The
non-Hermitian
skin
effect
is
a
unique
feature
of
systems,
in
which
an
extensive
number
boundary
modes
appear
under
the
open
conditions.
Here,
we
discover
higher-order
counterparts
that
exhibit
new
physics.
In
two-dimensional
systems
with
system
size
$L
\times
L$,
while
conventional
(first-order)
accompanies
$O\,(
L^{2}
)$
modes,
second-order
L
corner
modes.
This
also
contrasts
Hermitian
topological
insulators,
only
1
zero
appear.
Moreover,
for
third-order
three
dimensions,
from
all
L^{3}
We
demonstrate
originates
intrinsic
topology
protected
by
spatial
symmetry.
show
it
modification
non-Bloch
band
theory
higher
dimensions.
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.
Science Advances,
Journal Year:
2018,
Volume and Issue:
4(6)
Published: June 1, 2018
Three-dimensional
topological
(crystalline)
insulators
are
materials
with
an
insulating
bulk,
but
conducting
surface
states
which
topologically
protected
by
time-reversal
(or
spatial)
symmetries.
Here,
we
extend
the
notion
of
three-dimensional
to
systems
that
host
no
gapless
states,
exhibit
hinge
states.
Their
character
is
spatio-temporal
symmetries,
present
two
cases:
(1)
Chiral
higher-order
combination
and
a
four-fold
rotation
symmetry.
chiral
modes
bulk
topology
$\mathbb{Z}_2$-classified.
(2)
Helical
mirror
come
in
Kramers
pairs
$\mathbb{Z}$-classified.
We
provide
invariants
for
both
cases.
Furthermore
show
SnTe
as
well
surface-modified
Bi$_2$TeI,
BiSe,
BiTe
helical
propose
realistic
experimental
setup
detect
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.
