Paramagnon Model Research Articles

Pseudospin Paramagnons and the Superconducting Dome in Magic Angle Twisted Bilayer Graphene.

We present a theory of superconductivity in twisted bilayer graphene in which attraction is generated between electrons on the same honeycomb sublattice when the system is close to a sublattice polarization instability. The resulting Cooper pairs are spin-polarized valley singlets. Because the sublattice polarizability is mainly contributed by interband fluctuations, superconductivity occurs over a wide range of filling fraction. It is suppressed by (i)applying a sublattice polarizing field (generated by an aligned BN substrate) or (ii)changing moiré band filling to favor valley polarization. The enhanced intrasublattice attraction close to sublattice polarization instability is analogous to enhanced like-spin attraction in liquid ^{3}He near the melting curve and the enhanced valley-singlet repulsion close to valley-polarization instabilities is analogous to enhanced spin-singlet repulsion in metals that are close to a ferromagnetic instability. We comment on the relationship between our pseudospin paramagnon model and the rich phenomenology of superconductivity in twisted bilayer and multilayer graphene.

Theory of thermal expansion based on the localized paramagnon model

Theory of thermal expansion based on the localized paramagnon model

Magnetic field dependence of pairing interaction in ferromagnetic superconductors with triplet pairing

It is developed a microscopic description of superconductivity in ferromagnetic materials with triplet pairing triggered by the exchange of magnetic fluctuations. Instead widely used paramagnon model we work with phenomenological spectrum of fluctuations in the orthorhombic ferromagnet with strong magnetic anisotropy. Depending of the field orientation parallel or perpendicular to the direction of spontaneous magnetization the effective amplitude of pairing interaction proves to be decreasing or increasing function of magnetic field that allows to explain the drastic difference in magnitudes of upper critical field in these directions.

Low temperature heat capacity of Y 1− xNd xCo 2

We present the Heat capacity study of Y 1− x Nd x Co 2 ( x = 0 , 0.05, 0.1 and 0.5) in the presence of magnetic fields up to 14 T in the temperature range 2–300 K. The zero field C / T versus T 2 for Y Co 2 shows a mild upturn below 10 K which enhances with Nd doping up to a critical concentration and vanishes at higher concentrations of Nd where the system shows magnetic ordering in line with NdCo 2. The upturn of C / T vanishes at higher magnetic fields. The possible origin of the upturn in C / T is discussed as arising from spin fluctuations in the light of a paramagnon model and magnetic defects induced by the Schottky anomaly.

BCS Superfluidity in Ultracold Li-6 Gas

Recent progress toward degeneracy in ultracold Fermi gases raise hope to reach the BCS superfluuid transition in fermionic systems, the case of 6Li being very favorable in view of its expected large and negative scattering length. We discuss the physical situation in the high density regime where the critical temperature is expected to be large. Indirect interaction due to the exchange of density fluctuations should play an important role. We discuss the physical points involved in our approximate calculation of the critical temperature which retains the same set of diagrams as in the paramagnon model. Near the instability threshold, the attractive interaction due to density fluctuations gives rise to a strong increase in the critical temperature, providing a clear signature of the existence of fluctuation induced interactions.

Proposal for detecting the susceptibility maximum of liquid 3He with respect to field

Recently, Ishikawa and Kawasaki observed, contrary to Meyer's group (1970), a susceptibility maximum in liquid 3He as a function of temperature, and proved the breakdown of the paramagnon model. The Fermi liquid model predicts that a maximum should appear not only as a function of temperature but also as a function of field. Here we propose to detect the maximum with respect to field at temperatures lower than some critical value.

Paramagnon and Size Effects forTcin Superfluid3He Films

The symmetry of Cooper pairs and transition temperature T c of superfluid 3 He films thinner than coherence length with specularly reflecting boundary are investigated. Using the paramagnon model for the pairing interaction, we show the symmetry of pairs is likely p-wave and the gap at T c is the ABM (or Planer) type. The quantum size effect yields the oscillating behavior of T c as a function of the film thickness. On the contrary to the result of Tesanovic and Valls, the transition temperature we obtained is higher than that of the bulk system.

Trapped6Li: A HighTcSuperfluid?

We consider the effect of the indirect interaction due to the exchange of density fluctuations on the critical temperature of superfluid ${}^{6}\mathrm{Li}$. We obtain the strong coupling equation giving this critical temperature. This equation is solved approximately by retaining the same set of diagrams as in the paramagnon model. We show that, near the instability threshold, the attractive interaction due to density fluctuations gives rise to a strong increase in the critical temperature, providing a clear signature of the existence of fluctuation induced interactions.

Single-particle properties of a two-dimensional Fermi liquid at finite frequencies and temperatures

We review the leading momentum, frequency, and temperature dependences of the single-particle self-energy and the corresponding term in the entropy of a two-dimensional Fermi liquid (FL) with a free-particle spectrum. We calculate the corrections to these leading dependences for the paramagnon model and the electron gas and find that the leading dependences are limited to regions of energy and temperature which decrease with decreasing number density of fermions. This can make it difficult to identify the frequency- and temperature-dependent characteristics of a FL ground state in experimental quantities in low-density systems even when complications of band structure and other degrees of freedom are absent. This is an important consideration when the normal-state properties of the undoped cuprate superconductors are analyzed.

Two-dimensional Fermi liquid in the highly correlated regime: The second layer of 3He adsorbed on graphite.

We present results on the magnetic susceptibility of the second atomic layer fluid of $^{3}\mathrm{He}$ adsorbed on graphite over a large temperature and coverage range. The fluid is found to display the well characterized behavior of a Fermi liquid. The temperature dependence of the magnetic susceptibility can be described well by Dyugaev's phenomenological theory of Fermi liquids. The effective Fermi temperature has been determined as a function of coverage. We find that the susceptibility enhancement factor (with respect to the Fermi gas of the same density) reaches values larger than in bulk liquid $^{3}\mathrm{He}$ in high-areal-density fluids. In this regime the films constitute experimental model systems for the theory of strongly correlated fermions. Using previous heat-capacity measurements performed on the same system allows a direct comparison with the predictions of the quasilocalized model and the paramagnon model. \textcopyright{} 1996 The American Physical Society.

Spin fluctuations and zero-sound in normal liquid3He studied by neutron scattering

High-resolution neutron-inelastic-scattering measurements of liquid3He at a temperature of 120 mK and pressures between 0 and 20 bars are analyzed. The improved energy resolution provides for the first time information on the line shape of the spin-fluctuation peak. We find that the low-energy enhancement of the spin fluctuations is stronger than predicted by the paramagnon model (m*/m3 = 1), in particular at high pressures. Also, the spin dependent scattering extends to higher energies than can be accounted for in any simple random-phase-approximation (RPA) model that uses the Lindhard function with an effective mass of about 3 m3. This observation is independent of the interaction potential used in the RPA. However, we show that a simple RPA model where the Lindhard function has an effective mass of 1.9m3 gives a good description of the spin-fluctuation scattering. The zero-sound mode overlaps with both spin fluctuations and multipair excitations, and its energy and line width can only be obtained unambiguously at the smallest wave vectors. For wave vectors larger than 0.6 A−1, the energy and in particular the width of the zero-sound mode depend strongly on the models used for the spin fluctuations and the multipairs. Different damping mechanisms of the zero-sound mode are discussed, and the importance of coherent and incoherent multipairs is illustrated.

The role of spin and phonon fluctuations in Fe-Ni Invar alloys

We present an approach to the thermal magnetic properties of itinerant electron ferromagnets that takes account of spin and phonon fluctuations simultaneously. It is shown, that both contributions are important in the case of Fe 0.35Ni 0.65. For this alloy we show that it is necessary to consider the dependency of the bulk modulus and the shear modulus on the magnetization. We also discuss the possibility to describe spin fluctuations in the frame of the paramagnon model for weak itinerant ferromagnets and compare the results with experimental data.

Specific heat of amorphous U?Fe, U?Co and U?Ni-alloys

Alloys of U-X with X=Fe, Co, Ni were prepared by rapid quenching in the concentration range between 50 and 83 at% U. The samples were obtained in the amorphous state as determined by X-ray diffraction. Parts of the samples were used to measure the specific heat by the relaxation method. The calculated density of states is twice as large as that of transition metals like amorphous Zr-alloys. Therefore these results are discussed within the frame of the paramagnon model by taking into account values of the magnetic susceptibility and the supercon-ducting transition temperature.

Role of spin and phonon fluctuations in the temperature dependences of magnetic properties of iron-nickel Invar alloy

We present an approach to the thermal magnetic properties of itinerant electron ferromagnets that takes account of spin and phonon fluctuations simultaneously. The comparison of both fluctuation contributions is given in the case of the Invar alloy Fe 0.65Ni 0.35. For this alloy we demonstrate the necessity of taking into account the changes due to the magnetization not only of the bulk modulus but also of the shear modulus in the description of phonon fluctuations and also the possibility of the description of spin fluctuations in the frame of the paramagnon model of a weak itinerant ferromagnet.

Resistivity and superconductivity of uranium based metallic glasses

Amorphous U-Fe, U-Co and U-Ni alloys were prepared by splat quenching over the uranium concentration range of 50 – 83 at%. The temperature dependence of the electrical resistivity, ρ (T), was investigated in the range of 4.2 – 300 K. The results below the Debye temperature ( θ ≃ 165 K) may be explained within the frame of the extended Ziman theory and the paramagnon model. The concentration dependence of ρ and of the superconducting transition temperature T c might be explained by the variation of the d-electron contribution.

Momentum-dependent electron self-energy in nearly ferromagnetic systems: Comparison of spin fluctuations and phonons.

The self-energy \ensuremath{\Sigma} is calculated in a two-parameter spin-fluctuation model. In contrast to the electron-phonon system, paramagnons have considerable spectral weight at large energies, O(${E}_{F}$), even very near the magnetic transition. The momentum dependence of \ensuremath{\Sigma} is important and leads to significant changes in the chemical potential and in the ratio ${m}^{\mathrm{*}}$/m and to restoration of particle conservation, which is violated in the paramagnon model. The Eliashberg strong-coupling theory must be modified. Our results support resolution of the question of paramagnon model versus Fermi-liquid theory in favor of the latter.

Quasiparticle spectra and specific heat of a normal Fermi liquid in a spin-fluctuation model.

We calculate statistical and dynamical quasiparticle energies of a normal Fermi liquid in a spin-fluctuation model. The properties of spin fluctuations in the model are the same as those given by Landau Fermi-liquid theory at long wavelengths, low frequencies, and low temperatures if all Landau parameters except ${F}_{0}^{a}$ are neglected. The statistical quasiparticle spectrum is found to be significantly less dependent on momentum and temperature than the dynamical quasiparticle one. The specific heat is calculated both from the statistical quasiparticle spectrum and from the thermodynamic potential, and for parameters appropriate for liquid $^{3}\mathrm{He}$, the corrections to the leading low-temperature result (\ensuremath{\propto}T) are well characterized by ${T}^{3}$lnT behavior up to temperatures of order 100 mK, which is in qualitative agreement with what Greywall finds experimentally. If the Landau parameter ${F}_{1}^{a}$ is included in the calculation in addition to ${F}_{0}^{a}$, we find rather good agreement between theory and experiment. A further conclusion of our work is that the finite-temperature contributions to the specific heat are much less sensitive to variations of the cutoff momentum in our calculations than is the spin-fluctuation contribution to the effective mass. Spin fluctuations are therefore able to account for finite-temperature effects, even though they provide only a modest contribution to the effective mass. We also investigate the reason for earlier calculations in the paramagnon model giving very low estimates of the temperature below which the specific heat should exhibit ${T}^{3}$lnT behavior, and find that this is due to (i) the fact that the dynamical quasiparticle contribution to the specific heat was calculated and (ii) the use of the paramagnon model, rather than Landau theory.

Anderson localization in 3D nearly magnetic fermion systems

To understand the metal-insulator transition despite strong electron interactions, a cross-over is proposed within the paramagnon model: uniform paramagnons tend to switch to local ones; but the local paramagnon theory is known to scale to a zero interaction one, which therefore allows the Anderson localization to occur.

Spin susceptibility in three-dimensional nearly magnetic disordered fermion systems in the weakly localized regime.

The temperature dependence of the spin susceptibility \ensuremath{\chi}(T) is studied in a weakly disordered itinerant-fermion system close to a magnetic instability. The paramagnon model is used with a Hubbard-type contact repulsion among opposite spins, with the Stoner enhancement of the pure system (1-\ifmmode \bar{I}\else \={I}\fi{}${)}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\gg}1. The result is shown to be different from the usual one obtained in the case of a screened Coulomb interaction: The 2-phDP (two--particle-hole-diffusion-propagator) diagrams, which cancel altogether in the Coulomb interaction case, are shown to give, here, for the contact interaction, a finite contribution which is of the same order in (${\ensuremath{\varepsilon}}_{F}$\ensuremath{\tau}${)}^{\mathrm{\ensuremath{-}}1}$ as the 3-phDP and 4-phDP diagrams where \ensuremath{\tau} is the lifetime due to disorder, and ${\ensuremath{\varepsilon}}_{F}$ the Fermi energy. Instead of a unique temperature range T\ensuremath{\tau}\ensuremath{\ll}1 in the Coulomb case, here one has to distinguish two ranges:When T\ensuremath{\tau}\ensuremath{\ll}(1-\ifmmode \bar{I}\else \={I}\fi{}), the usual 3- and 4-phDP diagrams dominate and one recovers \ensuremath{\chi}(T)\ensuremath{\approxeq} \ensuremath{\surd}T\ensuremath{\tau} /(1-\ifmmode \bar{I}\else \={I}\fi{}${)}^{2}$ as was first announced by Al'tshuler and Aronov; but when (1-\ifmmode \bar{I}\else \={I}\fi{})\ensuremath{\ll}1, the 2-phDP diagrams dominate, yielding \ensuremath{\chi}(T)\ensuremath{\sim}(T\ensuremath{\tau}${)}^{3/2}$/(1-\ifmmode \bar{I}\else \={I}\fi{}${)}^{5/2}$, which is non-negligible near the magnetic instability. At T=0, the 2-phDP diagrams definitely dominate as they enhance the effective interaction (I${\ifmmode\bar\else\textasciimacron\fi{}}_{\mathrm{eff}}$-\ifmmode \bar{I}\else \={I}\fi{})\ensuremath{\approxeq}(${\ensuremath{\varepsilon}}_{F}$\ensuremath{\tau}${)}^{\mathrm{\ensuremath{-}}2}$(1 -\ifmmode \bar{I}\else \={I}\fi{}${)}^{\mathrm{\ensuremath{-}}1/2}$ and let the system be closer to magnetism, while the 3- and 4-phDP diagrams play a minor role at 0 K. The present study accounts only for phDP processes.Effects due to ppDP's (particle-particle diffusion propagators) should also be studied within the same framework to incorporate the contributions of the 2-ppDP diagrams. Finally, the latest developments using renormalization-group analysis of Finkel'stein and of Castellani et al. with a screened Coulomb interaction ought to be modified to account for the contact-interaction case where spin constraints yield the noncancellation of the 2-phDP---and also most likely of the 2-ppDP---diagrams.

Important modifications near a magnetic instability in the particle-hole propagator of weakly localized two-dimensional fermion systems

In the Hubbard-type paramagnon model important changes arise in the particle-hole propagator structure for weakly disordered, two-dimensional (2d), strongly interacting itinerant-fermion systems near a magnetic instability, when all momenta up to twice the Fermi momentum (0\ensuremath{\le}q\ensuremath{\le}2${k}_{F}$) are equally relevant. In 3d systems, the only vanishing momentum values (q\ensuremath{\sim}0) are the key ones, for which only the diffusive regime arises in the case of weak localization; in contrast, in 2d nearly magnetic systems, other regimes, in addition to the diffusive one, must be taken into account and be considered as playing equally important roles. Different temperature dependences follow for the physical properties of the system which furthermore do not vary the same way with the impurity concentration. Their relative weights are affected accordingly, which will be of importance for comparison with experiments.