1,557 research outputs found
MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
Magic-angle () twisted bilayer graphene (MATBG) has shown
two seemingly contradictory characters: the localization and quantum-dot-like
behavior in STM experiments, and delocalization in transport experiments. We
construct a model, which naturally captures the two aspects, from the
Bistritzer-MacDonald (BM) model in a first principle spirit. A set of local
flat-band orbitals () centered at the AA-stacking regions are responsible to
the localization. A set of extended topological conduction bands (), which
are at small energetic separation from the local orbitals, are responsible to
the delocalization and transport. The topological flat bands of the BM model
appear as a result of the hybridization of - and -electrons. This model
then provides a new perspective for the strong correlation physics, which is
now described as strongly correlated -electrons coupled to nearly free
topological semimetallic -electrons - we hence name our model as the
topological heavy fermion model. Using this model, we obtain the U(4) and
U(4)U(4) symmetries as well as the correlated insulator phases and
their energies. Simple rules for the ground states and their Chern numbers are
derived. Moreover, features such as the large dispersion of the charge
excitations and the minima of the charge gap at the point can now,
for the first time, be understood both qualitatively and quantitatively in a
simple physical picture. Our mapping opens the prospect of using heavy-fermion
physics machinery to the superconducting physics of MATBG.Comment: New references are added. Discussions on band geometry, relevant
experiments, and more terms in the exchange interactions are added to the
supplementary material
Dynamical Symmetry Indicators for Floquet Crystals
Various exotic topological phases of Floquet systems have been shown to arise
from crystalline symmetries. Yet, a general theory for Floquet topology that is
applicable to all crystalline symmetry groups is still in need. In this work,
we propose such a theory for (effectively) non-interacting Floquet crystals. We
first introduce quotient winding data to classify the dynamics of the Floquet
crystals with equivalent symmetry data, and then construct dynamical symmetry
indicators (DSIs) to sufficiently indicate the "inherently dynamical" Floquet
crystals. The DSI and quotient winding data, as well as the symmetry data, are
all computationally efficient since they only involve a small number of Bloch
momenta. We demonstrate the high efficiency by computing all elementary DSI
sets for all spinless and spinful plane groups using the mathematical theory of
monoid, and find a large number of different nontrivial classifications, which
contain both first-order and higher-order 2+1D anomalous Floquet topological
phases. Using the framework, we further find a new 3+1D anomalous Floquet
second-order topological insulator (AFSOTI) phase with anomalous chiral hinge
modes.Comment: Close to the published versio
Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
The topological phases of non-interacting fermions have been classified by
their symmetries, culminating in a modern electronic band theory where
wavefunction topology can be obtained (in part) from momentum space. Recently,
Real Space Invariants (RSIs) have provided a spatially local description of the
global momentum space indices. The present work generalizes this real space
classification to interacting 2D states. We construct many-body local RSIs as
the quantum numbers of a set of symmetry operators on open boundaries, but
which are independent of the choice of boundary. Using the particle
number, they yield many-body fragile topological indices, which we use to
identify which single-particle fragile states are many-body topological or
trivial at weak coupling. To this end, we construct an exactly solvable
Hamiltonian with single-particle fragile topology that is adiabatically
connected to a trivial state through strong coupling. We then define global
many-body RSIs on periodic boundary conditions. They reduce to Chern numbers in
the band theory limit, but also identify strongly correlated stable topological
phases with no single-particle counterpart. Finally, we show that the many-body
local RSIs appear as quantized coefficients of Wen-Zee terms in the topological
quantum field theory describing the phase.Comment: 5 + 36 page
TBG II: Stable Symmetry Anomaly in Twisted Bilayer Graphene
We show that the entire continuous model of twisted bilayer graphene (TBG)
(and not just the two active bands) with particle-hole symmetry is anomalous
and hence incompatible with a lattice model. Previous works, e.g., [Phys. Rev.
Lett. 123, 036401], [Phys. Rev. X 9, 021013], [Phys. Rev. B 99, 195455], and
others [1-4] found that the two flat bands in TBG possess a fragile topology
protected by the symmetry. [Phys. Rev. Lett. 123, 036401] also
pointed out an approximate particle-hole symmetry () in the
continuous model of TBG. In this work, we numerically confirm that
is indeed a good approximation for TBG and show that the fragile
topology of the two flat bands is enhanced to a -protected stable
topology. This stable topology implies () Dirac points
between the middle two bands. The -protected stable topology is
robust against arbitrary gap closings between the middle two bands the other
bands. We further show that, remarkably, this -protected stable
topology, as well as the corresponding Dirac points, cannot be
realized in lattice models that preserve both and
symmetries. In other words, the continuous model of TBG is anomalous and cannot
be realized on lattices. Two other topology related topics, with consequences
for the interacting TBG problem, i.e., the choice of Chern band basis in the
two flat bands and the perfect metal phase of TBG in the so-called second
chiral limit, are also discussed.Comment: references adde
Twisted bilayer graphene I. Matrix elements, approximations, perturbation theory and a 2-Band model
We investigate the Twisted Bilayer Graphene (TBG) model to obtain an analytic
understanding of its energetics and wavefunctions needed for many-body
calculations. We provide an approximation scheme which first elucidates why the
BM -point centered calculation containing only plane-waves provides a
good analytical value for the first magic angle. The approximation scheme also
elucidates why most many-body matrix elements in the Coulomb Hamiltonian
projected to the active bands can be neglected. By applying our approximation
scheme at the first magic angle to a -point centered model of 6
plane-waves, we analytically understand the small -point gap between
the active and passive bands in the isotropic limit . Furthermore, we
analytically calculate the group velocities of passive bands in the isotropic
limit, and show that they are \emph{almost} doubly degenerate, while no
symmetry forces them to be. Furthermore, away from and points,
we provide an explicit analytical perturbative understanding as to why the TBG
bands are flat at the first magic angle, despite it is defined only by
vanishing -point Dirac velocity. We derive analytically a connected "magic
manifold" , on which the bands remain
extremely flat as is tuned between the isotropic () and chiral
() limits. We analytically show why going away from the isotropic limit
by making less (but not larger) than increases the -
point gap between active and passive bands. Finally, perturbatively, we provide
an analytic point -band model that reproduces the TBG
band structure and eigenstates in a certain parameter range. Further
refinement of this model suggests a possible faithful -band point
model in the full parameter range.Comment: 25+21 pages, 13+7 figures. Published versio
Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
Adding magnetic flux to a band structure breaks Bloch's theorem by realizing
a projective representation of the translation group. The resulting Hofstadter
spectrum encodes the non-perturbative response of the bands to flux. Depending
on their topology, adding flux can enforce a bulk gap closing (a Hofstadter
semimetal) or boundary state pumping (a Hofstadter topological insulator). In
this work, we present a real-space classification of these Hofstadter phases.
We give topological indices in terms of symmetry-protected Real Space
Invariants (RSIs) which encode bulk and boundary responses of fragile
topological states to flux. In fact, we find that the flux periodicity in
tight-binding models causes the symmetries which are broken by the magnetic
field to reenter at strong flux where they form projective point group
representations. We completely classify the reentrant projective point groups
and find that the Schur multipliers which define them are Arahanov-Bohm phases
calculated along the bonds of the crystal. We find that a nontrivial Schur
multiplier is enough to predict and protect the Hofstadter response with only
zero-flux topology
Spin Space Groups: Full Classification and Applications
In this work, we exhaust all the spin-space symmetries, which fully
characterize collinear, non-collinear, commensurate, and incommensurate spiral
magnetism, and investigate enriched features of electronic bands that respect
these symmetries. We achieve this by systematically classifying the so-called
spin space groups (SSGs) - joint symmetry groups of spatial and spin operations
that leave the magnetic structure unchanged. Generally speaking, they are
accurate (approximate) symmetries in systems where spin-orbit coupling (SOC) is
negligible (finite but weaker than the interested energy scale); but we also
show that specific SSGs could remain valid even in the presence of a strong
SOC. By representing the SSGs as O() representations, we - for the first
time - obtain the complete classifications of 1421, 9542, and 56512 distinct
SSGs for collinear (), coplanar (), and non-coplanar ()
magnetism, respectively. SSG not only fully characterizes the symmetry of spin
d.o.f., but also gives rise to exotic electronic states, which, in general,
form projective representations of magnetic space groups (MSGs). Surprisingly,
electronic bands in SSGs exhibit features never seen in MSGs, such as
nonsymmorphic SSG Brillouin zone (BZ), where SSG operations behave as glide or
screw when act on momentum and unconventional spin-momentum locking, which is
completely determined by SSG, independent of Hamiltonian details. To apply our
theory, we identify the SSG for each of the 1604 published magnetic structures
in the MAGNDATA database on the Bilbao Crystallographic Server. Material
examples exhibiting aforementioned novel features are discussed with emphasis.
We also investigate new types of SSG-protected topological electronic states
that are unprecedented in MSGs
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