39 research outputs found
Quasiparticle picture of high temperature superconductors in the frame of Fermi liquid with the fermion condensate
A model of a Fermi liquid with the fermion condensate (FC) is applied to the
consideration of quasiparticle excitations in high temperature superconductors,
in their superconducting and normal states. Within our model the appearance of
the fermion condensate presents a quantum phase transition, that separates the
regions of normal and strongly correlated electron liquids. Beyond the phase
transition point the quasiparticle system is divided into two subsystems, one
containing normal quasiparticles and the other --- fermion condensate localized
at the Fermi surface and characterized by almost dispersionless single-particle
excitations. In the superconducting state the quasiparticle dispersion in
systems with FC can be presented by two straight lines, characterized by
effective masses and , respectively, and intersecting near
the binding energy which is of the order of the superconducting gap. This same
quasiparticle picture persists in the normal state, thus manifesting itself
over a wide range of temperatures as new energy scales. Arguments are presented
that fermion systems with FC have features of a quantum protectorate.Comment: 12 pages, Late
- Pairing in Dense Neutron Matter: The Spectrum of Solutions
The - pairing model is generally considered to provide an
adequate description of the superfluid states of neutron matter at densities
some 2-3 times that of saturated symmetrical nuclear matter. The problem of
solving the system of BCS gap equations expressing the - model is
attacked with the aid of the separation approach. This method, developed
originally for quantitative study of S-wave pairing in the presence of strong
short-range repulsions, serves effectively to reduce the coupled, singular,
nonlinear BCS integral equations to a set of coupled algebraic equations. For
the first time, sufficient precision becomes accessible to resolve small energy
splittings between the different pairing states. Adopting a perturbative
strategy, we are able to identify and characterize the full repertoire of real
solutions of the - pairing model, in the limiting regime of small
tensor-coupling strength. The P-F channel coupling is seen to lift the striking
parametric degeneracies revealed by a earlier separation treatment of the pure,
uncoupled pairing problem. Remarkably, incisive and robust results are
obtained solely on the basis of analytic arguments. Unlike the traditional
Ginzburg-Landau approach, the analysis is not restricted to the immediate
vicinity of the critical temperature, but is equally reliable at zero
temperature. Interesting connections and contrasts are drawn between triplet
pairing in dense neutron matter and triplet pairing in liquid He.Comment: 23 pages, 1 figur
Entropy paradox in strongly correlated Fermi systems
A system of interacting, identical fermions described by standard Landau
Fermi-liquid (FL) theory can experience a rearrangement of its Fermi surface if
the correlations grow sufficiently strong, as occurs at a quantum critical
point where the effective mass diverges. As yet, this phenomenon defies full
understanding, but salient aspects of the non-Fermi-liquid (NFL) behavior
observed beyond the quantum critical point are still accessible within the
general framework of the Landau quasiparticle picture. Self-consistent
solutions of the coupled Landau equations for the quasiparticle momentum
distribution and quasiparticle energy spectrum are shown
to exist in two distinct classes, depending on coupling strength and on whether
the quasiparticle interaction is regular or singular at zero momentum transfer.
One class of solutions maintains the idempotency condition of
standard FL theory at zero temperature while adding pockets to the Fermi
surface. The other solutions are characterized by a swelling of the Fermi
surface and a flattening of the spectrum over a range of momenta
in which the quasiparticle occupancies lie between 0 and 1 even at T=0. The
latter, non-idempotent solution is revealed by analysis of a Poincar\'e mapping
associated with the fundamental Landau equation connecting and
and validated by solution of a variational condition that yields
the symmetry-preserving ground state. Paradoxically, this extraordinary
solution carries the burden of a large temperature-dependent excess entropy
down to very low temperatures, threatening violation of the Nernst Theorem. It
is argued that certain low-temperature phase transitions offer effective
mechanisms for shedding the entropy excess. Available measurements in
heavy-fermion compounds provide concrete support for such a scenario.Comment: 34 pages, 6 figure
Neutron matter with a model interaction
An infinite system of neutrons interacting by a model pair potential is
considered. We investigate a case when this potential is sufficiently strong
attractive, so that its scattering length tends to infinity. It appeared, that
if the structure of the potential is simple enough, including no finite
parameters, reliable evidences can be presented that such a system is
completely unstable at any finite density. The incompressibility as a function
of the density is negative, reaching zero value when the density tends to zero.
If the potential contains a sufficiently strong repulsive core then the system
possesses an equilibrium density. The main features of a theory describing such
systems are considered.Comment: 8 pages, LaTeX. In press, Eur. Phys. J.
Energy scales and magnetoresistance at a quantum critical point
The magnetoresistance (MR) of CeCoIn_5 is notably different from that in many
conventional metals. We show that a pronounced crossover from negative to
positive MR at elevated temperatures and fixed magnetic fields is determined by
the scaling behavior of quasiparticle effective mass. At a quantum critical
point (QCP) this dependence generates kinks (crossover points from fast to slow
growth) in thermodynamic characteristics (like specific heat, magnetization
etc) at some temperatures when a strongly correlated electron system transits
from the magnetic field induced Landau Fermi liquid (LFL) regime to the
non-Fermi liquid (NFL) one taking place at rising temperatures. We show that
the above kink-like peculiarity separates two distinct energy scales in QCP
vicinity - low temperature LFL scale and high temperature one related to NFL
regime. Our comprehensive theoretical analysis of experimental data permits to
reveal for the first time new MR and kinks scaling behavior as well as to
identify the physical reasons for above energy scales.Comment: 7 pages, 6 figure
Interaction of the single-particle and collective degrees of freedom in non-magic nuclei: the role of phonon tadpole terms
A method of a consistent consideration of the phonon contributions to mass
and gap operators in non-magic nuclei is developed in the so-called g^2
approximation, where g is the low-lying phonon creation amplitude. It includes
simultaneous accounting for both the usual non-local terms and the phonon
tadpole ones. The relations which allow the tadpoles to be calculated without
any new parameters are derived. As an application of the results, the role of
the phonon tadpoles in the single-particle strength distribution and in the
single-particle energies and gap values has been considered. Relation to the
problem of the surface nature of pairing is discussed.Comment: 22 pages, 7 figure
Elimination of spurious states in the quasiparticle time blocking approximation
The quasiparticle time blocking approximation (QTBA) is considered as a model
for the description of excitations in open-shell nuclei. The QTBA is an
extension of the quasiparticle random phase approximation that includes
quasiparticle-phonon coupling. In the present version of the QTBA, the pairing
correlations are included within the framework of the BCS approximation. Thus,
in this model, the spurious states appear, which are caused by the
breaking of the symmetry related to the particle-number conservation. In this
work, the method is described which solves the problem of the spurious
states in the QTBA with the help of the projection technique. The method is
illustrated by calculations of excitations in Sn nucleus.Comment: 12 pages, 3 figures - To appear in the proceedings of the 59-th
International Meeting on Nuclear Spectroscopy and Nuclear Structure, June
15-19, 2009, Cheboksary, Russi
Triplet Pairing in Neutron Matter
The separation method developed earlier by us [Nucl. Phys. {\bf A598} 390
(1996)] to calculate and analyze solutions of the BCS gap equation for
S pairing is extended and applied to P--F pairing in
pure neutron matter. The pairing matrix elements are written as a separable
part plus a remainder that vanishes when either momentum variable is on the
Fermi surface. This decomposition effects a separation of the problem of
determining the dependence of the gap components in a spin-angle representation
on the magnitude of the momentum (described by a set of functions independent
of magnetic quantum number) from the problem of determining the dependence of
the gap on angle or magnetic projection. The former problem is solved through a
set of nonsingular, quasilinear integral equations, providing inputs for
solution of the latter problem through a coupled system of algebraic equations
for a set of numerical coefficients. An incisive criterion is given for finding
the upper critical density for closure of the triplet gap. The separation
method and its development for triplet pairing exploit the existence of a small
parameter, given by a gap-amplitude measure divided by the Fermi energy. The
revised BCS equations admit analysis revealing universal properties of the full
set of solutions for P pairing in the absence of tensor coupling,
referring especially to the energy degeneracy and energetic order of these
solutions. The angle-average approximation introduced by Baldo et al. is
illuminated in terms of the separation-transformed BCS problem and the small
parameter expansion..
Nodes of the Gap Function and Anomalies in Thermodynamic Properties of Superfluid He
Departures of thermodynamic properties of three-dimensional superfluid He
from the predictions of BCS theory are analyzed. Attention is focused on
deviations of the ratios and
from their BCS values, where is the pairing gap at zero
temperature, is the critical temperature, and and are the
superfluid and normal specific heats. We attribute these deviations to the
momentum dependence of the gap function , which becomes well
pronounced when this function has a pair of nodes lying on either side of the
Fermi surface. We demonstrate that such a situation arises if the P-wave
pairing interaction , evaluated at the Fermi surface, has a sign
opposite to that anticipated in BCS theory. Taking account of the momentum
structure of the gap function, we derive a closed relation between the two
ratios that contains no adjustable parameters and agrees with the experimental
data. Some important features of the effective pairing interaction are inferred
from the analysis.Comment: 17 pages, 4 figure
Adaptation of the Landau-Migdal Quasiparticle Pattern to Strongly Correlated Fermi Systems
A quasiparticle pattern advanced in Landau's first article on Fermi liquid
theory is adapted to elucidate the properties of a class of strongly correlated
Fermi systems characterized by a Lifshitz phase diagram featuring a quantum
critical point (QCP) where the density of states diverges. The necessary
condition for stability of the Landau Fermi Liquid state is shown to break down
in such systems, triggering a cascade of topological phase transitions that
lead, without symmetry violation, to states with multi-connected Fermi
surfaces. The end point of this evolution is found to be an exceptional state
whose spectrum of single-particle excitations exhibits a completely flat
portion at zero temperature. Analysis of the evolution of the temperature
dependence of the single-particle spectrum yields results that provide a
natural explanation of classical behavior of this class of Fermi systems in the
QCP region.Comment: 26 pages, 14 figures. Dedicated to 100th anniversary of A.B.Migdal
birthda