4,957 research outputs found
Valley contrasting physics in graphene: magnetic moment and topological transport
We investigate physical properties that can be used to distinguish the valley
degree of freedom in systems where inversion symmetry is broken, using graphene
systems as examples. We show that the pseudospin associated with the valley
index of carriers has an intrinsic magnetic moment, in close analogy with the
Bohr magneton for the electron spin. There is also a valley dependent Berry
phase effect that can result in a valley contrasting Hall transport, with
carriers in different valleys turning into opposite directions transverse to an
in-plane electric field. These effects can be used to generate and detect
valley polarization by magnetic and electric means, forming the basis for the
so-called valley-tronics applications
Berry Phase Effects on Electronic Properties
Ever since its discovery, the Berry phase has permeated through all branches
of physics. Over the last three decades, it was gradually realized that the
Berry phase of the electronic wave function can have a profound effect on
material properties and is responsible for a spectrum of phenomena, such as
ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall
effects, and quantum charge pumping. This progress is summarized in a
pedagogical manner in this review. We start with a brief summary of necessary
background, followed by a detailed discussion of the Berry phase effect in a
variety of solid state applications. A common thread of the review is the
semiclassical formulation of electron dynamics, which is a versatile tool in
the study of electron dynamics in the presence of electromagnetic fields and
more general perturbations. Finally, we demonstrate a re-quantization method
that converts a semiclassical theory to an effective quantum theory. It is
clear that the Berry phase should be added as a basic ingredient to our
understanding of basic material properties.Comment: 48 pages, 16 figures, submitted to RM
Expectile Matrix Factorization for Skewed Data Analysis
Matrix factorization is a popular approach to solving matrix estimation
problems based on partial observations. Existing matrix factorization is based
on least squares and aims to yield a low-rank matrix to interpret the
conditional sample means given the observations. However, in many real
applications with skewed and extreme data, least squares cannot explain their
central tendency or tail distributions, yielding undesired estimates. In this
paper, we propose \emph{expectile matrix factorization} by introducing
asymmetric least squares, a key concept in expectile regression analysis, into
the matrix factorization framework. We propose an efficient algorithm to solve
the new problem based on alternating minimization and quadratic programming. We
prove that our algorithm converges to a global optimum and exactly recovers the
true underlying low-rank matrices when noise is zero. For synthetic data with
skewed noise and a real-world dataset containing web service response times,
the proposed scheme achieves lower recovery errors than the existing matrix
factorization method based on least squares in a wide range of settings.Comment: 8 page main text with 5 page supplementary documents, published in
AAAI 201
Minimal field requirement in precessional magnetization switching
We investigate the minimal field strength in precessional magnetization
switching using the Landau-Lifshitz-Gilbert equation in under-critically damped
systems. It is shown that precessional switching occurs when localized
trajectories in phase space become unlocalized upon application of field
pulses. By studying the evolution of the phase space, we obtain the analytical
expression of the critical switching field in the limit of small damping for a
magnetic object with biaxial anisotropy. We also calculate the switching times
for the zero damping situation. We show that applying field along the medium
axis is good for both small field and fast switching times.Comment: 6 pages, 7 figure
Topological Classification of Crystalline Insulators with Point Group Symmetry
We show that in crystalline insulators point group symmetry alone gives rise
to a topological classification based on the quantization of electric
polarization. Using C3 rotational symmetry as an example, we first prove that
the polarization is quantized and can only take three inequivalent values.
Therefore, a Z3 topological classification exists. A concrete tight-binding
model is derived to demonstrate the Z3 topological phase transition. Using
first-principles calculations, we identify graphene on BN substrate as a
possible candidate to realize the Z3 topological states. To complete our
analysis we extend the classification of band structures to all 17
two-dimensional space groups. This work will contribute to a complete theory of
symmetry conserved topological phases and also elucidate topological properties
of graphene like systems
Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems
Based on standard perturbation theory, we present a full quantum derivation
of the formula for the orbital magnetization in periodic systems. The
derivation is generally valid for insulators with or without a Chern number,
for metals at zero or finite temperatures, and at weak as well as strong
magnetic fields. The formula is shown to be valid in the presence of
electron-electron interaction, provided the one-electron energies and wave
functions are calculated self-consistently within the framework of the exact
current and spin density functional theory.Comment: Accepted by Phys. Rev. Let
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