1,020 research outputs found
Spin Orbit Magnetism and Unconventional Superconductivity
We find an exotic spin excitation in a magnetically ordered system with spin
orbit magnetism in 2D, where the order parameter has a net spin current and no
net magnetization. Starting from a Fermi liquid theory, similar to that for a
weak ferromagnet, we show that this excitation emerges from an exotic magnetic
Fermi liquid state that is protected by a generalized Pomeranchuck condition.
We derive the propagating mode using the Landau kinetic equation, and find that
the dispersion of the mode has a behavior in leading order in 2D. We
find an instability toward superconductivity induced by this exotic mode, and a
further analysis based on the forward scattering sum rule strongly suggests
that this superconductivity has p-wave pairing symmetry. We perform similar
studies in the 3D case, with a slightly different magnetic system and find that
the mode leads to a Lifshitz-like instability most likely toward an
inhomogeneous magnetic state in one of the phases.Comment: 5 pages, 3 figure
Quantum spin transport and dynamics through a novel F/N junction
We study the spin transport in the low temperature regime (often referred to
as the precession-dominated regime) between a ferromagnetic Fermi liquid (FFL)
and a normal metal metallic Fermi liquid (NFL), also known as the F/N junction,
which is considered as one of the most basic spintronic devices. In particular,
we explore the propagation of spin waves and transport of magnetization through
the interface of the F/N junction where nonequilibrium spin polarization is
created on the normal metal side of the junction by electrical spin injection.
We calculate the probable spin wave modes in the precession-dominated regime on
both sides of the junction especially on the NFL side where the system is out
of equilibrium. Proper boundary conditions at the interface are introduced to
establish the transport of the spin properties through the F/N junction. A
possible transmission conduction electron spin resonance (CESR) experiment is
suggested on the F/N junction to see if the predicted spin wave modes could
indeed propagate through the junction. Potential applications based on this
novel spin transport feature of the F/N junction are proposed in the end.Comment: 7 pages, 2 figure
Non-Analytic Contributions to the Self-Energy and the Thermodynamics of Two-Dimensional Fermi Liquids
We calculate the entropy of a two-dimensional Fermi Liquid(FL) using a model
with a contact interaction between fermions. We find that there are
contributions to the entropy from interactions separate from those due to the
collective modes. These contributions arise from non-analytic corrections
to the real part of the self-energy which may be calculated from the leading
log dependence of the imaginary part of the self-energy through the
Kramers-Kronig relation. We find no evidence of a breakdown in Fermi Liquid
theory in 2D and conclude that FL in 2D are similar to 3D FL's.Comment: 12 pages (RexTex, no figures
Introduction to the Theory of -ODEs
We study the theory of ordinary differential equations over a commutative
finite dimensional real associative unital algebra . We call such
problems -ODEs. If a function is real differentiable and its
differential is in the regular representation of then we say the
function is -differentiable. In this paper, we prove an existence
and uniqueness theorem, derive Abel's formula for the Wronskian and establish
the existence of a fundamental solution set for many -ODEs. We
show the Wronskian of a fundamental solution set cannot be a divisor of zero.
Three methods to solve nondegenerate constant coefficient -ODE are
given. First, we show how zero-divisors complicate solution by factorization of
operators. Second, isomorphisms to direct product are shown to produce
interesting solutions. Third, our extension technique is shown to solve any
nondegenerate -ODE; we find a fundamental solution set by
selecting the component functions of the exponential on the characteristic
extension algebra. The extension technique produces all of the elementary
functions seen in the usual analysis by a bit of abstract algebra applied to
the appropriate exponential function. On the other hand, we show how
zero-divisors destroy both existence and uniqueness in degenerate
-ODEs. We also study the Cauchy Euler problem for
-Calculus and indicate how we may solve first order
-ODEs.Comment: 33 page
Exotic quantum statistics and thermodynamics from a number-conserving theory of Majorana fermions
We propose a closed form for the statistical distribution of non-interacting
Majorana fermions at low temperature. Majorana particles often appear in the
contemporary many-body literature in the Kitaev, Fu-Kane, or Sachdev-Ye-Kitaev
models, where the Majorana condition of self-conjugacy immediately results in
nonconserved particle number, non-trivial braiding statistics, and the absence
of a noninteracting limit. We deviate from this description and instead
consider a gas of noninteracting, spin-1/2 Majorana fermions that obey the
spin-statistics theorem via imposing a condensed matter analog of momentum
conservation. This allows us to build a quantum statistical theory of the
Majorana system in the low temperature, low density limit without the need to
account for strong fluctuations in the particle number. A combinatorial
analysis leads to a configurational entropy which deviates from the fermionic
result with an increasing number of available microstates. A number-conserving
Majorana distribution function is derived which shows signatures of a
sharply-defined Fermi surface at finite temperatures. Such a distribution is
then re-derived from a microscopic model in the form of a modified Kitaev chain
with a bosonic pair interaction. The thermodynamics of this free Majorana
system is found to be nearly identical to that of a free Fermi gas, except now
distinguished by a two-fold ground state degeneracy and, subsequently, a
residual entropy at zero temperature. Despite clear differences with the
anyonic or Sachdev-Ye-Kitaev models, we nevertheless find surprising agreement
between our theory and experimental signatures of Majorana excitations in
several materials. Experimental realization of our exactly solvable model is
also discussed in the realm of astrophysical and high-energy phenomena.Comment: 66 pages, 7 figures, 5 table
Universal Signatures of Majorana-like Quasiparticles in Strongly Correlated Landau-Fermi Liquids
Motivated by recent experiments in the Kitaev honeycomb lattice, Kondo
insulators, and the "Luttinger's theorem-violating" Fermi liquid phase of the
underdoped cuprates, we extend the theoretical machinery of Landau-Fermi liquid
theory to a system of itinerant, interacting Majorana-like particles. Building
upon a previously introduced model of "nearly self-conjugate" fermionic
polarons, a Landau-Majorana kinetic equation is introduced to describe the
collective modes and Fermi surface instabilities in a fluid of particles whose
fermionic degrees of freedom obey the Majorana reality condition. At large
screening, we show that the Landau-Majorana liquid harbors a Lifshitz
transition for specific values of the driving frequency. Moreover, we find the
dispersion of the zero sound collective mode in such a system, showing that
there exists a specific limit where the Landau-Majorana liquid harbors a
stability against Pomeranchuk deformations unseen in the conventional
Landau-Fermi liquid. With these results, our work paves the way for possible
extensions of the Landau quasiparticle paradigm to nontrivial metallic phases
of matter.Comment: 31 pages, 4 figures. Previously titled "Collective Excitations and
Robust Stability in a Landau-Majorana Liquid
Orbital Zeeman effect: Signature of a massive spin wave mode in ferromagnetism
By deriving the quantum hydrodynamic equations for an isotropic single-band
ferromagnet in an arbitrary magnetic field, we find that a massive mode
recently predicted splits under the action of the field. The splitting is a
peculiarity of charged fermions and is linear in the field to leading order in
bearing resemblance to the Zeeman effect in this limit, and providing a
clear signature for the experimental observation of this mode
Quantum spin hydrodynamics and a new spin-current mode in ferromagnetic metals
We derive the quantum spin hydrodynamic equations in a ferromagnetic metal.
From these equations we show the existence of a new massive spin-current
mode. This mode can be observed in neutron scattering experiments and we
discuss the difficulties in seeing it. At the end we discuss the existence of
this mode in localized ferromagnets
Fermi liquid behavior and Luttinger's theorem close to a diverging scattering length
Based on the results obtained in a previous paper (S. Gaudio et al.,
cond-mat/0505309}, we derive the thermodynamic properties of a Fermi gas, deep
into the quantum degenerate regime. We show that, if Luttinger's theorem holds,
a first order phase transition occurs in the normal phase as a function of the
interaction strength, U. We also show that a volume change occurs at finite
temperatures from the BEC to the BCS side of a diverging s-wave scattering
length, in the normal phase. The transition has an end point above the BCS
critical temperature. Also we show that a paramagnetic system in equilibrium,
close to the divergence of the scattering length, on the negative side, screens
out any applied magnetic field.Comment: 5 pages, 4 figure
Superfluid (Amplitude) Fluctuations Above in a Unitary Fermi Gas
We study the transport properties of a Fermi gas with strong attractive
interactions close to the unitary limit. In particular, we compute the spin
diffusion lifetime of the Fermi gas due to superfluid fluctuations above the
BCS transition temperature . To calculate the spin diffusion lifetime we
need the scattering amplitudes. The scattering amplitudes are dominated by the
superfluid fluctuations at temperatures just above . The normal scattering
amplitudes are calculated from the Landau parameters. These Landau parameters
are obtained from the local version of the induced interaction model for
computing Landau parameters. We also calculate the leading order finite
temperature correction to the diffusion lifetime. A calculation of the spin
diffusion coefficient is presented in the end. Upon choosing a proper value of
, we are able to present a good match between the theoretical result and
the experimental measurement which indicates the presence of the superfluid
fluctuations near .Comment: 5 pages, 4 figure
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