Physical Review Letters,
Journal Year:
2019,
Volume and Issue:
123(25)
Published: Dec. 18, 2019
A
second-order
topological
insulator
(SOTI)
in
d
spatial
dimensions
features
topologically
protected
gapless
states
at
its
(d-2)-dimensional
boundary
the
intersection
of
two
crystal
faces,
but
is
gapped
otherwise.
As
a
novel
state,
it
has
been
attracting
great
interest,
remains
challenge
to
identify
realistic
SOTI
material
(2D).
Here,
based
on
combined
first-principles
calculations
and
theoretical
analysis,
we
reveal
already
experimentally
synthesized
2D
graphdiyne
as
first
example
SOTI,
with
0D
corner
states.
The
role
crystalline
symmetry,
robustness
against
symmetry
breaking,
possible
experimental
characterization
are
discussed.
Our
results
uncover
hidden
character
promote
concrete
platform
for
exploring
intriguing
physics
higher-order
phases.
Advances In Physics,
Journal Year:
2020,
Volume and Issue:
69(3), P. 249 - 435
Published: July 2, 2020
A
review
is
given
on
the
foundations
and
applications
of
non-Hermitian
classical
quantum
physics.
First,
key
theorems
central
concepts
in
linear
algebra,
including
Jordan
normal
form,
biorthogonality,
exceptional
points,
pseudo-Hermiticity,
parity-time
symmetry,
are
delineated
a
pedagogical
mathematically
coherent
manner.
Building
these,
we
provide
an
overview
how
diverse
systems,
ranging
from
photonics,
mechanics,
electrical
circuits,
acoustics
to
active
matter,
can
be
used
simulate
wave
In
particular,
discuss
rich
unique
phenomena
found
therein,
such
as
unidirectional
invisibility,
enhanced
sensitivity,
topological
energy
transfer,
perfect
absorption,
single-mode
lasing,
robust
biological
transport.
We
then
explain
detail
operators
emerge
effective
description
open
systems
basis
Feshbach
projection
approach
trajectory
approach.
their
physical
relevant
variety
fields,
atomic,
molecular
optical
physics,
mesoscopic
nuclear
physics
with
emphasis
prominent
subjects
regimes,
resonances,
superradiance,
continuous
Zeno
effect,
critical
phenomena,
Dirac
spectra
chromodynamics,
nonunitary
conformal
field
theories.
Finally,
introduce
notion
band
topology
complex
present
classifications
by
providing
proof,
first
this
complete
manner,
well
number
instructive
examples.
Other
topics
related
nonreciprocal
transport,
speed
limits,
walk,
also
reviewed.
In
the
presence
of
crystalline
symmetries,
certain
topological
insulators
present
a
filling
anomaly:
mismatch
between
number
electrons
in
an
energy
band
and
required
for
charge
neutrality.
this
paper,
we
show
that
anomaly
can
arise
when
corners
are
introduced
$C_n$-symmetric
with
vanishing
polarization,
having
as
consequence
existence
corner-localized
charges
quantized
multiples
$\frac{e}{n}$.
We
characterize
systematically
build
indices
relate
symmetry
representations
occupied
bands
crystal
to
quanta
fractional
robustly
localized
at
its
corners.
When
additional
chiral
is
present,
$\frac{e}{2}$
corner
accompanied
by
zero-energy
states.
application
our
atomic
fragile
discuss
role
bound
disclinations
bulk
probes
these
phases.
Physical Review Letters,
Journal Year:
2019,
Volume and Issue:
122(23)
Published: June 14, 2019
The
studies
of
topological
phases
matter
have
been
developed
from
condensed
physics
to
photonic
systems,
resulting
in
fascinating
designs
robust
devices.
Recently,
higher-order
insulators
investigated
as
a
novel
phase
beyond
the
conventional
bulk-boundary
correspondence.
Previous
mainly
focused
on
multipole
systems
with
negative
coupling
between
lattice
sites.
Here
we
experimentally
demonstrate
that
second-order
insulating
without
can
be
realized
two-dimensional
dielectric
crystals.
We
visualize
both
one-dimensional
edge
states
and
zero-dimensional
corner
by
using
near-field
scanning
technique.
Our
findings
open
new
research
frontiers
for
provide
mechanism
light
manipulating
hierarchical
way.
Physical Review Letters,
Journal Year:
2019,
Volume and Issue:
122(23)
Published: June 14, 2019
Recently,
higher-order
topological
phases
that
do
not
obey
the
usual
bulk-edge
correspondence
principle
have
been
introduced
in
electronic
insulators
and
brought
into
classical
systems,
featuring
in-gap
corner
or
hinge
states.
In
this
Letter,
using
near-field
scanning
measurements,
we
show
direct
observation
of
states
second-order
photonic
crystal
slabs
consisting
periodic
dielectric
rods
on
a
perfect
electric
conductor.
Based
generalized
two-dimensional
Su-Schrieffer-Heeger
model,
emergence
roots
nonzero
edge
dipolar
polarization
instead
bulk
quadrupole
polarization.
We
demonstrate
transition
Zak
by
tuning
intracell
distances
between
two
neighboring
rods.
also
directly
observe
one-dimensional
zero-dimensional
microwave
regime.
Our
work
presents
slab
is
powerful
platform
to
paves
way
study
insulators.
Here,
higher-order
topological
insulators
and
superconductors
protected
by
inversion
symmetry
are
investigated.
These
phases
characterized
gapped
bulk
surface
with
gapless
modes
confined
to
hinges
or
corners
of
the
sample.
Such
states
can
be
understood
as
defects
that
globally
stabilized
inversion.
They
built
using
a
layer
construction
embeds
standard
insulator/superconductor
into
higher
dimension
symmetrically
adding
it
copies
itself.
Using
this
procedure,
complete
classification
such
in
any
is
obtained
several
examples
for
possible
physical
realizations
provided.
Reviews of Modern Physics,
Journal Year:
2021,
Volume and Issue:
93(2)
Published: April 26, 2021
A
confluence
of
precise
theoretical
predictions
shows
that
carefully
fabricated
three-dimensional
(3D)
semimetals
can
host
a
variety
exotic
phases
dominated
by
topological
constraints.
This
experimental
review
3D
addresses
the
role
electronic
structure
and
associated
band
crossings
play
in
validating
Dirac
Weyl
fermion
descriptions
have
analogies
with
elementary
particles
quantum
field
theory.
The
importance
Fermi
arcs,
nodal
geometries,
symmetry,
spin-orbit
coupling,
dimensionality
is
highlighted.
list
confirmed
presented
suggestions
for
future
research
applications.
