41 research outputs found

### Shift insulators: rotation-protected two-dimensional topological crystalline insulators

We study a two-dimensional (2D) tight-binding model of a topological
crystalline insulator (TCI) protected by rotation symmetry. The model is built
by stacking two Chern insulators with opposite Chern numbers which transform
under conjugate representations of the rotation group, e.g. $p_\pm$ orbitals.
Despite its apparent similarity to the Kane-Mele model, it does not host stable
gapless surface states. Nevertheless the model exhibits topological responses
including the appearance of quantized fractional charge bound to rotational
defects (disclinations) and the pumping of angular momentum in response to
threading an elementary magnetic flux, which are described by a mutual
Chern-Simons coupling between the electromagnetic gauge field and an effective
gauge field corresponding to the rotation symmetry. In addition, we show that
although the filled bands of the model do not admit a symmetric Wannier
representation, this obstruction is removed upon the addition of appropriate
atomic orbitals, which implies `fragile' topology. As a result, the response of
the model can be derived by representing it as a superposition of atomic
orbitals with positive and negative integer coefficients. Following the
analysis of the model, which serves as a prototypical example of 2D TCIs
protected by rotation, we show that all TCIs protected by point group
symmetries which do not have protected surface states are either atomic
insulators or fragile phases. Remarkably, this implies that gapless surface
states exist in free electron systems if and only if there is a stable Wannier
obstruction. We then use dimensional reduction to map the problem of
classifying 2D TCIs protected by rotation to a zero-dimensional (0D) problem
which is then used to obtain the complete non-interacting classification of
such TCIs as well as the reduction of this classification in the presence of
interactions.Comment: 33 pages, 16 figure

### From electrons to baby skyrmions in Chern ferromagnets: A topological mechanism for spin-polaron formation in twisted bilayer graphene

The advent of Moir\'e materials has galvanized interest in the nature of
charge carriers in topological bands. In contrast to conventional materials
where charge carriers are electron-like quasiparticles, topological bands allow
for more exotic possibilities where charge is carried by nontrivial topological
textures, such as skyrmions. However, the real space description of skyrmions
is ill-suited to address the limit of small or `baby' skyrmions which consist
of an electron and a few spin flips. Here, we study the formation of the
smallest skyrmions -- spin polarons, formed as bound states of an electron and
a spin flip -- in Chern ferromagnets. We show that, quite generally, there is
an attraction between an electron and a spin flip that is purely topological in
origin and of $p$-wave symmetry, which promotes the formation of spin polarons.
Applying our results to the topological bands of twisted bilayer graphene, we
identify a range of parameters where spin polarons are formed and are lower in
energy than electrons. In particular, spin polarons are found to be
energetically cheaper on doping correlated insulators at integer fillings
towards charge neutrality, consistent with the absence of quantum oscillations
and the rapid onset of flavor polarization (cascade) transition in this regime.
Our study sets the stage for pairing of spin polarons, helping bridge skyrmion
pairing scenarios and momentum space approaches to superconductivity.Comment: 7 page

### Symmetry constraints on superconductivity in twisted bilayer graphene: Fractional vortices, $4e$ condensates or non-unitary pairing

When two graphene sheets are twisted relative to each other by a small angle,
enhanced correlations lead to superconductivity whose origin remains under
debate. Here, we derive some general constraints on superconductivity in
twisted bilayer graphene (TBG), independent of its underlying mechanism.
Neglecting weak coupling between valleys, the global symmetry group of TBG
consists of independent spin rotations in each valley in addition to valley
charge rotations, ${\rm SU}(2) \times {\rm SU}(2) \times {\rm U}_V(1)$. This
symmetry is further enhanced to a full ${\rm SU}(4)$ in the idealized chiral
limit. In both cases, we show that any charge $2e$ pairing must break the
global symmetry. Additionally, if the pairing is unitary the resulting
superconductor admits fractional vortices. This leads to the following general
statement: Any superconducting condensate in either symmetry class has to
satisfy one of three possibilities: (i) the superconducting pairing is
non-unitary, (ii) the superconducting condensate has charge $2e$ but admits at
least half quantum vortices which carry a flux of $h/4e$, or (iii) the
superconducting condensate has charge $2me$, $m>1$, with vortices carrying
$h/2me$ flux. The latter possibility can be realized by a symmetric charge $4e$
superconductor ($m=2$). Non-unitary pairing (i) is expected in TBG for
superconductors observed in the vicinity of flavor polarized states. On the
other hand, in the absence of flavor polarization, e.g. in the vicinity of
charge neutrality, one of the two exotic possibilities (ii) and (iii) is
expected. We sketch how all three scenarios can be realized in different limits
within a strong coupling theory of superconductivity based on skyrmions.
Finally we discuss the effect of symmetry lowering anisotropies and
experimental implications of these scenarios.Comment: 9+2 pages, 1 Tabl

### Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene

Two monolayers of graphene twisted by a small `magic' angle exhibit nearly
flat bands leading to correlated electronic states and superconductivity, whose
precise nature including possible broken symmetries, remain under debate. Here
we theoretically study a related but different system with reduced symmetry -
twisted {\em double} bilayer graphene (TDBLG), consisting of {\em two} Bernal
stacked bilayer graphene sheets, twisted with respect to one another. Unlike
the monolayer case, we show that isolated flat bands only appear on application
of a vertical displacement field $D$. We construct a phase diagram as a
function of twist angle and $D$, incorporating interactions via a Hartree-Fock
approximation. At half filling, ferromagnetic insulators are stabilized,
typically with valley Chern number $C_v=2$. Ferromagnetic fluctuations in the
metallic state are argued to lead to spin triplet superconductivity from
pairing between electrons in opposite valleys. Response of these states to a
magnetic field applied either perpendicular or parallel to the graphene sheets
is obtained, and found to compare favorably with a recent experiment. We
highlight a novel orbital effect arising from in-plane fields that can exceed
the Zeeman effect and plays an important role in interpreting experiments.Comment: main 15 pages, appendix 11 page

### Untwisting moir\'e physics: Almost ideal bands and fractional Chern insulators in periodically strained monolayer graphene

Moir\'e systems have emerged in recent years as a rich platform to study
strong correlations. Here, we will discuss a simple, experimentally feasible
setup based on periodically strained graphene that reproduces several key
aspects of twisted moir\'e heterostructures -- but without introducing a twist.
We consider a monolayer graphene sheet subject to a $C_2$-breaking periodic
strain-induced psuedomagnetic field (PMF) with period $L_M \gg a$, along with a
scalar potential of the same period. This system has {\it almost ideal} flat
bands with valley-resolved Chern number $\pm 1$, where the deviation from ideal
band geometry is analytically controlled and exponentially small in the
dimensionless ratio $(L_M/l_B)^2$ where $l_B$ is the magnetic length
corresponding to the maximum value of the PMF. Moreover, the scalar potential
can tune the bandwidth far below the Coulomb scale, making this a very
promising platform for strongly interacting topological phases. Using a
combination of strong-coupling theory and self-consistent Hartree fock, we find
quantum anomalous Hall states at integer fillings. At fractional filling, exact
diagonaliztion reveals a fractional Chern insulator at parameters in the
experimentally feasible range. Overall, we find that this system has larger
interaction-induced gaps, smaller quasiparticle dispersion, and enhanced
tunability compared to twisted graphene systems, even in their ideal limit.Comment: 5 pages + supplemen