224 research outputs found
Geometrical relations and plethysms in the Homfly skein of the annulus
The oriented framed Homfly skein C of the annulus provides the natural
parameter space for the Homfly satellite invariants of a knot. It contains a
submodule C+ isomorphic to the algebra of the symmetric functions.
We collect and expand formulae relating elements expressed in terms of
symmetric functions to Turaev's geometrical basis of C+. We reformulate the
formulae of Rosso and Jones for quantum sl(N) invariants of cables in terms of
plethysms of symmetric functions, and use the connection between quantum sl(N)
invariants and C+ to give a formula for the satellite of a cable as an element
of C+. We then analyse the case where a cable is decorated by the pattern which
corresponds to a power sum in the symmetric function interpretation of C+ to
get direct relations between the Homfly invariants of some diagrams decorated
by power sums.Comment: 28 pages, 15 figure
Spin-dependent Fano resonance induced by conducting chiral helimagnet contained in a quasi-one-dimensional electron waveguide
Fano resonance appears for conduction through an electron waveguide
containing donor impurities. In this work, we consider the thin-film conducting
chiral helimagnet (CCH) as the donor impurity in a one-dimensional waveguide
model. Due to the spin spiral coupling, interference between the direct and
intersubband transmission channels gives rise to spin-dependent Fano resonance
effect. The spin-dependent Fano resonance is sensitively dependent on the
helicity of the spiral. By tuning the CCH potential well depth and the incident
energy, this provides a potential way to detect the spin structure in the CCH.Comment: 14 pages, 6 figure
Spin-orbit torques in a Rashba honeycomb antiferromagnet
Recent experiments on switching antiferromagnetic domains by electric current
pulses have attracted a lot of attention to spin-orbit torques in
antiferromagnets. In this work, we employ the tight-binding model solver,
kwant, to compute spin-orbit torques in a two-dimensional antiferromagnet on a
honeycomb lattice with strong spin-orbit interaction of Rashba type. Our model
combines spin-orbit interaction, local s-d-like exchange, and scattering of
conduction electrons on on-site disorder potential to provide a microscopic
mechanism for angular momentum relaxation. We consider two versions of the
model: one with preserved and one with broken sublattice symmetry. A
non-equilibrium staggered polarization, that is responsible for the so-called
Neel spin-orbit torque, is shown to vanish identically in the symmetric model
but may become finite if sublattice symmetry is broken. Similarly, anti-damping
spin-orbit torques vanish in the symmetric model but become finite and
anisotropic in a model with broken sublattice symmetry. As expected,
anti-damping torques also reveal a sizable dependence on impurity
concentration. Our numerical analysis also confirms symmetry classification of
spin-orbit torques and strong torque anisotropy due to in-plane confinement of
electron momenta.Comment: 14 pages, 12 figure
Shuffle relations for regularised integrals of symbols
We prove shuffle relations which relate a product of regularised integrals of
classical symbols to regularised nested (Chen) iterated integrals, which hold
if all the symbols involved have non-vanishing residue. This is true in
particular for non-integer order symbols. In general the shuffle relations hold
up to finite parts of corrective terms arising from renormalisation on tensor
products of classical symbols, a procedure adapted from renormalisation
procedures on Feynman diagrams familiar to physicists. We relate the shuffle
relations for regularised integrals of symbols with shuffle relations for
multizeta functions adapting the above constructions to the case of symbols on
the unit circle.Comment: 40 pages,latex. Changes concern sections 4 and 5 : an error in
section 4 has been corrected, and the link between section 5 and the previous
ones has been precise
New Perspectives for Rashba Spin-Orbit Coupling
In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling
to explain certain peculiarities in the electron spin resonance of
two-dimensional semiconductors. Over the past thirty years, similar ideas have
been leading to a vast number of predictions, discoveries, and innovative
concepts far beyond semiconductors. The past decade has been particularly
creative with the realizations of means to manipulate spin orientation by
moving electrons in space, controlling electron trajectories using spin as a
steering wheel, and with the discovery of new topological classes of materials.
These developments reinvigorated the interest of physicists and materials
scientists in the development of inversion asymmetric structures ranging from
layered graphene-like materials to cold atoms. This review presents the most
remarkable recent and ongoing realizations of Rashba physics in condensed
matter and beyond.Comment: 56 pages, 7 figures, 3 boxes; Accepted for publication in Nature
Materials. The present version is the original one, before passing by the
referee
A Perspective on Regularization and Curvature
A global connection on the Connes Marcolli renormalization bundle relates
-functions of a class of regularization schemes by gauge
transformations, as well as local solutions to -functions over curved
space-time.Comment: As publishe
Overview of (pro-)Lie group structures on Hopf algebra character groups
Character groups of Hopf algebras appear in a variety of mathematical and
physical contexts. To name just a few, they arise in non-commutative geometry,
renormalisation of quantum field theory, and numerical analysis. In the present
article we review recent results on the structure of character groups of Hopf
algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild
assumptions on the Hopf algebra or the target algebra the character groups
possess strong structural properties. Moreover, these properties are of
interest in applications of these groups outside of Lie theory. We emphasise
this point in the context of two main examples: The Butcher group from
numerical analysis and character groups which arise from the Connes--Kreimer
theory of renormalisation of quantum field theories.Comment: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on
"New Developments in Discrete Mechanics, Geometric Integration and
Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spai
Femtosecond control of electric currents at the interfaces of metallic ferromagnetic heterostructures
The idea to utilize not only the charge but also the spin of electrons in the
operation of electronic devices has led to the development of spintronics,
causing a revolution in how information is stored and processed. A novel
advancement would be to develop ultrafast spintronics using femtosecond laser
pulses. Employing terahertz (10 Hz) emission spectroscopy, we
demonstrate optical generation of spin-polarized electric currents at the
interfaces of metallic ferromagnetic heterostructures at the femtosecond
timescale. The direction of the photocurrent is controlled by the helicity of
the circularly polarized light. These results open up new opportunities for
realizing spintronics in the unprecedented terahertz regime and provide new
insights in all-optical control of magnetism.Comment: 3 figures and 2 tables in the main tex
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