56 research outputs found
Classification of flat bands according to the band-crossing singularity of Bloch wave functions
We show that flat bands can be categorized into two distinct classes, that
is, singular and nonsingular flat bands, by exploiting the singular behavior of
their Bloch wave functions in momentum space. In the case of a singular flat
band, its Bloch wave function possesses immovable discontinuities generated by
the band-crossing with other bands, and thus the vector bundle associated with
the flat band cannot be defined. This singularity precludes the compact
localized states from forming a complete set spanning the flat band. Once the
degeneracy at the band crossing point is lifted, the singular flat band becomes
dispersive and can acquire a finite Chern number in general, suggesting a new
route for obtaining a nearly flat Chern band. On the other hand, the Bloch wave
function of a nonsingular flat band has no singularity, and thus forms a vector
bundle. A nonsingular flat band can be completely isolated from other bands
while preserving the perfect flatness. All one-dimensional flat bands belong to
the nonsingular class. We show that a singular flat band displays a novel
bulk-boundary correspondence such that the presence of the robust boundary mode
is guaranteed by the singularity of the Bloch wave function. Moreover, we
develop a general scheme to construct a flat band model Hamiltonian in which
one can freely design its singular or nonsingular nature. Finally, we propose a
general formula for the compact localized state spanning the flat band, which
can be easily implemented in numerics and offer a basis set useful in analyzing
correlation effects in flat bands.Comment: 23 pages, 13 figure
Perfect transmission and Aharanov-Bohm oscillations in topological insulator nanowires with nonuniform cross section
Topological insulator nanowires with uniform cross section, combined with a
magnetic flux, can host both a perfectly transmitted mode and Majorana zero
modes. Here we consider nanowires with rippled surfaces---specifically, wires
with a circular cross section with a radius varying along its axis---and
calculate their transport properties. At zero doping, chiral symmetry places
the clean wires (no impurities) in the AIII symmetry class, which results in a
topological classification. A magnetic flux threading the wire
tunes between the topologically distinct insulating phases, with perfect
transmission obtained at the phase transition. We derive an analytical
expression for the exact flux value at the transition. Both doping and disorder
breaks the chiral symmetry and the perfect transmission. At finite doping, the
interplay of surface ripples and disorder with the magnetic flux modifies
quantum interference such that the amplitude of Aharonov-Bohm oscillations
reduces with increasing flux, in contrast to wires with uniform surfaces where
it is flux-independent.Comment: 12 pages, 6 figures. v2. 2 new figures and a new appendi
Flat bands in Network Superstructures of Atomic Chains
We investigate the origin of the ubiquitous existence of flat bands in the
network superstructures of atomic chains, where one-dimensional(1D) atomic
chains array periodically. While there can be many ways to connect those
chains, we consider two representative ways of linking them, the dot-type and
triangle-type links. Then, we construct a variety of superstructures, such as
the square, rectangular, and honeycomb network superstructures with dot-type
links and the honeycomb superstructure with triangle-type links. These links
provide the wavefunctions with an opportunity to have destructive interference,
which stabilizes the compact localized state(CLS). The CLS is a localized
eigenstate whose amplitudes are finite only inside a finite region and
guarantees the existence of a flat band. In the network superstructures, there
exist multiple flat bands proportional to the number of atoms of each chain,
and the corresponding eigenenergies can be found from the stability condition
of the compact localized state. Finally, we demonstrate that the finite
bandwidth of the nearly flat bands of the network superstructures arising from
the next-nearest-neighbor hopping processes can be suppressed by increasing the
length of the chains consisting of the superstructures.Comment: 8pages, 4figure
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