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.
Physical Review Letters,
Journal Year:
2019,
Volume and Issue:
122(7)
Published: Feb. 20, 2019
A
d-dimensional
second-order
topological
insulator
(SOTI)
can
host
topologically
protected
(d-2)-dimensional
gapless
boundary
modes.
Here,
we
show
that
a
2D
non-Hermitian
SOTI
zero-energy
modes
at
its
corners.
In
contrast
to
the
Hermitian
case,
these
be
localized
only
one
corner.
3D
is
shown
support
modes,
which
are
not
along
hinges
but
anomalously
The
usual
bulk-corner
(hinge)
correspondence
in
(3D)
system
breaks
down.
winding
number
(Chern
number)
based
on
complex
wave
vectors
used
characterize
phases
(3D).
possible
experimental
situation
with
ultracold
atoms
also
discussed.
Our
work
lays
cornerstone
for
exploring
higher-order
phenomena
systems.
Higher-order
topological
insulators
(HOTIs)
which
go
beyond
the
description
of
conventional
bulk-boundary
correspondence,
broaden
understanding
insulating
phases.
Being
mainly
focused
on
electronic
materials,
HOTIs
have
not
yet
been
found
in
photonic
crystals.
Here,
we
propose
a
type
two-dimensional
second-order
crystals
with
zero-dimensional
corner
states
and
one-dimensional
boundary
for
optical
frequencies.
All
these
are
topologically
nontrivial
can
be
understood
based
theory
polarization.
Moreover,
by
tuning
easily
fabricated
structure
crystals,
different
phases
realized
straightforwardly.
Our
study
generalized
to
higher
dimensions
provides
platform
higher-order
semimetals.
Physical Review Letters,
Journal Year:
2019,
Volume and Issue:
123(1)
Published: July 2, 2019
Higher-order
phases
are
characterized
by
corner
or
hinge
modes
that
arise
due
to
the
interesting
interplay
of
localization
mechanisms
along
two
more
dimensions.
In
this
work,
we
introduce
and
construct
a
novel
class
``hybrid''
higher-order
skin-topological
boundary
in
nonreciprocal
systems
with
open
boundaries.
Their
existence
crucially
relies
on
pumping
addition
topological
localization.
Unlike
usual
non-Hermitian
``skin''
modes,
they
can
exist
lattices
vanishing
net
reciprocity
selective
nature
pumping:
While
bulk
remain
extended
cancellation
nonreciprocity
within
each
unit
cell,
experience
curious
spontaneous
breaking
presence
localization,
thereby
experiencing
skin
effect.
The
number
possible
hybridization
channels
increases
rapidly
dimensionality,
leading
proliferation
distinct
phases.
addition,
hybrid
restore
unitarity
hence
stable,
allowing
for
experimental
observations
manipulations
photonic
electrical
metamaterials.
Abstract
Over
the
past
decade,
topology
has
emerged
as
a
major
branch
in
broad
areas
of
physics,
from
atomic
lattices
to
condensed
matter.
In
particular,
received
significant
attention
photonics
because
light
waves
can
serve
platform
investigate
nontrivial
bulk
and
edge
physics
with
aid
carefully
engineered
photonic
crystals
metamaterials.
Simultaneously,
provides
enriched
that
arises
spin-1
vectorial
electromagnetic
fields.
Here,
we
review
recent
progress
growing
field
topological
three
parts.
The
first
part
is
dedicated
basics
band
theory
introduces
various
two-dimensional
phases.
second
reviews
three-dimensional
phases
numerous
approaches
achieve
them
photonics.
Last,
present
recently
emerging
fields
have
not
yet
been
reviewed.
This
includes
degeneracies
nonzero
dimensions,
unidirectional
Maxwellian
spin
waves,
higher-order
phases,
stacking
attain
layer
pseudospin.
addition
for
realizing
also
discuss
interaction
between
matter
efforts
towards
practical
applications
Classifications
of
symmetry-protected
topological
phases
provide
a
framework
to
understand
systematically
the
physical
properties
and
potential
applications
systems.
Here,
authors
derive
comprehensive
38-fold
classification
non-Hermitian
systems
with
generic
symmetry
classes.
Two
independent
generalizations
Kramers'
degeneracy
setting
are
presented.
The
nature
invariants
obtained
in
this
is
explained
through
worked-out
examples,
thus
providing
for
experimental
design
engineering
Second-order
topological
insulators
and
superconductors
have
a
gapped
excitation
spectrum
in
bulk
along
boundaries,
but
protected
zero
modes
at
corners
of
two-dimensional
crystal
or
gapless
hinges
three-dimensional
crystal.
A
second-order
phase
can
be
induced
by
the
presence
crystalline
symmetry.
Building
on
Shiozaki
Sato's
complete
classification
phases
with
an
order-two
symmetry
[Phys.\
Rev.\
B
{\bf
90},
165114
(2014)],
such
as
mirror
reflection,
twofold
rotation,
inversion
symmetry,
we
classify
all
corresponding
superconductors.
The
also
includes
antiunitary
symmetries
antisymmetries.
