Condensed Matter

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 [1] 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 [2]. 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).

[1] F. Flicker and Jasper van Wezel, Physical Review Letters 115, 236401

(2015), Natural 1D Quasicrystals from Incommensurate Charge Order

[2] S. Barja et al., Nature Physics 12, 751-757 (2016), Charge density

wave order in 1D mirror twin boundaries of single-layer MoSe2

Dimer models have long been a fruitful playground for understanding topological physics. We introduce a new class -- termed Majorana-dimer models -- where the dimers represent pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian Ising quasiparticles, and a topological (p − ip) superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We present parent Hamiltonians for this phase and unambiguously identify the topological order from entanglement measurement of the ground-state manifold on torus.