Special CM Seminar, Felix Flicker, UC Berkeley, "Charge Order, Quasicrystals, and the Quantum Hall Effect"

Thu, Jan 7, 2016, 1:30 pm to 3:00 pm
PCTS Seminar Room
Recent experimental observations have been argued to demonstrate that one-dimensional quasicrystals - quasiperiodic slices through two-dimensional crystals - adopt the topological quantum numbers of their higher-dimensional parent lattice, exhibiting an equivalent to the quantum Hall effect. I demonstrate that the mathematics of both quasicrystals and the quantum Hall effect can be considered as different limits of a third problem: incommensurate charge order. The analysis suggests only 2D families of quasicrystals are able to demonstrate 2D quantum numbers, in agreement with the usual topological classification of free fermion systems. Transcending the mathematical equivalence, I provide a free energy analysis showing that charge order in real materials can lead to a true quasicrystalline ground state. This greatly extends the number of natural quasicrystals beyond the two known cases, both discovered in the same Siberian meteorite by Princeton-led teams.