Incommensurate charge order is a phenomenon in which the electrons in a crystal attempt to order with a period irrationally-related to that of
the lattice spacing. In the first half of this talk I will present recent work  in which we demonstrate that incommensurately charge-ordered systems can lower their free energy by forming quasicrystals: slices through higher-dimensional crystals with properties lying between periodicity and disorder. The result potentially greatly increases the number of known, naturally-occuring quasicrystals from the two present examples, both of which were found in the same Siberian meteorite. In the second half I will present work from an ongoing experimental collaboration in which atomically-resolved scanning tunneling microscopy and atomic force microscopy on semiconducting monolayers of molybdenum diselenide (MoSe2) see conducting edge states along one-dimensional mirror twin boundaries. Remarkably, these edge states then develop their own energy gap via charge ordering . We see a number of features suggestive of incommensurate order. By employing a simple analytical model we demonstrate that the effect is in fact a result of fine-tuning between charge ordering and quantum well physics coming from the small system size (on the order of thirty atoms).
 F. Flicker and Jasper van Wezel, Physical Review Letters 115, 236401
(2015), Natural 1D Quasicrystals from Incommensurate Charge Order
 S. Barja et al., Nature Physics 12, 751-757 (2016), Charge density
wave order in 1D mirror twin boundaries of single-layer MoSe2
- Condensed Matter
- Scientific Series