Two-dimensional Fermi Gas Research Articles

Finite-Volume Fractional-Moment Criteria¶for Anderson Localization

A technically convenient signature of localization, exhibited by discrete operators with random potentials, is exponential decay of the fractional moments of the Green function within the appropriate energy ranges. Known implications include: spectral localization, absence of level repulsion, strong form of dynamical localization, and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. We present a family of finite-volume criteria which, under some mild restrictions on the distribution of the potential, cover the regime where the fractional moment decay condition holds. The constructive criteria permit to establish this condition at spectral band edges, provided there are sufficient `Lifshitz tail estimates' on the density of states. They are also used here to conclude that the fractional moment condition, and thus the other manifestations of localization, are valid throughout the regime covered by the ``multiscale analysis''. In the converse direction, the analysis rules out fast power-law decay of the Green functions at mobility edges.

Compton mechanism of neutrino and axion production on an effectively two-dimensional magnetized fermi gas

The Compton channels for the production of axions γe→ea and neutrinos γ e→vv in a magnetic field are examined on the basis of a two-dimensionally covariant formalism developed in this paper. Expressions are obtained for the cross sections of the processes as well as the power of the radiation per unit volume in a degenerate and nondegenerate electron gas. It is shown that the axion luminosity of white dwarfs on account of the Compton generation mechanism is at least four orders of magnitude less than the photon luminosity, and the axion luminosity for magnetic neutron stars approaches the neutrino luminosity in magnitude.

Constructive fractional-moment criteria for localization in random operators

We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.

The Bloch - Grüneisen regime in a one-dimensional electron gas

The momentum relaxation of one-dimensional electrons scattered by acoustic phonons has been investigated in the Bloch - Grüneisen temperature range. The temperature dependence of mobility follows the same, (for deformation acoustic interaction) and (for piezoelectric interaction), power laws as known for two-dimensional and three-dimensional Fermi gases. The calculations performed estimate to be at and at low electron concentrations. The specific feature of a one-dimensional gas is an intermediate temperature region, where an exponential temperature dependence of mobility is traced.

Pairing instability in an interacting Fermi gas

The Cooper instability in an interacting Fermi gas is examined by using the perturbational diagram approach. A graphical derivative method based on Ward's identity is introduced to represent the contributions to the interparticle interactions from different channels. It is shown that pairing instability for the electrons excited from the Fermi sea may happen as a result of the presence of holes even when the original interaction is repulsive. Thus, in contrast to the Cooper instability caused by a given attractive interaction, the pairing instability can be induced by the particle - hole excitations. The application of the results to a layered two-dimensional Fermi gas is considered.

Superconductivity and Metal-Insulator Phase Transition in a Layered Two-Dimensional Fermi Gas

Using the Fermi-liquid approach with vertex corrections, the effects of exchange and correlation are considered in a layered two-dimensional electron gas. It is shown that the interaction in the particle-hole channel can induce the metal-insulator phase transition when the Fermi momentum is comparable with the inverse interlayer spacing, p F 1/c. The possibility of superconductivity in the region between the insulator and normal metal phases, taking into account the particle-hole excitations, is discussed. A smooth crossover from weak to strong coupling superconductivity with the decrease of the 2D carrier density is obtained. The results suggest a new way in the explanation of the phase diagram of layered high-T C superconductors.

Effects of electron-phonoe interaction on the critical temperature of a layered two-dimensional superconductor

The critical temperature of a superconductor with a layered structure has been calculated. The influence of the electron-electron and electron-phonon interaction was considered in a microscopic model based on the layered two-dimensional Fermi gas. The calculations have been performed using the influence of the electron-phonon interaction on the Coulomb potential. An increasing of the critical temperatureT c was obtained due to the influenceof the electron-phonon interaction.

Bifurcation of quantum nonlinear resonances induced by a time-periodic vector potential

The quantum mechanics of a two-dimensional ideal electron Fermi gas in a cylindrical cavity in the presence of a weak time-periodic vector potential is studied. Floquet eigenstates are obtained numerically and Husimi distribution functions are used to show the bifurcation and appearance of quantum nonlinear resonances. For electrons at the Fermi surface, if the frequency of the vector potential ${\mathrm{\ensuremath{\omega}}}_{0}$ is lower than a certain critical frequency ${\mathrm{\ensuremath{\omega}}}_{\mathrm{cr}}$ then there is no electron having a primary resonance. If ${\mathrm{\ensuremath{\omega}}}_{0}$ is higher than ${\mathrm{\ensuremath{\omega}}}_{\mathrm{cr}}$, electrons with certain angular momenta will have primary resonances.

Dynamical susceptibility of a thermally excited neutral Fermi-liquid film.

We perform a detailed study of the dynamical susceptibility of two-dimensional Fermi gases and liquids, in terms of the momentum and energy transferred to the system by an external probe, and both at zero and at finite temperatures. The response of a noninteracting system is computed and analyzed together with that of a liquid subjected to a monopole interaction, paying special attention to the Landau limit. The disappearance of Pauli blocking associated with thermal effects is examined in the frame of the collisional Landau regime. All results are compared to the equivalent ones obtained for a three-dimensional Fermi liquid. \textcopyright{} 1996 The American Physical Society.

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.

Dynamical universality class of Brownian motion and exact results for a single-impurity s=1/2 XY chain.

Relaxation phenomena in a class of nondissipative systems with two highly disparate time scales (i.e., Brownian systems) have unique commonalities quantifiable via two scalars. It is shown that the exactly solvable problem of the dynamics of a weakly linked impurity spin in a s=1/2 XY chain belongs to this dynamical universality class and so does that of a heavy mass in an infinite harmonic oscillator chain and a spinless quasi two-dimensional attractive Fermi gas in the long-wavelength limit. The case of the strongly linked impurity in the XY chain is also discussed along with the corresponding limits in the harmonic oscillator chain and the electron-gas problems. \textcopyright{} 1996 The American Physical Society.

Two-Dimensional Fermi Gas at Half Filling is a Luttinger Liquid

It is shown that in a model with a regular long range interaction, a 2D fermion gas at half filling of the band is a Luttinger Liquid. It is found that under certain conditions the jump in the momentum distribution of such a gas at the Fermi surface depends on the filling factor ν in the form ∼|[(2ν-1)/Λ| 2α , where Λ -1 is the range of the interaction and α is a positive function of the position k on the Fermi surface. The jump vanishes when ν = 1/2.

Time-resolved study of carrier capture and recombination in monolayer Be δ-doped GaAs

The first measurements of subpicosecond dynamics of carrier capture and decay in Be δ-doped GaAs structures with p-doping density ranging from 6×1012 to 2×1014 cm−2 and spatial distribution on monolayer scale show that photoexcited carriers are captured in the δ-doped layer in <1 ps. Luminescence decay rates show a strong dependence on energy of the hole in the two-dimensional Fermi gas. We attribute this to a change in the spatial electron-hole overlap resulting from band-mixing effects. We show that Be density fluctuations lead to strong carrier localization.

Pair excitations in the ground state of a two-dimensional attractive Fermi gas.

Pair excitations in the ground state of a two-dimensional attractive Fermi gas.

Superfluidity of a two-dimensional dilute attractive Fermi gas.

It is demonstrated that the interaction between fluctuations of the pairing field in a two-dimensional (2D) dilute attractive Fermi gas stabilizes the low-temperature phase of the system. This result, which is valid for all values of the "coupling parameter" $\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}$ (where ${\ensuremath{\varepsilon}}_{0}$ is the two-fermion binding energy and ${\ensuremath{\varepsilon}}_{F}$ is the Fermi energy), then allows one to conclude that a 2D dilute attractive Fermi gas is superfluid at small but finite temperature.

Pair fluctuations in the ground state of a two-dimensional attractive Fermi gas

The excitation spectrum of pair fluctuations in the ground state of a dilute two-dimensional (2D) attractive Fermi-gas is studied for different coupling regimes. In the strong-coupling limit the spectrum has the Bogolubov form, but in the weak-coupling regime there are two types of the pair excitations (different from two-fermion scattering states): (i) long-wavelength collective mode with the cutoff at momentum q c ∼ 1/ ξ 0, where ξ 0 is the pair size, and (ii) pair excitations with q ⩾ √8 μm.

Fermion current-current interactions and orthogonality in two dimensions

Abstract The wavefunction renormalization Z of a two-dimensional Fermi gas with current-current interaction mediated by an unscreened transverse gauge field is discussed within a simple Hartree approximation for self-field effects. In the case of a three-dimensional gauge field, a critical coupling strength is required before level crossing and strict orthogonality occur. In the case of a two-dimensional gauge field, any finite coupling guarantees orthogonality beyond a critical system size.

Theory of p-wave pairing in a two-dimensional Fermi gas.

The specific heat and susceptibility data for $^{3}\mathrm{He}$ on Grafoil are analyzed in the framework of the Landau Fermi-liquid theory. The data suggest that the dominant interaction between $^{3}\mathrm{He}$ quasiparticles is an attraction in the p-wave channel. We have calculated explicitly the superfluid transition temperature in a two-dimensional Fermi gas and found that the prefactor in ${\mathit{T}}_{\mathit{c}}$ is very small (\ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}2}$--${10}^{\mathrm{\ensuremath{-}}3}$ depending on the form of the potential). For moderate areal densities of $^{3}\mathrm{He}$, ${\mathit{T}}_{\mathit{c}}$ is estimated to be on the scale of several millikelvin. The relevance of these results to the change in the temperature behavior of the specific heat observed below ${\mathit{T}}_{\mathit{k}}$=3.2 mK is discussed.

Two-dimensional Fermi gas with Heisenberg interaction within the Fermi sphere

A two-dimensional Fermi gas with a Heisenberg interaction within a sphere of radius p 0 in momentum space is investigated. Mean-field description of the system is exact in the thermodynamic limit. For small densities and strong coupling there is a second order phase transition and for high densities and strong coupling a first order transition, in both cases into a ferromagnetic phase. If p 0 is equal to the Fermi wave number of the system and the density of admissible states is vanishing in some interval above p 2 0 2 m for T >T c , the phase transition transforms the system from an insulator into a metal. A metal-insulator transition is also possible if p 2 0 2 m is twice the Fermi level.

LOW DENSITY HUBBARD MODEL IN TWO AND THREE DIMENSIONS

We consider two- and three-dimensional repulsive Hubbard models at low density, using the gas approximation. The large-U three-dimensional model is shown to behave as a Fermi liquid and the corresponding two-particle scattering length is found. In the two-dimensional case we find that the gas approximation is inconsistent, as indicated by an isolated pole of the two-particle Green function below the occupied states in the upper half-plane. This behaviour is specific to the lattice system as opposed to the continuum two-dimensional Fermi gas with short-range repulsion.