382 research outputs found
Sum Rules and Ward Identities in the Kondo Lattice
We derive a generalized Luttinger-Ward expression for the Free energy of a
many body system involving a constrained Hilbert space. In the large limit,
we are able to explicity write the entropy as a functional of the Green's
functions. Using this method we obtain a Luttinger sum rule for the Kondo
lattice. One of the fascinating aspects of the sum rule, is that it contains
two components, one describing the heavy electron Fermi surface, the other, a
sea of oppositely charged, spinless fermions. In the heavy electron state, this
sea of spinless fermions is completely filled and the electron Fermi surface
expands by one electron per unit cell to compensate the positively charged
background, forming a ``large'' Fermi surface. Arbitrarily weak magnetism
causes the spinless Fermi sea to annihilate with part of the Fermi sea of the
conduction electrons, leading to a small Fermi surface. Our results thus enable
us to show that the Fermi surface volume contracts from a large, to a small
volume at a quantum critical point. However, the sum rules also permit the
possible formation of a new phase, sandwiched between the antiferromagnet and
the heavy electron phase, where the charged spinless fermions develop a true
Fermi surface.Comment: 24 pages, 4 figures. Version two contains a proof of the "Entropy
formula" which connects the entropy directly to the Green's functions.
Version three contains corrections to typos and a more extensive discussion
of the physics at finite
Quantum replica approach to the under-screened Kondo model
We extend the Schwinger boson large N treatment of the underscreened Kondo
model in a way that correctly captures the finite elastic phase shift in the
singular Fermi liquid. The new feature of the approach, is the introduction of
a flavor quantum number with K possible values, associated with the Schwinger
boson representation. The large N limit is taken maintaining the ratio k=K/N
fixed. This approach differs from previous approaches, in that we do not
explicitly enforce a constraint on the spin representation of the Schwinger
bosons. Instead, the energetics of the Kondo model cause the bosonic degrees of
freedom to ``self assemble'' into a ground-state in which the spins of K bosons
and N-K conduction electrons are antisymmetrically arranged into a Kondo
singlet. With this device, the large N limit can be taken, in such a way that a
fraction K/N of the Abrikosov Suhl resonance is immersed inside the Fermi sea.
We show how this method can be used to model the full energy dependence of the
singular Abrikosov Suhl resonance in the underscreened Kondo model and the
field-dependent magnetization.Comment: Revised draft, with plots explicitly showing logarithmic scaling of
inverse coupling constant. Small corrections prior to submission to journa
Gapless Color Superconductivity
We present the dispersion relations for quasiparticle excitations about the
color-flavor locked ground state of QCD at high baryon density. In the presence
of condensates which pair light and strange quarks there need not be an energy
gap in the quasiparticle spectrum. This raises the possibility of gapless color
superconductivity, with a Meissner effect but no minimum excitation energy.
Analysis within a toy model suggests that gapless color superconductivity may
occur only as a metastable phase.Comment: 4 pages, Revtex, eps figures include
Nucleation of superconducting pairing states at mesoscopic scales at zero temperature
We find the spin polarized disordered Fermi liquids are unstable to the
nucleation of superconducting pairing states at mesoscopic scales even when
magnetic fields which polarize the spins are substantially higher than the
critical one. We study the probability of finding superconducting pairing
states at mesoscopic scales in this limit. We find that the distribution
function depends only on the film conductance. The typical length scale at
which pairing takes place is universal, and decreases when the magnetic field
is increased. The number density of these states determines the strength of the
random exchange interactions between mesoscopic pairing states.Comment: 11 pages, no figure
Fermi liquid identities for the Infinite U Anderson Model
We show how the electron gas methods of Luttinger, Ward and Nozi\`eres can be
applied to the infinite U Anderson impurity model within a Schwinger boson
treatment. Working to all orders in a 1/N expansion, we show how the Friedel
Langreth relationship, the Yamada-Yosida-Yoshimori and the Shiba-Korringa
relations can be derived, under the assumption that the spinon and holon fields
are gapped. One of the remarkable features of this treatment, is that the
Landau amplitudes depend on the exchange of low energy virtual spinons and
holons. We end the paper with a discussion on the extension of our approach to
the lattice, where the spinon-holon is expected to close at a quantum critical
point.Comment: 18 pages. Version 2 revised after referees comment
Anisotropy of Thermal Conductivity and Possible Signature of the Fulde-Ferrell-Larkin-Ovchinnikov state in CeCoIn_5
We have measured the thermal conductivity of the heavy-fermion superconductor
CeCoIn_5 in the vicinity of the upper critical field, with the magnetic field
perpendicular to the c axis. Thermal conductivity displays a discontinuous jump
at the superconducting phase boundary below critical temperature T_0 ~ 1 K,
indicating a change from a second to first order transition and confirming the
recent results of specific heat measurements on CeCoIn_5. In addition, the
thermal conductivity data as a function of field display a kink at a field H_k
below the superconducting critical field, which closely coincides with the
recently discovered anomaly in specific heat, tentatively identified with the
appearance of the spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov
(FFLO) superconducting state. Our results indicate that the thermal
conductivity is enhanced within the FFLO state, and call for further
theoretical investigations of the order parameter's real space structure (and,
in particular, the structure of vortices) and of the thermal transport within
the inhomogeneous FFLO state.Comment: 19 pages, 6 figures, submitted to Prhys. Rev.
Andreev magnetotransport in low-dimensional proximity structures: Spin-dependent conductance enhancement
We study the excess conductance due to the superconducting proximity effect
in a ballistic two-dimensional electron system subject to an in-plane magnetic
field. We show that under certain conditions the interplay of the Zeeman spin
splitting and the effect of a screening supercurrent gives rise to a
spin-selective Andreev enhancement of the conductance and anomalies in its
voltage, temperature and magnetic field characteristics. The magnetic-field
influence on Andreev reflection is discussed in the context of using
superconducting hybrid junctions for spin detection.Comment: 4 pages, 5 figure
Universal Spin-Flip Transition in Itinerant Antiferromagnets
We report a universal spin flip (SF) transition as a function of temperature
in spin-density-wave (SDW) systems. At low temperatures the antiferromagnetic
(AFM) polarization is parallel to the applied field and above a critical
temperature the AFM polarization {\it flips} perpendicular to the field. This
transition occurs in {\it any} SDW system and may be considered as a
qualitative probe of the itinerant character of AFM in a given material. Our SF
transition resolves the longstanding puzzle of the SF transition observed in
cromium and may be at the origin of the equally puzzling SDW-I to SDW-II
transition in Bechgaard salts for which we make experimental predictions
Non-equilibrium Differential Conductance through a Quantum Dot in a Magnetic Field
We derive an exact expression for the differential conductance for a quantum
dot in an arbitrary magnetic field for small bias voltage. The derivation is
based on the symmetric Anderson model using renormalized perturbation theory
and is valid for all values of the on-site interaction including the Kondo
regime. We calculate the critical magnetic field for the splitting of the Kondo
resonance to be seen in the differential conductivity as function of bias
voltage. Our calculations for small field show that the peak position of the
component resonances in the differential conductance are reduced substantially
from estimates using the equilibrium Green's function. We conclude that it is
important to take the voltage dependence of the local retarded Green's function
into account in interpreting experimental resultsComment: 8 pages, 4 figures; Replaced by a fully revised version with minor
corrections in the tex
Nonperturbative Scaling Theory of Free Magnetic Moment Phases in Disordered Metals
The crossover between a free magnetic moment phase and a Kondo phase in low
dimensional disordered metals with dilute magnetic impurities is studied.
We perform a finite size scaling analysis of the distribution of the Kondo
temperature as obtained from a numerical renormalization group calculation of
the local magnetic susceptibility and from the solution of the self-consistent
Nagaoka-Suhl equation. We find a sizable fraction of free (unscreened) magnetic
moments when the exchange coupling falls below a disorder-dependent critical
value . Our numerical results show that between the free moment
phase due to Anderson localization and the Kondo screened phase there is a
phase where free moments occur due to the appearance of random local pseudogaps
at the Fermi energy whose width and power scale with the elastic scattering
rate .Comment: 4 pages, 6 figure
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