Two-dimensional Fermi System Research Articles

Monolayers of 3He on the surface of bulk superfluid 4He

We have used quantum evaporation to investigate the two-dimensional fermion system that forms at the free surface of (initially isotopically pure) 4He when small quantities of 3He are added to it. By measuring the first-arrival times of the evaporated atoms, we have determined that the 3He– 3He potential in this system is V 3 S /k B =0.23±0.02 K nm 2 (repulsive) and estimated a value of m 3S=(1.53±0.02) m 3 for the zero-coverage effective mass. We have also observed the predicted second layer-state which becomes occupied once the first layer-state density exceeds about 0.6 monolayers.

The Two-Dimensional World of 3He in 3He-4He Mixture Films

For thin films of 4 He at low temperatures the addition of sub-monolayer numbers of 3 He atoms results in the 3 He residing in a ground state at the free surface of the 4 He film. For low 3 He coverage the 3 He are a nearly ideal two-dimensional Fermi system. With increasing numbers of 3 He atoms the interactions among the 3 He increase. The results from a number of experiments that reveal the remarkable properties of this rich, interacting, two-dimensional 3 He system are described. These results include the magnetization, the energetics of the 3 He atoms in quantum states, the diffusion of the 3 He along the 4 He film, and the 3 He effective mass. The techniques employed include NMR, specific heat, quartz crystal microbalance and third sound. A clearer picture of the properties of the 3 He is now emerging, and preliminary numbers for the 3 He coverage dependence of the Fermi Liquid parameters are presented. Prospects for the observation of superfluidity of the 3 He in this system are discussed.

Paramagnon-Mediatedd-Wave Pairing in Two-Dimensional Isotropic Fermi Liquid

It is studied which type of superfluidity is induced by the paramagnon-mediated interaction in a two-dimensional isotropic Fermion system. The stability of various types of Cooper pairing is invest...

Nonanalytic Contribution to the Free Energy of Interacting Two-Dimensional Fermion Systems

The nonanalytic contribution to the free energy of interacting two-dimensional fermion systems is studied numerically. It is found that the numerical result for the singular contribution is well fi...

Fermion loops, loop cancellation, and density correlations in two-dimensional Fermi systems

We derive explicit results from an exact expression for fermion loops with an arbitrary number of density vertices in two dimensions at zero temperature, which has been obtained recently by Feldman et al. [in Singularities, edited by G. M. Greuel (Birkhaeuser, Basel, 1998)]. The 3-loop is an elementary function of the three external momenta and frequencies, and the N-loop can be expressed as a linear combination of 3-loops with coefficients that are rational functions of momenta and frequencies. We show that the divergencies of single loops for low energy and small momenta cancel each other when loops with permutated external variables are summed. The symmetrized N-loop, i.e., the connected N-point density-correlation function of the Fermi gas, does not diverge for low energies and small momenta. In the dynamical limit, where momenta scale to zero at fixed finite energy variables, the symmetrized N-loop vanishes as the $(2N\ensuremath{-}2)\mathrm{th}$ power of the scale parameter.

Theory of the pseudogap formation in 2D attracting fermion systems

The two-dimensional fermion system with the indirect Einstein phonon-exchange attraction and additional local four-fermion interaction is considered. It is shown that as a result of the attraction between fermions, the normal phase of such a system is divided into two regions. In one of them, called the pseudogap region, the absolute value of the order parameter exists as essentially nonzero value, but its phase is a random quantity. It is important that in the case of attraction due to the phonons, this abnormal region appears at rather low carrier concentrations, i.e., it decreases appreciably with increasing doping. The relevance of the results obtained for high-temperature superconductors is speculated.

Ring contribution to the neutral two-dimensional Fermi gas

This paper concentrates on the hitherto ignored long-range correlations in neutral two-dimensional Fermi systems, embodied in the ring diagrams or polarization insertions. In turns out that their effects are crucial regarding the quasiparticle lifetime, but marginal so far as the effective mass and single-particle energies are concerned. It also sheds some light on the effective interaction due to these correlations.

Confined two-dimensional fermions at finite density.

We introduce the chemical potential in a system of two-dimensional massless fermions, confined to a finite region, by imposing twisted boundary conditions in the Euclidean time direction. We explore in this simple model the application of functional techniques which could be used in more complicated situations.

Marginal behavior of a Fermi system interacting with bosonic excitations

We calculated the self-energy of a Fermi system interacting with bosonic excitation. If the bosonic system is near instability, the imaginary part of the self-energy which measures the lifetime of quasiparticles is of the order of (ɛ(p)-ɛ F ) which is typical for a marginal Fermi liquid. Such a behavior can appear for three- and two-dimensional Fermi systems.

Disorder effects in two-dimensional Fermi systems with conical spectrum: exact results for the density of states

The influence of weak non-magnetic disorder on the single-particle density of states ϱ( ω) of two-dimensional electron systems with a conical spectrum is studied. We use a non-perturbative approach, based on the replica trick with subsequent mapping of the effective action onto a one-dimensional model of interacting fermions, the latter being treated by abelian and non-abelian bosonization methods. Specifically, we consider a weakly disordered p- or d-wave superconductor, in which case the problem reduces to a model of (2+l)-dimensional massless Dirac fermions coupled to random, static, generally non-abelian gauge fields. It is shown that the density of states of a two-dimensional p- or d-wave superconductor, averaged over randomness, follows a non-trivial power-law behavior near the Fermi energy: ϱ( ω) ∼ 1 | ω| α . The exponent α > 0 is exactly calculated for several types of disorder. We demonstrate that the property ϱ(0) = 0 is a direct consequence of a continuous symmetry of the effective fermoic model, whose breakdown is forbidden in two dimensions. As a counter example, we also discuss another model with a conical spectrum - a two-dimensional orbital antiferromagnet, where static disorder leads to a finite ϱ(0) due to the breakdown of a discrete (particle-hole) symmetry.

Energy density in the Maxwell-Chern-Simons theory.

A two-dimensional nonrelativistic fermion system coupled to both electromagnetic gauge fields and Chern-Simons gauge fields is analysed. Polarization tensors relevant in the quantum Hall effect and anyon superconductivity are obtained as simple closed integrals and are evaluated numerically for all momenta and frequencies. The correction to the energy density is evaluated in the random phase approximation (RPA), by summing an infinite series of ring diagrams. It is found that the correction has significant dependence on the particle number density. In the context of anyon superconductivity, the energy density relative to the mean field value is minimized at a hole concentration per lattice plaquette (0.05 \sim 0.06) (p_c a/\hbar)^2 where p_c and a are the momentum cutoff and lattice constant, respectively. At the minimum the correction is about -5 % \sim -25 %, depending on the ratio (2m \omega_c)/(p_c^2) where \omega_c is the frequency cutoff. In the Jain-Fradkin-Lopez picture of the fractional quantum Hall effect the RPA correction to the energy density is very large. It diverges logarithmically as the cutoff is removed, implying that corrections beyond RPA become important at large momentum and frequency.

Low-energy properties of fermions with singular interactions.

We calculate the fermion Green function and particle-hole susceptibilities for a degenerate two-dimensional fermion system with a singular gauge interaction. We show that this is a strong-coupling problem, with no small parameter other than the fermion spin degeneracy N. We consider two interactions, one arising in the context of the t-J model and the other in the theory of half-filled Landau level. For the fermion self-energy we show that the qualitative behavior found in the leading order of perturbation theory is preserved to all orders in the interaction. The susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathit{Q}}$ at a general wave vector Q\ensuremath{\ne}2${\mathbf{p}}_{\mathbf{F}}$ retains the Fermi-liquid form. However, the 2${\mathit{p}}_{\mathit{F}}$ susceptibility ${\mathrm{\ensuremath{\chi}}}_{2\mathit{p}\mathit{F}}$ either diverges as T\ensuremath{\rightarrow}0 or remains finite but with nonanalytic wave-vector, frequency, and temperature dependence. We express our results in the language of recently discussed scaling theories, give the fixed-point action, and show that at this fixed point the fermion-gauge-field interaction is marginal in d=2, but irrelevant at low energies in d\ensuremath{\ge}2.

Observable zero sound in strongly correlated metals.

The slow zero-sound mode expected near the Mott transition in strongly interacting two-dimensional Fermi systems that are neutral is shown to persist as the physical sound mode in the case that the fermion carries electronic charge and is embedded in a positive ionic background. The latter sound velocity softens completely precisely at the Mott transition, indicating that a zone-center structural transition will occur in the system. We suggest that this phonon-softening mechanism is related to the structural transitions commonly observed in the oxide superconductors.

One and one half: Frontiers in FQHE theory

The fractional quantum Hall effect is a consequence of strong correlations among interacting electrons in two dimensions in high magnetic fields. Because of the Landau level degeneracy in these systems, expectations based on the properties of non-interacting electrons can fail completely and many novel electron-electron interaction effects occur. Recently, qualitatively new behavior has been uncovered in the properties of single-layer quantum Hall systems with Landau level filling factor equal to one half ( v = 1 2 and in the properties of double-layer systems with v = 1 2 per layer. The single-layer v = 1 2 system appears to have some properties similar to those of two-dimensional fermion systems at zero magnetic field. The double-layer v = 1 2 system has a spontaneoulsy broken symmetry analogous to that of quantum easy-plane ferromagnets and in a parallel magnetic field a commensurate-incommensurate phase transition occurs.

Singularities in the Vertex Function in Two-Dimensional Tight-Binding Fermi Systems11The project supported by National Natural Science Foundation of China

The singularities in the vertex function are studied within the ladder approximation for a non-half-filled two-dimensional tight-binding Fermi system. The location of all the possible poles of the vertex function has been clarified for both repulsive and attractive interacting cases. The scattering phase shift is examined and found not always zero at Fermi energy. The Kohn-Luttinger-like singularity is also briefly discussed.

Marginal fermi liquid behavior for a two-dimensional electronic system

The imaginary part of the self-energy of a two-dimensional Fermi system interacting with bosonic excitations has been calculated analytically and numerically. The result shows a marginal Fermi liquid behavior. The model can be a reasonable approach for studying the marginal behavior of a two-dimensional Millis-Monien-Pines phenomenological model.

Low-density repulsive Fermi gas in two dimensions: Bound-pair excitations and Fermi-liquid behavior.

We study the dilute-gas expansion for a two-dimensional Fermi system with arbitrary short-range repulsive interactions. In contrast with the three-dimensional case, we find an unusual pole in the vertex part in the particle-particle channel, for all center-of-mass momenta q2${\mathit{k}}_{\mathit{F}}$. We show that this represents an excitation consisting of bound hole pairs, which disperses down to zero energy at q=2${\mathit{k}}_{\mathit{F}}$. We study the effect of these bound states on the single-particle self-energy and find that the quasiparticles are well defined. Thus in the low-density regime, there is no breakdown of Fermi-liquid theory. In the Appendix we discuss the two-particle phase shift in the dilute Fermi gas, its connection with bound states, and the analogy with the potential scattering phase shift.

Landau f function for the dilute Fermi gas in two dimensions.

We study the Landau f function for a two-dimensional repulsive Fermi system in the dilute limit. We find the leading terms in the low-density expansion using second-order perturbation theory, following a method of Abrikosov and Khalatnikov. Further, using diagrammatic methods, we determine the essentially singular contribution coming from the two-hole bound state. The absence of a divergence in the f function, together with our earlier results on the quasiparticle lifetime, clearly demonstrates that the system is a Fermi liquid in the low-density regime.

Effect of singular interaction terms on two-dimensional Fermi liquids.

The structure of perturbation theory for an interacting two-dimensional Fermi system is analyzed, in the case where singular terms exist in the quasiparticle interactions. These give a hierarchy of singular terms in the one-particle self-energy. The dominant terms are self-consistently summed, to give a quasiparticle pole vanishing as Z(\ensuremath{\omega})\ensuremath{\sim}(\ensuremath{\omega}/${\mathrm{\ensuremath{\omega}}}_{0}$${)}_{0}^{\mathrm{\ensuremath{\rho}},\mathrm{\ensuremath{\delta}}2}$/${\mathrm{\ensuremath{\Elzxh}}}^{2}$N(0)${\mathrm{\ensuremath{\omega}}}_{0}$ near the Fermi energy (signaling a breakdown of Fermi-liquid theory), and a form for the scattering amplitude which is consistent with the assumed form for the quasiparticle interaction.

Temperature Dependence of ElectricalResistivity in Two-Dimensional Fermi Systems

The temperature ( T ) dependence of the resistivity due to the electron-electron scattering in two-dimensional Fermi systems is discussed. First, we consider an isotropic Fermi system. It is shown that the resistivity is proportional to T 2 , if 4 k F is larger than the smallest absolute value of the reciprocal lattice vectors, though the T -dependence of the damping is T 2 ln T . Next, we consider the Hubbard model. In the half-filled case, the resistivity is proportional to T ln T . The logarithmic correction is due to van Hove singularity. In the nearly half-filled case, it is pointed out that the main T -dependence of the resistivity is not T , but T 2 , and that the discussion on the T -dependence of the resistivity in the nested Fermi-liquid presented recently by Virosztek and Ruvalds is misleading.