707 research outputs found
Topological Insulators with Inversion Symmetry
Topological insulators are materials with a bulk excitation gap generated by
the spin orbit interaction, and which are different from conventional
insulators. This distinction is characterized by Z_2 topological invariants,
which characterize the groundstate. In two dimensions there is a single Z_2
invariant which distinguishes the ordinary insulator from the quantum spin Hall
phase. In three dimensions there are four Z_2 invariants, which distinguish the
ordinary insulator from "weak" and "strong" topological insulators. These
phases are characterized by the presence of gapless surface (or edge) states.
In the 2D quantum spin Hall phase and the 3D strong topological insulator these
states are robust and are insensitive to weak disorder and interactions. In
this paper we show that the presence of inversion symmetry greatly simplifies
the problem of evaluating the Z_2 invariants. We show that the invariants can
be determined from the knowledge of the parity of the occupied Bloch
wavefunctions at the time reversal invariant points in the Brillouin zone.
Using this approach, we predict a number of specific materials are strong
topological insulators, including the semiconducting alloy Bi_{1-x} Sb_x as
well as \alpha-Sn and HgTe under uniaxial strain. This paper also includes an
expanded discussion of our formulation of the topological insulators in both
two and three dimensions, as well as implications for experiments.Comment: 16 pages, 7 figures; published versio
Nonrelativistic spin splittings in twisted bilayers of centrosymmetric antiferromagnets: A case study of MnPSe3 and MnSe
Antiferromagnetism-induced spin splittings--even without atomic spin-orbit
coupling--are promising for highly efficient spintronics applications. Although
two-dimensional (2D) centrosymmetric antiferromagnetic materials are abundant,
they have not received extensive research attention owing to PT
symmetry-enforced net zero spin polarization and magnetization. Here, we
demonstrate a paradigm to harness nonrelativistic spin splitting (NRSS) by
twisting the bilayer of type-III centrosymmetric antiferromagnets. We predict
by first-principles simulations and symmetry analysis on prototypes MnPSe3 and
MnSe antiferromagnets (in the monolayer limit) that Rashba-Dresselhaus and
Zeeman-like NRSSs arise along specific paths in the Brillouin zone. The
strength of Rashba-Dresselhaus spin splitting (up to 90 meV{\AA})
induced by twisting is comparable to that of spin-orbit coupling. The results
also demonstrate how applying biaxial strain and a perpendicular electric field
could be envisaged to tune the magnitude of NRSS. The findings reveal the
untapped potential of centrosymmetric antiferromagnets and thus expand the
materials to look for spintronics
Simplicity in simplicial phase space
A key point in the spin foam approach to quantum gravity is the
implementation of simplicity constraints in the partition functions of the
models. Here, we discuss the imposition of these constraints in a phase space
setting corresponding to simplicial geometries. On the one hand, this could
serve as a starting point for a derivation of spin foam models by canonical
quantisation. On the other, it elucidates the interpretation of the boundary
Hilbert space that arises in spin foam models.
More precisely, we discuss different versions of the simplicity constraints,
namely gauge-variant and gauge-invariant versions. In the gauge-variant
version, the primary and secondary simplicity constraints take a similar form
to the reality conditions known already in the context of (complex) Ashtekar
variables. Subsequently, we describe the effect of these primary and secondary
simplicity constraints on gauge-invariant variables. This allows us to
illustrate their equivalence to the so-called diagonal, cross and edge
simplicity constraints, which are the gauge-invariant versions of the
simplicity constraints. In particular, we clarify how the so-called gluing
conditions arise from the secondary simplicity constraints. Finally, we discuss
the significance of degenerate configurations, and the ramifications of our
work in a broader setting.Comment: Typos and references correcte
Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
We introduce the notion of algebraic higher symmetry, which generalizes
higher symmetry and is beyond higher group. We show that an algebraic higher
symmetry in a bosonic system in -dimensional space is characterized and
classified by a local fusion -category. We find another way to describe
algebraic higher symmetry by restricting to symmetric sub Hilbert space where
symmetry transformations all become trivial. In this case, algebraic higher
symmetry can be fully characterized by a non-invertible gravitational anomaly
(i.e. an topological order in one higher dimension). Thus we also refer to
non-invertible gravitational anomaly as categorical symmetry to stress its
connection to symmetry. This provides a holographic and entanglement view of
symmetries. For a system with a categorical symmetry, its gapped state must
spontaneously break part (not all) of the symmetry, and the state with the full
symmetry must be gapless. Using such a holographic point of view, we obtain (1)
the gauging of the algebraic higher symmetry; (2) the classification of
anomalies for an algebraic higher symmetry; (3) the equivalence between classes
of systems, with different (potentially anomalous) algebraic higher symmetries
or different sets of low energy excitations, as long as they have the same
categorical symmetry; (4) the classification of gapped liquid phases for
bosonic/fermionic systems with a categorical symmetry, as gapped boundaries of
a topological order in one higher dimension (that corresponds to the
categorical symmetry). This classification includes symmetry protected trivial
(SPT) orders and symmetry enriched topological (SET) orders with an algebraic
higher symmetry.Comment: 61 pages, 31 figure
Residues and World-Sheet Instantons
We reconsider the question of which Calabi-Yau compactifications of the
heterotic string are stable under world-sheet instanton corrections to the
effective space-time superpotential. For instance, compactifications described
by (0,2) linear sigma models are believed to be stable, suggesting a remarkable
cancellation among the instanton effects in these theories. Here, we show that
this cancellation follows directly from a residue theorem, whose proof relies
only upon the right-moving world-sheet supersymmetries and suitable compactness
properties of the (0,2) linear sigma model. Our residue theorem also extends to
a new class of "half-linear" sigma models. Using these half-linear models, we
show that heterotic compactifications on the quintic hypersurface in CP^4 for
which the gauge bundle pulls back from a bundle on CP^4 are stable. Finally, we
apply similar ideas to compute the superpotential contributions from families
of membrane instantons in M-theory compactifications on manifolds of G_2
holonomy.Comment: 47 page
Vortex solitons in twisted circular waveguide arrays
We address the formation of topological states in twisted circular waveguide
arrays and find that twisting leads to important differences of the fundamental
properties of new vortex solitons with opposite topological charges that arise
in the nonlinear regime. We find that such system features the rare property
that clockwise and counter-clockwise vortex states are nonequivalent. Focusing
on arrays with C_{6v} discrete rotation symmetry, we find that a longitudinal
twist stabilizes the vortex solitons with the lowest topological charges m=+-1,
which are always unstable in untwisted arrays with the same symmetry. Twisting
also leads to the appearance of instability domains for otherwise stable
solitons with m=+-2 and generates vortex modes with topological charges m=+-3
that are forbidden in untwisted arrays. By and large, we establish a rigorous
relation between the discrete rotation symmetry of the array, its twist
direction, and the possible soliton topological charges.Comment: 6 pages, 5 figures, to appear in Physical Review Letter
Loop and surface operators in N=2 gauge theory and Liouville modular geometry
Recently, a duality between Liouville theory and four dimensional N=2 gauge
theory has been uncovered by some of the authors. We consider the role of
extended objects in gauge theory, surface operators and line operators, under
this correspondence. We map such objects to specific operators in Liouville
theory. We employ this connection to compute the expectation value of general
supersymmetric 't Hooft-Wilson line operators in a variety of N=2 gauge
theories.Comment: 60 pages, 11 figures; v3: further minor corrections, published
versio
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