As
the
zero-field
analogue
of
fractional
quantum
Hall
states,
Chern
insulator
states
emerge
from
topologically
nontrivial
flat
bands
realized
in
lattice
systems.
Recently,
a
series
fractionally
quantized
resistance
plateaus
have
been
observed
rhombohedral
pentalayer
graphene-hBN
moir\'e
superlattices
under
zero
magnetic
field,
needing
theoretical
understanding.
The
authors
developed
workflow,
discovering
both
integer
and
multilayer
superlattices,
which
are
consistent
with
recent
experimental
results.
Science Advances,
Journal Year:
2023,
Volume and Issue:
9(36)
Published: Sept. 6, 2023
We
propose
magic-angle
helical
trilayer
graphene
(HTG),
a
structure
featuring
identical
rotation
angles
between
three
consecutive
layers
of
graphene,
as
unique
and
experimentally
accessible
platform
for
realizing
exotic
correlated
topological
states
matter.
While
nominally
forming
supermoiré
(or
moiré-of-moiré)
structure,
we
show
that
HTG
locally
relaxes
into
large
regions
periodic
single-moiré
flat
bands
carrying
nontrivial
valley
Chern
number.
These
feature
near-ideal
quantum
geometry
are
isolated
from
remote
by
very
energy
gap,
making
promising
experimental
realization
such
integer
fractional
anomalous
Hall
states.
Physical Review Letters,
Journal Year:
2024,
Volume and Issue:
132(9)
Published: March 1, 2024
We
explain
the
appearance
of
magic
angles
and
fractional
Chern
insulators
in
twisted
K-valley
homobilayer
transition
metal
dichalcogenides
by
mapping
their
continuum
model
to
a
Landau
level
problem.
Our
approach
relies
on
an
adiabatic
approximation
for
quantum
mechanics
valence
band
holes
layer-pseudospin
field
that
is
valid
sufficiently
small
twist
lowest
large
angles.
It
provides
simple
qualitative
explanation
nearly
ideal
geometry
moir\'e
miniband
at
particular
angles,
predicts
topological
flat
bands
occur
only
when
valley-dependent
potential
strong
compared
interlayer
tunneling
amplitude,
convenient
starting
point
study
interactions.
Science,
Journal Year:
2024,
Volume and Issue:
384(6693), P. 343 - 347
Published: April 18, 2024
Semiconductor
moiré
superlattices
have
been
shown
to
host
a
wide
array
of
interaction-driven
ground
states.
However,
twisted
homobilayers
difficult
study
in
the
limit
large
wavelengths,
where
interactions
are
most
dominant.
In
this
study,
we
conducted
local
electronic
compressibility
measurements
bilayer
WSe
Science,
Journal Year:
2024,
Volume and Issue:
384(6696), P. 647 - 651
Published: May 9, 2024
The
quantum
anomalous
Hall
effect
(QAHE)
is
a
robust
topological
phenomenon
that
features
quantized
resistance
at
zero
magnetic
field.
We
report
the
QAHE
in
rhombohedral
pentalayer
graphene-monolayer
tungsten
disulfide
(WS
Fractionally
filled
Chern
bands
with
strong
interactions
may
give
rise
to
fractional
insulator
(FCI)
states,
the
zero-field
analog
of
quantum
Hall
effect.
Recent
experiments
have
demonstrated
existence
FCIs
in
twisted
bilayer
${\mathrm{MoTe}}_{2}$
without
external
magnetic
fields---most
robust
at
$\ensuremath{\nu}=\ensuremath{-}2/3$---as
well
as
insulators
(CIs)
$\ensuremath{\nu}=\ensuremath{-}1$.
Although
appearance
both
these
states
is
theoretically
natural
an
interacting
topological
system,
repeatedly
observe
nonmagnetic
(or
weakly
magnetic)
(lacking
FCIs)
$\ensuremath{\nu}=\ensuremath{-}1/3$
and
$\ensuremath{-}4/3$,
a
puzzling
result,
which
has
not
been
fully
explained.
In
this
paper,
we
perform
Hartree-Fock
exact
diagonalization
calculations
test
whether
standard
moir\'e
model
(greatly
varying)
parameter
values
available
literature
can
reproduce
nonmagnetic/weakly
$\ensuremath{-}4/3$
unison
FCI
$\ensuremath{\nu}=\ensuremath{-}2/3$
CI
state
We
focus
on
experimentally
relevant
twist
angles
and,
crucially,
include
remote
bands.
find
that
parameters
proposed
Wang
et
al.
[arXiv:2306.02501]
nearly
capture
experimental
phenomena
$\ensuremath{\nu}=\ensuremath{-}1/3,\ensuremath{-}2/3,\ensuremath{-}1,\ensuremath{-}4/3$
simultaneously,
although
predicted
ground
are
still
mostly
larger
dielectric
constant
$\ensuremath{\epsilon}>10$
than
typical
hexagonal
boron
nitride
(h-BN)
substrate
$\ensuremath{\epsilon}\ensuremath{\sim}6$
required.
Our
results
show
importance
identifying
competing
orders
lay
groundwork
for
further
study
realistic
phase
diagram.
