Dimensional Fermi Liquid Research Articles

Simplified approach of investigation of binding energy for fermionic pairing in two dimensional Fermi liquid type superconducting materials at finite low temperature

Relation between the binding energy of pair of fermions and the magnitude of the attractive interaction between them is investigated theoretically with the help of mean field approximation, for a two-dimensional (2D) Fermi liquid type superconducting material. Here the fermion pair has finite center of mass momentum (CMM). The fermion pair is considered to be formed in the presence of an active Fermi sea having multiple pairs with inclusion of the effect of Pauli exclusion principle, at finite low temperature. Our calculations show that co-existence of true bound state (TB) and Cooper pair state (CP) with various CMMs can occur only beyond a critical attractive interaction strength which is similar to the results obtained at T=0 K[1]. We establish that Coopers pair state to true bound state crossover can be possible to achieve controlling the value of CMM of the fermion pairs. This could lead to the well-studied phenomena Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein Condensed (BEC) crossover and also the formation of incoherent pairs, under strong coupling regime. This throws a significant emphasis on the normal state anomalies seen in some of the exotic superconductors.

Hidden and mirage collective modes in two dimensional Fermi liquids

The longstanding view of the zero sound mode in a Fermi liquid is that for repulsive interaction it resides outside the particle-hole continuum and gives rise to a sharp peak in the corresponding susceptibility, while for attractive interaction it is a resonance inside the particle-hole continuum. We argue that in a two-dimensional Fermi liquid there exist two additional types of zero sound: “hidden” and “mirage” modes. A hidden mode resides outside the particle-hole continuum already for attractive interaction. It does not appear as a sharp peak in the susceptibility, but determines the long-time transient response of a Fermi liquid and can be identified in pump-probe experiments. A mirage mode emerges for strong enough repulsion. Unlike the conventional zero sound, it does not correspond to a true pole, yet it gives rise to a peak in the particle-hole susceptibility. It can be detected by measuring the width of the peak, which for a mirage mode is larger than the single-particle scattering rate.

Atypical behavior of collective modes in two-dimensional Fermi liquids

Using the Landau kinetic equation to study the non-equilibrium behavior of interacting Fermi systems is one of the crowning achievements of Landau’s Fermi liquid theory. While thorough study of transport modes has been done for standard three-dimensional Fermi liquids, an equally in-depth analysis for two dimensional Fermi liquids is lacking. In applying the Landau kinetic equation (LKE) to a two-dimensional Fermi liquid, we obtain unconventional behavior of the zero sound mode c0. As a function of the usual dimensionless parameter s = ω/qvF, we find two peculiar results: first, for |s| > 1 we see the propagation of an undamped mode for weakly interacting systems. This differs from the three dimensional case where an undamped mode only propagates for repulsive interactions and the mode experiences Landau damping for any arbitrary attractive interaction. Second, we find that regardless of interaction strength, a propagating mode is forbidden for |s| < 1. This is profoundly different from the three-dimensional case where a mode can propagate, albeit damped. In addition, we present a revised Pomeranchuk instability condition for a two-dimensional Fermi liquid as well as equations of motion for the fluid that follow directly from the LKE. In two dimensions, we find a constant minimum for all Landau parameters for ℓ ⩾ 1 which differs from the three dimensional case. Finally we discuss the effect of a Coulomb interaction on the system resulting in the plasmon frequency ωp exhibiting a crossover to the zero sound mode.

Exchange-Correlation Effects and the Quasiparticle Properties in a Two-Dimensional Dipolar Fermi Liquid

We investigate the effects of exchange and correlation on the quasiparticle properties such as the self-energy, the many-body effective mass and the renormalization constant in a two-dimensional system of ultracold dipolar fermions with dipole moments aligned in the perpendicular direction to the plane. We use the G0W approximation along with the generalized random phase approximation, where the many-body effects have been incorporated in the effective interaction W through the Hubbard local-field factor. The many-body effective mass and the renormalization constant are reduced with the increase of coupling strength. We also study the effect of dipole-dipole interaction on the single-particle spectral function of the two dimensional dipolar Fermi liquid. We observe composite hole-zero sound excitation which is a bound state of quasiparticles with the collective mode (i.e. zero-sound) at intermediate and high coupling constants. These composite excitations are undamped at small wave vectors. Due to repulsion between quasiparticle and composite excitation resonances, we find a gap-like feature between quasiparticle and composite excitation dispersions at long wavelengths.

Electronic sound modes and plasmons in hydrodynamic two-dimensional metals

Using an analytically tractable kinetic model of a two dimensional Fermi liquid of electrons, we characterize the crossovers between zero sound, first sound and plasmons. For experimentally realized Fermi liquids in a hydrodynamic limit, both zero and first sound waves are essentially replaced by plasmons. The plasmon dispersion relation is robust against hydrodynamic effects, up to acquiring the viscous-limited decay rate of a first sound wave in the hydrodynamic limit. We discuss implications for experiments in clean two dimensional electron gases.

Effect of paramagnetic fluctuations on a Fermi-surface topological transition in two dimensions

We study the Fermi surface topological transition of the pocket-opening type in a two dimensional Fermi liquid. We find that the paramagnetic fluctuations in an interacting Fermi liquid typically drive the transition first order at zero temperature. We first gain insight from a calculation using second order perturbation theory in the self-energy. This is valid for weak interaction and far from instabilities. We then extend the results to stronger interaction, using the self-consistent fluctuation approximation. Experimental signatures are given in the light of these results.

Shear Viscosity of Sr2RuO4 in the Normal state

The shear viscosity tensor of Sr2RuO4 is calculated. It is assumed that the low temperature metallic state of it is a two dimensional Fermi liquid. The Boltzmann equation has been solved in the normal state by using new method of calculation which is completely different from that of Abrikosov-Khalatnikov approximation. We show that the normal state viscosity coefficients varies with temperature as T−1 which in agreement with experimental results.

Inelastic neutron scattering study of the magnetic fluctuations in Sr2RuO4

By performing time-of-flight neutron scattering measurements on a large amount of single crystals of Sr$_2$RuO$_4$, we studied detailed structure of the imaginary part of the dynamic spin susceptibility over a wide range of phase space. In the normal state at T=5 K, strong incommensurate (IC) peaks were clearly observed at around $\mathbf{Q}_\text{c}=(0.3,0.3)$ up to at least $\hbar\omega=80$ meV. In addition, our data also show strong magnetic fluctuations that exist on the ridges connecting the IC peaks around the $(\pi,\pi)$ point rather than around the $\Gamma$ point. Our results are consistent with the semi-mean-field random phase approximation calculation for a two dimensional Fermi liquid with a characteristic energy of 5.0 meV. Furthermore, the IC fluctuations were observed even at room temperature.

Particle–Hole Ladders

A self contained analysis demonstrates that the sum of all particle-hole ladder contributions for a two dimensional, weakly coupled fermion gas with a strictly convex Fermi curve at temperature zero is bounded. This is used in our construction of two dimensional Fermi liquids. This summary article contains the statements of the main results. The proofs are contained in the full, electronic, article. Electronic Supplementary Material: Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00220-004-1038-2.

Friedel oscillations in a two dimensional Fermi liquid

Within linear response the long range oscillations caused by short or long ranged impurities embedded in an otherwise homogeneous electron gas reflect the singularities of the static response function. By making use of the theory of the many-body local fields and the results of recent quantum Monte Carlo studies we have calculated the exact dependence of the amplitude of these oscillations on the density in a two dimensional electron Fermi liquid.

INTERACTIONS IN QUASICRYSTALS

Although the effects of interactions in solid state systems still remains a widely open subject, some limiting cases such as the three dimensional Fermi liquid or the one-dimensional Luttinger liquid are by now well understood when one is dealing with interacting electrons in periodic crystalline structures. This problem is much more fascinating when periodicity is lacking as it is the case in quasicrystalline structures. Here, we discuss the influence of the interactions in quasicrystals and show, on a controlled one-dimensional model, that they lead to anomalous transport properties, intermediate between those of an interacting electron gas in a periodic and in a disordered potential.

The effect of parallel magnetic field on the Boltzmann conductivity and the Hall coefficient of a disordered two-dimensional Fermi liquid

Screening of an external random potential by a two dimensional (2D) Fermi liquid may be strongly dependent on the degree of its polarization. This is considered as a possible mechanism for the observed strong magnetoresistance of the 2D electron liquid in the magnetic field parallel to the electron plane. A Hartree-Fock calculation for the weakly disordered Hubbard model which qualitatively describes the experiments on the diagonal and the Hall resisitivity in the finite-temperature metallic state in the high mobility Si inversion layers is presented.

Orbital effect of a magnetic field on two-leg Hubbard ladder

We study the effect of a magnetic field on the dimensional crossover of weakly coupled two-leg Hubbard ladders under pressure. Our model is based on the perturbative renormalization approach (PRG) with two cut-off parameters, the bandwidth E0 and a characteristic magnetic energy ωc. We determine the temperature-pressure phase diagram for different values of the magnetic field and discuss the relative stability of the d-wave superconducting phase (SCd) and the two dimensional Fermi liquid phase (2D) which appear at zero field. We show that the field induces a reduction in the effective dimensionality of the system and confines the electron motion within the ladder. In fact, we find that with increasing magnetic field, the isolated ladder phase gets wider at the expense of the SCd phase which disappears at a critical magnetic field Hc. The superconducting transition temperature Tc is found to decrease as the field increases up to Hc for which Tc falls to zero. Concerning the 2D phase, we show that it is destroyed for ωc greater than the crossover temperature at which the system crosses to 2D phase at zero magnetic field.

Effect of relevant umklapp process on the two-leg Hubbard ladder with a half-filled band under pressure

By means of perturbative renormalization approach we study the effect of relevant umklapp process on dimensional crossover caused by interladder one particle hopping t⊥ in weakly coupled two-leg Hubbard ladders with a half filled-band. We found that a crossover takes place at a finite value t⊥ which increases as the amplitude of umklapp process increases. For t⊥ t⊥c the system undergoes a crossover to the two dimensional Fermi liquid phase via one particle hopping process.

Hidden Spin-Current Conservation in 2D Fermi Liquids

We report the existence of regimes of the two dimensional Fermi liquid that show unusual conservation of the spin current and may be tuned by varying some parameter like the density of fermions. We show that for reasonable models of the effective interaction the spin current may be conserved in general in 2d, not only for a particular regime. Low temperature spin waves propagate distinctively in these regimes and entirely new ``spin-acoustic'' modes are predicted for scattering-dominated temperature ranges. These new high-temperature propagating spin waves provide a clear signature for the experimental search of such regimes.

Dynamical properties of quantum Hall edge states.

We consider the dynamical properties of simple edge states in integer ($\nu = 1$) and fractional ($ \nu = 1/2m+1$) quantum Hall (QH) liquids. The influence of a time-dependent local perturbation on the ground state is investigated. It is shown that the orthogonality catastrophe occurs for the initial and final state overlap $|<i|f>| \sim L^{-{1\over{2\nu}}({\delta\over{\pi}})^2}$ with the phase shift $\delta$. The transition probability for the x-ray problem is also found with the index, dependent on $\nu$. Optical experiments that measure the x-ray response of the QH edge are discussed. We also consider electrons tunneling from one dimensional Fermi liquid into a QH fluid. It is argued that for any filling fraction the tunneling from a Fermi liquid to the QH edge is suppressed at low temperatures and we find the nonlinear $I-V$ characteristics $I\sim V^{1/\nu}$.

Vertex-correction-driven intersubband spin-density excitonic instability in double quantum well structures.

We show that exchange-correlation induced many-body excitonic vertex correction may lead to an instability in the normal ground state of a semiconductor double quantum well structure by suppressing the symmetric-antisymmetric intersubband gap at low but accessible (\AA{} 0.7 \ifmmode\times\else\texttimes\fi{} ${10}^{11}$ ${\mathrm{cm}}^{\ensuremath{-}2}$) electron densities. We predict as a consequence a novel electronic phase transition where the lowest intersubband spin-density-excitation gap vanishes giving rise to a new many-body triplet excitonic liquid ground state which is more stable at low densities than the usual two dimensional Fermi liquid phase.

Staggered Spin Susceptibility in YBa2Cu3O6.98andYBa2Cu4O8Observed by Cu Nuclear Spin-Spin Relaxation

The temperature ( T ) dependence of the static staggered spin susceptibility χ( Q ) for the high T c Cu oxides, YBa 2 Cu 3 O 6.98 and YBa 2 Cu 4 O 8 , extracted from the Cu nuclear spin-spin relaxation measurements is discussed. The self-consistent-renormalization (SCR) calculation for a two dimensional antiferromagnetic Fermi liquid well reporoduces the experimental Curie-Weiss-type T -dependence of χ( Q ), but the random-phase-approximation does not. This shows that the Curie-Weiss-type χ( Q ) of the high T c Cu oxides results from the SCR spin fluctuations at finite temperatures but not from the strong nesting of the Fermi surface.

Similarity of the leading contributions to the self-energy and the thermodynamics in two- and three- dimensional Fermi liquids

We compare the self-energy and entropy of a two- and three- dimensional Fermi Liquids(FLs) using a model with a contact interaction between fermions. For a two-dimensional(2D) FL we find that there are T 2 contributions to the entropy from interactions separate from those due to the collective modes. These T 2 contributions arise from non-analytic corrections to the real part of the self-energy and are analogous to T 3 lnT contributions present in the entropy of a three-dimensional(3D) FL. The difference between the 2D and 3D results arises solely from the different phase space factors.

Observation of quantum size effects in thin films of liquid 3He adsorbed on graphite

The nuclear magnetic susceptibility of multilayer liquid 3He films adsorbed on the surface of graphite has been measured. The surface density dependence shows evidence of distinct step structure that has been studied up to five liquid layers. This is attributed to quantum size effects arising from the finite film thickness, leading to a description of the growth of the film in terms of the population of a set of two dimensional Fermi liquids. The Fermi liquid interactions in this system are discussed.