272 research outputs found

### Diffusive-Ballistic Crossover and the Persistent Spin Helix

Conventional transport theory focuses on either the diffusive or ballistic
regimes and neglects the crossover region between the two. In the presence of
spin-orbit coupling, the transport equations are known only in the diffusive
regime, where the spin precession angle is small. In this paper, we develop a
semiclassical theory of transport valid throughout the diffusive - ballistic
crossover of a special SU(2) symmetric spin-orbit coupled system. The theory is
also valid in the physically interesting regime where the spin precession angle
is large. We obtain exact expressions for the density and spin structure
factors in both 2 and 3 dimensional samples with spin-orbit coupling.Comment: 4 pages, 3 figure

### Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators

The energy and entanglement spectrum of fractionally filled interacting
topological insulators exhibit a peculiar manifold of low energy states
separated by a gap from a high energy set of spurious states. In the current
manuscript, we show that in the case of fractionally filled Chern insulators,
the topological information of the many-body state developing in the system
resides in this low-energy manifold. We identify an emergent many-body
translational symmetry which allows us to separate the states in
quasi-degenerate center of mass momentum sectors. Within one center of mass
sector, the states can be further classified as eigenstates of an emergent (in
the thermodynamic limit) set of many-body relative translation operators. We
analytically establish a mapping between the two-dimensional Brillouin zone for
the Fractional Quantum Hall effect on the torus and the one for the fractional
Chern insulator. We show that the counting of quasi-degenerate levels below the
gap for the Fractional Chern Insulator should arise from a folding of the
states in the Fractional Quantum Hall system at identical filling factor. We
show how to count and separate the excitations of the Laughlin, Moore-Read and
Read-Rezayi series in the Fractional Quantum Hall effect into two-dimensional
Brillouin zone momentum sectors, and then how to map these into the momentum
sectors of the Fractional Chern Insulator. We numerically check our results by
showing the emergent symmetry at work for Laughlin, Moore-Read and Read-Rezayi
states on the checkerboard model of a Chern insulator, thereby also showing, as
a proof of principle, that non-Abelian Fractional Chern Insulators exist.Comment: 32 pages, 9 figure

### Berry-phase description of Topological Crystalline Insulators

We study a class of translational-invariant insulators with discrete
rotational symmetry. These insulators have no spin-orbit coupling, and in some
cases have no time-reversal symmetry as well, i.e., the relevant symmetries are
purely crystalline. Nevertheless, topological phases exist which are
distinguished by their robust surface modes. Like many well-known topological
phases, their band topology is unveiled by the crystalline analog of Berry
phases, i.e., parallel transport across certain non-contractible loops in the
Brillouin zone. We also identify certain topological phases without any robust
surface modes -- they are uniquely distinguished by parallel transport along
bent loops, whose shapes are determined by the symmetry group. Our findings
have experimental implications in cold-atom systems, where the crystalline
Berry phase has been directly measured.Comment: Latest version is accepted to PR

### $\mathbb Z_2$ fractional topological insulators in two dimensions

We propose a simple microscopic model to numerically investigate the
stability of a two dimensional fractional topological insulator (FTI). The
simplest example of a FTI consists of two decoupled copies of a Laughlin state
with opposite chiralities. We focus on bosons at half filling. We study the
stability of the FTI phase upon addition of two coupling terms of different
nature: an interspin interaction term, and an inversion symmetry breaking term
that couples the copies at the single particle level. Using exact
diagonalization and entanglement spectra, we numerically show that the FTI
phase is stable against both perturbations. We compare our system to a similar
bilayer fractional Chern insulator. We show evidence that the time reversal
invariant system survives the introduction of interaction coupling on a larger
scale than the time reversal symmetry breaking one, stressing the importance of
time reversal symmetry in the FTI phase stability. We also discuss possible
fractional phases beyond $\nu = 1/2$.Comment: 15 pages, 18 figure

### Wilson-Loop Characterization of Inversion-Symmetric Topological Insulators

The ground state of translationally-invariant insulators comprise bands which
can assume topologically distinct structures. There are few known examples
where this distinction is enforced by a point-group symmetry alone. In this
paper we show that 1D and 2D insulators with the simplest point-group symmetry
- inversion - have a $Z^{\geq}$ classification. In 2D, we identify a relative
winding number that is solely protected by inversion symmetry. By analysis of
Berry phases, we show that this invariant has similarities with the first Chern
class (of time-reversal breaking insulators), but is more closely analogous to
the $Z_2$ invariant (of time-reversal invariant insulators). Implications of
our work are discussed in holonomy, the geometric-phase theory of polarization,
the theory of maximally-localized Wannier functions, and in the entanglement
spectrum.Comment: The updated version is accepted in Physical Review

### Twisted Bilayer Graphene: A Phonon Driven Superconductor

We study the electron-phonon coupling in twisted bilayer graphene (TBG),
which was recently experimentally observed to exhibit superconductivity around
the magic twist angle $\theta\approx 1.05^\circ$. We show that phonon-mediated
electron electron attraction at the magic angle is strong enough to induce a
conventional intervalley pairing between graphene valleys $K$ and $K'$ with a
superconducting critical temperature $T_c\sim1K$, in agreement with the
experiment. We predict that superconductivity can also be observed in TBG at
many other angles $\theta$ and higher electron densities in higher Moir\'e
bands, which may also explain the possible granular superconductivity of highly
oriented pyrolytic graphite. We support our conclusions by \emph{ab initio}
calculations.Comment: 6+20 pages, 4+6 figure

### Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars

We revisit the $\eta$-pairing states in Hubbard models and explore their
connections to quantum many-body scars to discover a universal scars mechanism.
$\eta$-pairing occurs due to an algebraic structure known as a Spectrum
Generating Algebra (SGA), giving rise to equally spaced towers of eigenstates
in the spectrum. We generalize the original $\eta$-pairing construction and
show that several Hubbard-like models on arbitrary graphs exhibit SGAs,
including ones with disorder and spin-orbit coupling. We further define a
Restricted Spectrum Generating Algebra (RSGA) and give examples of
perturbations to the Hubbard-like models that preserve an equally spaced tower
of the original model as eigenstates. The states of the surviving tower exhibit
a sub-thermal entanglement entropy, and we analytically obtain parameter
regimes for which they lie in the bulk of the spectrum, showing that they are
exact quantum many-body scars. The RSGA framework also explains the equally
spaced towers of eigenstates in several well-known models of quantum scars,
including the AKLT model.Comment: 13 pages v2: typos corrected, references adde

- …