.e. the crystal appears the same whether time runs forward or backwards); various discrete rotations (for example, a cubic crystal looks the same if turned by 90 degrees); and discrete translations (when viewed on an atomic scale, the crystal can be moved a tiny distance corresponding to the size of the crystal unit cell). Time reversal symmetry is broken in magnetic crystals, which means that the direction of the magnetisation depends on the direction of time. In addition to time reversal symmetry breaking, other symmetries may be broken as well. In superconductors, a more complicated kind of symmetry, called gauge symmetry, is broken. This may also be accompanied by other kinds of symmetry-breaking, including broken time reversal symmetry.