19 research outputs found
Electronic states of pseudospin-1 fermions in dice lattice ribbons
Boundary conditions for the two-dimensional fermions in ribbons of the
hexagonal lattice are studied in the dice model whose energy spectrum in
infinite system consists of three bands with one completely flat band of zero
energy. Like in graphene the regular lattice terminations are of the armchair
and zigzag types. However, there are four possible zigzag edge terminations in
contrast to graphene where only one type of zigzag termination is possible.
Determining the boundary conditions for these lattice terminations, the energy
spectra of pseudospin-1 fermions in dice model ribbons with zigzag and armchair
boundary conditions are found. It is shown that the energy levels for armchair
ribbons display the same features as in graphene except the zero energy flat
band inherent to the dice model. In addition, unlike graphene, there are no
propagating edge states localized at zigzag boundary and there are specific
zigzag terminations which give rise to bulk modes of a metallic type in dice
model ribbons. We find that the existence of the flat zero-energy band in the
dice model is very robust and is not affected by the zigzag and armchair
boundaries.Comment: 16 pages, 7 figure
Size effects on atomic collapse in the dice lattice
We study the role of size effects on atomic collapse of charged impurity in
the flat band system. The tight-binding simulations are made for the dice
lattice with circular quantum dot shapes. It is shown that the mixing of in-gap
edge states with bound states in impurity potential leads to increasing the
critical charge value. This effect, together with enhancement of gap due to
spatial quantization, makes it more difficult to observe the
dive-into-continuum phenomenon in small quantum dots. At the same time, we show
that if in-gap states are filled, the resonant tunneling to bound state in the
impurity potential might occur at much smaller charge, which demonstrates
non-monotonous dependence with the size of sample lattice. In addition, we
study the possibility of creating supercritical localized potential well on
different sublattices, and show that it is possible only on rim sites, but not
on hub site. The predicted effects are expected to naturally occur in
artificial flat band lattices.Comment: 7 pages, 6 figure
Current distribution and group velocities for electronic states on lattice ribbons in a magnetic field
We study the group velocities of electronic states and distributions of
currents in lattice ribbons under a uniform
perpendicular magnetic field. Using the effective low-energy model we analyze
all possible simple configurations of lattice termination with zigzag and
armchair boundaries. We show that the edge current depends on the type of
zigzag termination, and can be zero or finite near the edge. Also similar
dependence is observed in the case of armchair termination and is related to
the size of the ribbon. The nonzero current flowing along the edge can be used
a signature of formation of propagating edge states. Also we show the
qualitative difference in the distribution of the edge current between the case
of (dice model) and other values of model parameter
for armchair-terminated ribbons.Comment: 11 pages, 6 figure
Shot noise distinguishes Majorana fermions from vortices injected in the edge mode of a chiral p-wave superconductor
The chiral edge modes of a topological superconductor support two types of
excitations: fermionic quasiparticles known as Majorana fermions and
-phase domain walls known as edge vortices. Edge vortices are injected
pairwise into counter-propagating edge modes by a flux bias or voltage bias
applied to a Josephson junction. An unpaired edge mode carries zero electrical
current on average, but there are time-dependent current fluctuations. We
calculate the shot noise power produced by a sequence of edge vortices and find
that it increases logarithmically with their spacing - even if the spacing is
much larger than the core size so the vortices do not overlap. This nonlocality
produces an anomalous V log V increase of the shot noise in a voltage-biased
geometry, which serves as a distinguishing feature in comparison with the
linear-in-V Majorana fermion shot noise.Comment: 15 pages, 4 figure
Optical conductivity of bilayer dice lattices
We calculate optical conductivity for bilayer dice lattices in commensurate
vertically aligned stackings. The interband optical conductivity reveals a rich
activation behavior unique for each of the four stackings. We found that the
intermediate energy band, which corresponds to the flat band of a single-layer
dice lattice, plays a different role for different stackings. The interband
selection rules, which are crucial for the single-layer lattice, may become
lifted in bilayer lattices. The results for effective and tight-binding models
are found to be in qualitative agreement for some of the stackings and the
reasons for the discrepancies for others are identified. Our findings propose
optical conductivity as an effective tool to distinguish between different
stackings in bilayer dice lattices.Comment: 22 pages, 14 multi-panel figure
Stackings and effective models of bilayer dice lattices
We introduce and classify nonequivalent commensurate stackings for bilayer
dice or lattice. For each of the four stackings with vertical
alignment of sites in two layers, a tight-binding model and an effective model
describing the properties in the vicinity of the threefold band-crossing points
are derived. Focusing on these band-crossing points, we found that although the
energy spectrum remains always gapless, depending on the stacking, different
types of quasiparticle spectra arise. They include those with flat, tilted,
anisotropic semi-Dirac, and -corrugated energy bands. We use the derived
tight-binding models to calculate the density of states and the spectral
function. The corresponding results reveal drastic redistribution of the
spectral weight due to the inter-layer coupling that is unique for each of the
stackings.Comment: 15 pages, 9 multi-panel figure