643 research outputs found
Effects of Zeeman spin splitting on the modular symmetry in the quantum Hall effect
Magnetic-field-induced phase transitions in the integer quantum Hall effect
are studied under the formation of paired Landau bands arising from Zeeman spin
splitting. By investigating features of modular symmetry, we showed that
modifications to the particle-hole transformation should be considered under
the coupling between the paired Landau bands. Our study indicates that such a
transformation should be modified either when the Zeeman gap is much smaller
than the cyclotron gap, or when these two gaps are comparable.Comment: 8 pages, 4 figure
An RG potential for the quantum Hall effects
The phenomenological analysis of fully spin-polarized quantum Hall systems,
based on holomorphic modular symmetries of the renormalization group (RG) flow,
is generalized to more complicated situations where the spin or other "flavors"
of charge carriers are relevant, and where the symmetry is different. We make
the simplest possible ansatz for a family of RG potentials that can interpolate
between these symmetries. It is parametrized by a single number and we show
that this suffices to account for almost all scaling data obtained to date. The
potential is always symmetric under the main congruence group at level two, and
when takes certain values this symmetry is enhanced to one of the maximal
subgroups of the modular group. We compute the covariant RG -function,
which is a holomorphic vector field derived from the potential, and compare the
geometry of this gradient flow with available temperature driven scaling data.
The value of is determined from experiment by finding the location of a
quantum critical point, i.e., an unstable zero of the -function given by
a saddle point of the RG potential. The data are consistent with , which together with the symmetry leads to a generalized
semi-circle law.Comment: 10 figures, sligthly updated discussion and refs, accepted for PR
Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling
In this work, we explore the rich variety of topological states that arise in
two-dimensional systems, by considering the competing effects of spin-orbit
couplings and a perpendicular magnetic field on a honeycomb lattice. Unlike
earlier approaches, we investigate minimal models in order to clarify the
effects of the intrinsic and Rashba spin-orbit couplings, and also of the
Zeeman splitting, on the quantum Hall states generated by the magnetic field.
In this sense, our work provides an interesting path connecting quantum Hall
and quantum spin Hall physics. First, we consider the properties of each term
individually and we analyze their similarities and differences. Secondly, we
investigate the subtle competitions that arise when these effects are combined.
We finally explore the various possible experimental realizations of our model.Comment: 19 pages, 15 figure
Van der Waals Engineering of Ferromagnetic Semiconductor Heterostructures for Spin and Valleytronics
The integration of magnetic material with semiconductors has been fertile
ground for fundamental science as well as of great practical interest toward
the seamless integration of information processing and storage. Here we create
van der Waals heterostructures formed by an ultrathin ferromagnetic
semiconductor CrI3 and a monolayer of WSe2. We observe unprecedented control of
the spin and valley pseudospin in WSe2, where we detect a large magnetic
exchange field of nearly 13 T and rapid switching of the WSe2 valley splitting
and polarization via flipping of the CrI3 magnetization. The WSe2
photoluminescence intensity strongly depends on the relative alignment between
photo-excited spins in WSe2 and the CrI3 magnetization, due to ultrafast
spin-dependent charge hopping across the heterostructure interface. The
photoluminescence detection of valley pseudospin provides a simple and
sensitive method to probe the intriguing domain dynamics in the ultrathin
magnet, as well as the rich spin interactions within the heterostructure.Comment: Supplementary Materials included. To appear in Science Advance
The Quantum Hall Effect in Graphene: Emergent Modular Symmetry and the Semi-circle Law
Low-energy transport measurements in Quantum Hall systems have been argued to
be governed by emergent modular symmetries whose predictions are robust against
many of the detailed microscopic dynamics. We propose the recently-observed
quantum Hall effect in graphene as a test of these ideas, and identify to this
end a class of predictions for graphene which would follow from the same
modular arguments. We are led to a suite of predictions for high mobility
samples that differs from those obtained for the conventional quantum Hall
effect in semiconductors, including: predictions for the locations of the
quantum Hall plateaux; predictions for the positions of critical points on
transitions between plateaux; a selection rule for which plateaux can be
connected by low-temperature transitions; and a semi-circle law for
conductivities traversed during these transitions. Many of these predictions
appear to provide a good description of graphene measurements performed with
intermediate-strength magnetic fields.Comment: 4 pages, 2 figure
Spin - or, actually: Spin and Quantum Statistics
The history of the discovery of electron spin and the Pauli principle and the
mathematics of spin and quantum statistics are reviewed. Pauli's theory of the
spinning electron and some of its many applications in mathematics and physics
are considered in more detail. The role of the fact that the tree-level
gyromagnetic factor of the electron has the value g = 2 in an analysis of
stability (and instability) of matter in arbitrary external magnetic fields is
highlighted. Radiative corrections and precision measurements of g are
reviewed. The general connection between spin and statistics, the CPT theorem
and the theory of braid statistics are described.Comment: 50 pages, no figures, seminar on "spin
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