2,680 research outputs found
Fractional Chern insulator edges and layer-resolved lattice contacts
Fractional Chern insulators (FCIs) realized in fractional quantum Hall
systems subject to a periodic potential are topological phases of matter for
which space group symmetries play an important role. In particular, lattice
dislocations in an FCI can host topology-altering non-Abelian topological
defects, known as genons. Genons are of particular interest for their potential
application to topological quantum computing. In this work, we study FCI edges
and how they can be used to detect genons. We find that translation symmetry
can impose a quantized momentum difference between the edge electrons of a
partially-filled Chern band. We propose {\it layer-resolved lattice contacts},
which utilize this momentum difference to selectively contact a particular FCI
edge electron. The relative current between FCI edge electrons can then be used
to detect the presence of genons in the bulk FCI. Recent experiments have
demonstrated graphene is a viable platform to study FCI physics. We describe
how the lattice contacts proposed here could be implemented in graphene subject
to an artificial lattice, thereby outlining a path forward for experimental
dectection of non-Abelian topological defects.Comment: 5+7 pages, 10 figures, v2: modified figure
Hofstadter subband ferromagnetism and symmetry broken Chern insulators in twisted bilayer graphene
In bilayer graphene rotationally faulted to theta=1.1 degrees, interlayer
tunneling and rotational misalignment conspire to create a pair of low energy
flat band that have been found to host various correlated phenomena at partial
filling. Most work to date has focused on the zero magnetic field phase
diagram, with magnetic field (B) used as a probe of the B=0 band structure.
Here, we show that twisted bilayer graphene (tBLG) in a B as low as 2T hosts a
cascade of ferromagnetic Chern insulators with Chern number |C|=1,2 and 3. We
argue that the emergence of the Chern insulators is driven by the interplay of
the moire superlattice with the B, which endow the flat bands with a
substructure of topologically nontrivial subbands characteristic of the
Hofstadter butterfly. The new phases can be accounted for in a Stoner picture
in which exchange interactions favor polarization into one or more spin- and
valley-isospin flavors; in contrast to conventional quantum Hall ferromagnets,
however, electrons polarize into between one and four copies of a single
Hofstadter subband with Chern number C=-1. In the case of the C=\pm3 insulators
in particular, B catalyzes a first order phase transition from the spin- and
valley-unpolarized B=0 state into the ferromagnetic state. Distinct from other
moire heterostructures, tBLG realizes the strong-lattice limit of the
Hofstadter problem and hosts Coulomb interactions that are comparable to the
full bandwidth W and are consequently much stronger than the width of the
individual Hofstadter subbands. In our experimental data, the dominance of
Coulomb interactions manifests through the appearance of Chern insulating
states with spontaneously broken superlattice symmetry at half filling of a
C=-2 subband. Our experiments show that that tBLG may be an ideal venue to
explore the strong interaction limit within partially filled Hofstadter bands.Comment: 17 pages, 15 figure
Nanofilters for Optical Nanocircuits
We theoretically and numerically study the design of optical 'lumped'
nanofiltering devices in the framework of our recently proposed paradigm for
optical nanocircuits. In particular, we present the design of basic filtering
elements, such as low-pass, band-pass, stop-band and high-pass 'lumped'
nanofilters, for use in optical nanocircuits together with more complex
designs, such as multi-zero or multi-pole nanofilters, to work at THz, infrared
and optical frequencies. Following the nanocircuit theory, we show how it is
possible to design such complex frequency responses by simple rules, similar to
RF circuit design, and we compare the frequency response of these optical
nanofilters with classic filters in RF circuits. These results may provide a
theoretical foundation for fabricating nanofilters in optical lumped
nanocircuit devices.Comment: 34 pages, 14 figure
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