383 research outputs found
Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
Recent developments in the relationship between bulk topology and surface
crystal symmetry have led to the discovery of materials whose gapless surface
states are protected by crystal symmetries. In fact, there exists only a very
limited set of possible surface crystal symmetries, captured by the 17
"wallpaper groups." We show that a consideration of symmetry-allowed band
degeneracies in the wallpaper groups can be used to understand previous
topological crystalline insulators, as well as to predict new examples. In
particular, the two wallpaper groups with multiple glide lines, and
, allow for a new topological insulating phase, whose surface spectrum
consists of only a single, fourfold-degenerate, true Dirac fermion. Like the
surface state of a conventional topological insulator, the surface Dirac
fermion in this "nonsymmorphic Dirac insulator" provides a theoretical
exception to a fermion doubling theorem. Unlike the surface state of a
conventional topological insulator, it can be gapped into topologically
distinct surface regions while keeping time-reversal symmetry, allowing for
networks of topological surface quantum spin Hall domain walls. We report the
theoretical discovery of new topological crystalline phases in the AB
family of materials in SG 127, finding that SrPb hosts this new
topological surface Dirac fermion. Furthermore, (100)-strained AuY and
HgSr host related topological surface hourglass fermions. We also
report the presence of this new topological hourglass phase in
BaInSb in SG 55. For orthorhombic space groups with two glides, we
catalog all possible bulk topological phases by a consideration of the allowed
non-abelian Wilson loop connectivities, and we develop topological invariants
for these systems. Finally, we show how in a particular limit, these
crystalline phases reduce to copies of the SSH model.Comment: Final version, 6 pg main text + 29 pg supplement, 6 + 13 figure
Designing colloidal ground state patterns using short-range isotropic interactions
DNA-coated colloids are a popular model system for self-assembly through
tunable interactions. The DNA-encoded linkages between particles theoretically
allow for very high specificity, but generally no directionality or long-range
interactions. We introduce a two-dimensional lattice model for particles of
many different types with short-range isotropic interactions that are pairwise
specific. For this class of models, we address the fundamental question whether
it is possible to reliably design the interactions so that the ground state is
unique and corresponds to a given crystal structure. First, we determine lower
limits for the interaction range between particles, depending on the complexity
of the desired pattern and the underlying lattice. Then, we introduce a
`recipe' for determining the pairwise interactions that exactly satisfies this
minimum criterion, and we show that it is sufficient to uniquely determine the
ground state for a large class of crystal structures. Finally, we verify these
results using Monte Carlo simulations.Comment: 19 pages, 7 figure
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