Fermi Liquid Model Research Articles

Triplanar model for the gap and penetration depth inYBa2Cu3O7s

${\mathrm{YBaCuO}}_{7}$ is a trilayer material with a unit cell consisting of a ${\mathrm{CuO}}_{2}$ bilayer with a CuO plane of chains in between. Starting with a model of isolated planes coupled through a transverse matrix element, we consider the possibility of intra- as well as interplane pairing within a nearly antiferromagnetic Fermi-liquid model. Solutions of a set of three coupled BCS equations for the gap exhibit orthorhombic symmetry with s- as well as d-wave contributions. The temperature dependence and a-b in-plane anisotropy of the resulting penetration depth is discussed and compared with experiment.

On the almost localized Fermi liquid model for 3He

A new model for normal degenerate liquid 3He based on the variational Gutzwiller approach is proposed. The internal energy of liquid 3He at T = 0 K is calculated. It is shown that the theoretical P- V diagram is consistent with experimental data.

Low-temperature NMR studies of strongly correlated electron systems

The low-temperature properties of some f-electron alloys, in composition close to compounds exhibiting low-temperature instabilities, have been found to diverge from the predictions of simple Fermi-liquid models. We discuss the cases of Y 0.8U 0.2Pd 3 and UCu 3.5Pd 1.5 for which thermal and transport properties display significant departures from Fermi-liquid behaviour and provide some preliminary microscopic evidence for anomalous behaviour obtained by measuring NMR relaxation rates T 1 −1 below 1 K. We have also studied CePd 2In in which, below 1.2 K, small moment antiferromagnetic order coexists with a substantial amount of Kondo screening. Both the magnetic order and the Kondo screening are strongly suppressed by external magnetic fields of the order of 4 T. Finally, we discuss the case of CeAl 3 where microscopically a strange inhomogeneous electronic ground state, characterised by the coexistence of two magnetically inequivalent phases, has been identified.

Temperature crossovers in cuprates

We study the temperature crossovers seen in the magnetic and transport properties of cuprates using a nearly antiferromagnetic Fermi-liquid model (NAFLM). We distinguish between underdoped and overdoped systems on the basis of their low-frequency magnetic behaviour and so classify the optimally doped cuprates as a special case of the underdoped cuprates. For the overdoped cuprates, we find, in agreement with earlier work, mean-field z = 2 behaviour of the magnetic variables associated with the fact that the damping rate of their spin fluctuations is essentially independent of temperature, while the resistivity exhibits a crossover from Fermi-liquid behaviour at low temperature to linear-in-T behaviour above a certain temperature . We demonstrate that above the proximity of the quasiparticle Fermi surface to the magnetic Brillouin zone boundary brings about the measured linear-in-T resistivity. For the underdoped cuprates we argue that the sequence of crossovers identified by Barzykin and Pines in the low-frequency magnetic behaviour (from mean-field z = 2 behaviour at high temperatures, , to non-universal z = 1 scaling behaviour at intermediate temperatures, , to pseudogap behaviour below ) reflects the development in the electronic structure of a precursor to a spin-density-wave state. This development begins at with a thermal evolution of the quasiparticle spectral weight which brings about temperature-dependent spin damping and ends at where the Fermi surface has lost pieces near corners of the magnetic Brillouin zone. For the resistivity is linear in T because this change in spectral weight does not affect the resistivity significantly; below vertex corrections act to bring about the measured downturn in and approximately quadratic-in-T resistivity for .

Spin pseudo-gap and z = 1 pseudo-scaling in cuprate superconductors

Abstract We determine the magnetic phase diagram for the YBa2Cu3O6+x and La2-xSrxCuO4 systems from nuclear magnetic resonance (NMR) experiments. We show that there is an extensive temperature regime in metallic underdoped cuprates in which the behaviour of the dynamic magnetic response function is qualitatively similar to the z = 1 quantum critical scaling for the insulator, where the characteristic energy scale is set by temperature, and the correlation length ξ ∞ 1/T. Quantitatively, however, the universal ratios predicted from the z = 1 scaling theory turn out to be non-universal in experiment, so that what is being measured is perhaps best described as z = 1 pseudo-scaling. We discuss a possible interpretation of the observed temperature dependences of the NMR relaxation rates in terms of the nearly antiferromagnetic Fermi-liquid model.

Nuclear shape fluctuations in Fermi-liquid drop model

Within the nuclear Fermi-liquid drop model, quantum and thermal fluctuations are considered using the Landau-Vlasov-Langevin equation. The spectral correlation function of the nuclear surface fluctuations is evaluated in a simple model of and incompressible anrotational Fermi liquid. The dependence of the spectral correlation function on the dynamical Fermi-surface distortion is established. The temperature at which the eigenvibrations become overdamped is calculated. It is shown that, for realistic values of the relaxation time parameter and in the high-temperature regime, there is a particular eigenmode of the Fermi-liquid drop where the restoring force is exclusively due to the dynamical Fermi-surface distortion.

Quantum Oscillations in the Layered Perovskite Superconductor Sr2RuO4

We report a comprehensive study of magneto-oscillatory phenomena in the normal state of S${\mathrm{r}}_{2}$Ru${\mathrm{O}}_{4}$, the first layered perovskite superconductor $({T}_{c}\ensuremath{\cong}1\mathrm{K})$ not based on copper. The form of the quasiparticle spectrum observed may be interpreted in terms of an almost two-dimensional Fermi liquid model which is consistent with Luttinger's theorem and successfully predicts bulk thermodynamic and transport properties at low temperatures. A study of the spectra and transport along the c axis provides insights into the different normal state and superconducting behavior of S${\mathrm{r}}_{2}$Ru${\mathrm{O}}_{4}$ and the cuprates.

Fermi liquid description of the anomalous magnetic susceptibility of FeSi

The Fermi liquid model of itinerant electron magnetism is applied to the calculation of the magnetic susceptibility of narrow gap semiconductors. The anomalous temperature dependence of susceptibility as has been observed for FeSi is obtained. It is shown that the Fermi liquid effect which gives rise to the susceptibility maximum in metals, also plays a crucial role in the susceptibility maximum in narrow gap systems.

The exchange and correlation contribution to the electron - electron scattering part of the thermal resistivity in alkali metals

We have calculated the pressure-dependent electron - electron scattering part of the thermal resistivity, , for three alkali metals, Li, Na and K, using a Fermi liquid model. Within this model, the electron - electron interaction is given by self-energy derivatives. A first-order perturbation expansion of the self-energy gives the commonly used GW-approximation. We have compared this with a -approximation, where is a vertex correction. By using a sum rule, we show that the -approximation should be preferred in calculating the electron - electron interaction. We use four different static dielectric functions, describing the exchange and correlation, in the screening potential W, namely the RPA function, the SSTL function, an LDA function and a Hubbard modified version of the LDA function, HUB. We have also calculated the exchange and correlation contribution including dynamic dielectric functions, within the GW-approximation. The results for the sum rule indicate that the dynamic approximation that we use is not suitable for calculating the electron - electron interaction. The thermal resistivity is calculated in the pressure region 0 - 120 kbar for Na and K, and in the region 0 - 100 kbar for Li. The LDA dielectric function gives results for for Li and K that are 10 to 20 times higher than the other dielectric functions, and also compared to experimental results. This has its origin in the approximation for the function, which breaks down for small enough densities, when the electron density parameter is . The SSTL and Hubbard functions show quite similar behaviour for all three of the metals, except for at higher pressures in K ( kbar), where the SSTL function causes a more rapid increase in . The RPA function, finally, gives a similar behaviour to the SSTL and Hubbard functions in for Na and K, while it results in a lowering of of for Li. We have also calculated the quasiparticle mass and the magnetic susceptibility, and compared these with experiment. Even in these cases it is the LDA function that gives the largest deviations from experiments.

Dynamical susceptibility of Nd2−x Ce x CuO4

We calculate the low-temperature dynamical susceptibility for a Fermi liquid model which was developed for magnetic ions in metals with strongly correlated conduction electrons. The results are in fair agreement with neutron scattering data for the rare earth cuprates Nd2−xCexCuO4.

Near metamagnetism and susceptibility maximum of liquid3He

The prediction of the Fermi liquid model as to the universal appearance of the susceptibility maximum and the occurrence of metamagnetism is verified experimentally in itinerant electron systems. In accordance with this, it is concluded that, by analysing recent experiments throughout the world, liquid3He is nearly metamagnetic and its susceptibility is likely to show a maximum at about 40 mK.

Critical behaviour of ZrZn 2

The nature of the metallic state of the low temperature itinerant ferromagnet ZrZn 2 in the vicinity of a magnetic quantum phase transition has been studied in a series of susceptibility and resistivity measurements under high pressures. A pressure-temperature phase diagram has been constructed on the basis of the susceptibility data. The magnetic transition temperature is observed to follow T c 4 3 ∼ (p c − p) down to temperatures of order 1 K. No evidence for a first order transition was found at any pressure, but a clearly defined and moderately pressure-dependent maximum was observed in the susceptibility in the paramagnetic regime, i.e. for p > p c. The temperature dependence of the resistivity is found to differ from that of the conventional Fermi liquid model over a wide range of temperature and pressure. The shape of the phase diagram and the observed behaviour of the resistivity have been interpreted in terms of a quantum Ginzburg Landau model for the magnetic fluctuation spectrum.

Static Spin Susceptibility with Anisotropic Superconducting Gap Parameter in High-TcCu Oxides

The wave-number dependent BCS spin susceptibility χ( q ) with various-type anisotropic superconducting gap parameters Δ( q ) is calculated for a two dimensional nearly antiferromagnetic Fermi liquid model with the random-phase-approximation (RPA). The Δ( q ) anisotropic but gapful on the Fermi surface gives rise to a significant reduction of χ( q ) around q = Q [=(π,π)]. The enhanced χ( q ∼ Q ) below T c as large as above T c can be traced to the d ( x 2 - y 2 )-wave gap parameter or the nodeless anisotropic gap parameter with the specific minimum gap, Δ m i n (0.35<2 Δ m i n / k B T c <0.7), on the Fermi surface. From the experimental findings on the enhanced χ( q ∼ Q ) below T c and the anisotropic Δ( q ) on the Fermi surface for the high- T c Cu oxides, we conclude that the d ( x 2 - y 2 )-wave gap parameter is realized but not the other types in the high- T c superconductivity, except the additional change of the order parameter.

Scaling Relation of Electron Spin-Spin Correlation in High-Temperature Superconductors

Temperature ( T ) dependence of the static and the dynamic electron spin-spin correlation is discussed through the planar 63 Cu(2) nuclear spin-spin relaxation rate 1/ 63 T G and the spin-lattice relaxation rate 1/ 63 T 1 T for YBa 2 Cu 3 O 6.6 ( T c ∼60 K), YBa 2 Cu 4 O 8 ( T c ∼82 K), YBa 2 Cu 3 O 6.98 ( T c ∼92 K), and Tl 2 Ba 2 CuO 6+δ ( T c ∼85 K). The restricted moment sums S =( 63 T 1 T ) AF /( 63 T G ) 2 [∼χ( Q )Γ( Q )] for the lightly doped Cu oxides tend to have constant values at high temperatures and those for the other ones are nearly T -independent at all the measured T ( T c < T <300 K). The T -independent S indicates the validity of (1/ 63 T 1 ) AF ∝ T χ( Q ) for the antiferromagnetic Fermi liquid model. From the experimental values of S , we estimate the ratio 2α s T A / T 0 of the characteristic spin-fluctuation parameters 2α s T A and T 0 .

Fermi-liquid-type spectral function and angle resolved photoelectron spectra of the Ti-3d z2-band of TiTe 2

Angle and temperature dependent photoelectron spectra with high energy and momentum resolution (Δ E = 300 meV, Δθ< ±0.5°) were taken near the Fermi energy ( E b < 1 eV) of the quasi-two-dimensional, metallic layer compound TiTe 2 along the direction ΓM . The aim was to test the range of the validity of the Fermi liquid model using a Taylor expansion for the self-energy used by Claessen et al. [1] for a system whose low energy properties are those of a normal metal. Single crystalline samples have been prepared by vapor growth technique using different amounts of Te in order to influence the intercalation of surplus Ti. We found a dependence of the dispersion of the Ti-3d z 2 -derived band on the stoichiometry of the samples. For an exact line shape analysis the spectra were fitted by a least-squares-method to a Fermi-liquid-type spectral function taking into account the crucial effects due to the apparatus, as there are the energy resolution and finite angle resolution which leads to a limited integration in k-space. In the region where the Ti-3d z 2 -derived band crosses the Fermi level we found excellent agreement between the experimental line shape and the Fermi liquid model. On the other hand there are distinct deviations between the theoretical and the experimental line shape at the Brillouin zone boundary even for a self-energy proposed by Matho [2] without Taylor expansion.

Fermi-liquid description for itinerant-electron magnetism

Abstract On the basis of the Fermi-liquid model the magnetic susceptibility for paramagnetic or ferromagnetic metals carrying itinerant electrons is evaluated as a function of temperature. It is shown that for the paramagnetic regime, at low temperatures, the susceptibility definitely shows a maximum which is responsible for universal phenomena observed in 4d and 5d metals, Laves phase compounds and heavy-fermion compounds. The present model explains the concurrence of the susceptibility maximum and Curie-Weiss susceptibility in nearly ferromagnetic metals, the appearance of thermally induced ferromagnetism and the precise Curie-Weiss law for relatively weak ferromagnets. The Fermi-liquid effect produces logarithmic terms in the free energy with respect to temperature, magnetization M etc. Because of the M 4 In M term of the energy, some Laves phase compounds are shown to exhibit a metamagnetic transition. This term is also the origin of peculiar nonlinear magnetization curves observed for CeRu2Si2.

Theoretical analysis of heat conductivity in high-T c oxides

Using a screened ionic model for the electron-photon interaction the temperature dependence of the lattice and electronic contributions to the heat conductivity and of the Wiedemann-Franz ratio is calculated. It is shown that the experimental data can reasonably well be explained in this model assuming a strong electron-phonon coupling. A similar good agreement can be achieved within a marginal Fermi liquid model, however, such an explanation would require an unreasonably small electron-phonon coupling.

Quantum statistical foundation to the fermi liquid model and Ginzburg-Landau wave function

An energy eigenvalue equation for a quasi-particle is derived, starting with the Heisenberg equation of motion for an annihilation operator. An elementary derivation of the Fermi liquid model having a sharply defined Fermi surface in the k-space is given, starting with a realistic model of a metal including the Coulomb interaction among and between electrons and lattice-ions. The Ginzburg-Landau wave function [Psi][sub [sigma]](r), where [sigma] represents the superconducting pairon (Cooper-pair) state, is shown to be connected with the one-pairon density operator n by [Psi][sub [sigma]](r) = [l angle]r[vert bar]n[sup 1/2][vert bar][sigma][r angle]. A close analogy between supercurrent and laser is indicated. 31 refs.

Universal trend in the heat capacity of YBa2Cu3O7-x near Tc(x).

The reduction in transition temperature that occurs as oxygen is removed from YBa[sub 2]Cu[sub 3]O[sub 7[minus][ital x]] is accompanied by a rapid decrease in the size of the heat-capacity anomaly at [ital T][sub [ital c]]. We treat the fluctuation effects in the context of [ital XY]-like behavior and demonstrate that their dependence on the transition temperature agrees in detail with a relationship between [ital T][sub [ital c]] and the hole concentration proposed by Schneider and Keller. Further, we show that this empirical relationship can be understood by combining scaling arguments with the nearly antiferromagnetic Fermi-liquid model of Monthoux and Pines.

Thermoelectric power of the thallium-based superconductor Tl2Ba2Ca2Cu3O10- delta.

The temperature dependence of the thermoelectric power of the high-temperature superconductor ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{10\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ is reported. The contribution of holes from the valence band satisfying a Fermi-liquid model gives the major part of the measured thermoelectric power. The results show that the conduction-band electrons also contribute to the total output of the thermoelectric power and the portion of the electron's contribution increases with temperature. An explicit expression for the thermolectric power of the 2:2:2:3 phase was derived based on a two-band model and the experimental data, which is given as S(\ensuremath{\mu}V)=0.121T-(280-0.2T)${\mathit{e}}^{\mathrm{\ensuremath{-}}550/\mathit{T}}$. A general formula, S=AT+(B\ensuremath{\lambda}+CT)exp(-\ensuremath{\lambda}/T), is found to give a close description of the thermoelectric power of various cuprate high-${\mathit{T}}_{\mathit{c}}$ superconductors.