Superlattice
potential
modulation
can
produce
flat
minibands
in
Bernal-stacked
bilayer
graphene.In
this
work
we
study
how
band
topology
and
interaction-induced
symmetry-broken
phases
system
are
controlled
by
tuning
the
displacement
field
shape
strength
of
superlattice
potential.We
use
an
analytic
perturbative
analysis
to
demonstrate
that
topological
bands
favored
a
honeycomb-lattice-shaped
potential,
numerics
show
robustness
depends
on
both
periodicity
potential.At
integer
fillings
bands,
tune
phase
transitions
between
quantum
anomalous
Hall
insulator,
trivial
metallic
states.We
present
mean-field
diagrams
gate
voltage
parameter
space
at
filling
factor
ν
=
1,
discuss
prospects
realizing
insulators
fractional
Chern
when
is
produced
dielectric
patterning
or
adjacent
moiré
materials.
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.
The
researchers
here
shed
new
light
on
the
elusive
single-particle
model
of
twisted
bilayer
MoTe${}_{2}$,
a
material
recently
highlighted
for
hosting
fractional
Chern
insulators
at
zero
magnetic
field.
By
leveraging
an
advanced
machine
learning
method
and
density
functional
theory,
team
meticulously
maps
out
band
structure
across
various
twist
angles,
revealing
pivotal
inversion
refining
theoretical
landscape.
enhancing
continuum
with
higher
harmonic
terms,
they
unveil
opposite
numbers
in
valence
bands
key
paving
way
predicting
diverse
states.
This
comprehensive
analysis
lays
groundwork
accurately
pinpointing
correlated
phases
this
intriguing
material,
offering
beacon
future
explorations.
Physical Review Letters,
Journal Year:
2024,
Volume and Issue:
133(20)
Published: Nov. 12, 2024
Recent
experiments
on
rhombohedral
pentalayer
graphene
with
a
substrate-induced
moiré
potential
have
identified
both
Chern
insulators
and
fractional
quantum
Hall
states
at
zero
magnetic
field.
Surprisingly,
these
are
observed
in
strong
displacement
fields
where
the
effects
of
lattice
weak,
seem
to
be
readily
accessed
without
fine-tuning.
To
address
experimental
puzzles,
we
study
model
interacting
electrons
this
geometry.
Within
self-consistent
Hartree-Fock
(SCHF)
calculations,
find
an
isolated
band
small
bandwidth
good
Exact
diagonalization
density-matrix
renormalization
group
calculations
confirm
hosts
Remarkably,
is
stable
wide
range
angles,
four
through
six
layers,
varying
hopping
parameters,
and-most
strikingly-survives
SCHF
when
vanishes.
In
limit,
state
spontaneously
breaks
time-reversal
translation
symmetry
simultaneously,
giving
topological
crystalline
that
term
"anomalous
crystal."
We
argue
general
mechanism
create
bands
multilayer
graphene,
opening
door
studying
interplay
between
electronic
topology,
fractionalization,
spontaneous
breaking.
Physical Review Letters,
Journal Year:
2024,
Volume and Issue:
133(20)
Published: Nov. 12, 2024
Remarkable
recent
experiments
on
the
moir\'e
structure
formed
by
pentalayer
rhombohedral
graphene
aligned
with
a
hexagonal
boron
nitride
substrate
report
discovery
of
zero
field
fractional
quantum
Hall
effect.
These
``(fractional)
anomalous
Hall''
[(F)QAH]
phases
occur
for
one
sign
perpendicular
displacement
field,
and
correspond,
experimentally,
to
full
or
partial
filling
valley
polarized
Chern-1
band.
Such
band
is
absent
in
noninteracting
structure.
Here
we
show
that
electron-electron
interactions
play
crucial
role,
present
microscopic
theoretical
calculations
demonstrating
emergence
nearly
flat,
isolated,
FQAH
this
system.
We
also
study
four-
six-layer
analogs
identify
parameters
where
flat
isolated
emerges
which
may
be
suitable
host
physics.
Remarkable
recent
experiments
have
observed
fractional
quantum
anomalous
Hall
effects
at
zero
field
and
unusually
high
temperatures
in
twisted
semiconductor
bilayer
tMoTe2,
hence
realizing
the
first
genuine
Chern
insulators.
Intriguing
observations
these
experiments,
such
as
absence
of
integer
twist
angles
where
a
effect
is
observed,
do
however
remain
unexplained.
The
experimental
phase
diagram
function
angle
remains
to
be
established.
By
comprehensive
numerical
study,
including
entanglement
spectroscopy,
we
show
that
band
mixing
has
large
qualitative
quantitative
on
energetics
competing
states
their
energy
gaps
throughout
range
θ≤4∘.
This
lays
foundation
for
detailed
realistic
study
rich
variety
strongly
correlated
moiré
superlattices
an
understanding
fascinating
systems.
Published
by
American
Physical
Society
2024
