arXiv subjects

Carl A. Kukkonen

Publications and source records attributed to Carl A. Kukkonen.

5 recordsLinked to original sources

arXiv2026

The exact universal exchange-only local field factor of the uniform electron gas and its near-cancellation by parallel-spin correlation near 2kF

The exchange-only local field factor Gx(q,omega) of the uniform electron gas is exact and universal, a single curve at every density when q is measured in units of kF and omega in units of the Fermi energy. This paper assembles the known pieces of the static Gx(q,0) into one expression, evaluates it exactly at every wavevector, and releases it as a short Python module. It rises as (q/kF)^2/4, has a large peak of 1.99 just below 2kF, passes through the exact value pi^2/6 at 2kF, and tends to 1/3. Used alone in static linear response it predicts a spin density wave at rs = 4.96 and a charge density wave at rs = 10.62. Quantum Monte Carlo shows the gas has neither. Exchange enters the measured density and spin factors G+ and G- identically, so their difference, twice the antiparallel-spin factor, contains no exchange at all and is measured to be small and smooth through 2kF. Whatever removed the exchange peak is therefore in the parallel-spin channel, where everything beyond first-order exchange is large, negative, and mirrors the exchange peak. In the measured G+ the net removal is 40 to 48 percent of the peak at rs = 1 to 10. The stability of the metallic electron gas against exchange-driven density waves is a parallel-spin effect, and the decomposition shows where microscopic calculations of each channel should go.

cond-mat.supr-con↗

arXiv2024

Charge density waves and superconductivity in the electron-positive fermion gas using a simple intuitive model. Part I: The model, instabilities, and phase diagram

The electron-positive fermion gas in three dimensions and $T=0$ is modeled as two independent fermion gases interacting via the coulomb interaction. The main advantage of the simple model is that all existing results from the electron gas can be directly used for the positive fermion gas, which is the same as the electron gas, but scaled for the mass of the positive fermion. Additional screening from the positive fermions together with use of an accurate local field factor naturally introduces charge density waves in addition to the $q=0$ instability that occurs when the bulk modulus equals zero. The electron-positive fermion gas is completely specified by the density $r_s$ and the mass ratio $M/m$. Although the problem and model can be simply stated, the resulting phase diagram is complex and not fully understood. The results of the simple model are exact formulas, and are in close agreement with earlier numerical results obtained using density functional theory in their region of overlap. Using these results, the electron-electron, positive fermion-positive fermion and electron-positive fermion many body effective interactions are calculated in the following paper. For conditions close to the charge density wave, the positive fermion contribution to the electron-electron interaction, which is attractive and the source of the superconductivity, becomes large and significantly enhances the superconducting transition temperature, as well as leading to a large $T^2$ contribution to the normal state electrical resistivity.

cond-mat.supr-con↗

arXiv2024

Charge density waves and superconductivity in the electron-positive fermion gas using a simple intuitive model. Part II: Collective modes, effective interactions, superconductivity, and transport

Superconductivity and the normal state electrical resistivity which varies as $T^2$ are strongly enhanced near the compressibility and charge density wave instabilities in the electron-positive fermion gas. The additional screening from the positive fermions introduces an attractive term in the effective electron-electron interaction that is the basis for superconductivity. Electron-positive fermion scattering is the source of the $T^2$ term in the electrical resistivity. At an instability, both interactions are divergent. The superconducting transition temperature is estimated using the McMillan formula. The electron-positive fermion gas conducts electricity and heat. Because electron-electron and positive fermion-positive fermion scattering conserve momentum, they do not contribute to the electrical resistivity, but electron-positive fermion scattering does. All three scattering mechanisms contribute to the thermal resistivity. The simple model for the electron-positive fermion gas is physically intuitive and naturally introduces instabilities at $q=0$ when the bulk modulus becomes zero and charge density waves at finite $q$ under some circumstances. For each mass ratio $M/m$, there is a unique density $r_s$ where the energy is a minimum. For different mass ratios, the interactions are investigated at several values of $r_s$ ranging from below the energy minimum to that of the instability.

cond-mat.supr-con↗

arXiv2023

QMC-consistent static spin and density local field factors for the uniform electron gas

Analytic mathematical models for the static spin ($G_-$) and density ($G_+$) local field factors for the uniform electron gas (UEG) as functions of wavevector and density are presented. These models closely fit recent quantum Monte Carlo (QMC) data and satisfy exact asymptotic limits. This model for $G_-$ is available for the first time, and the present model for $G_+$ is an improvement over previous work. The QMC-computed $G_\pm$ are consistent with a rapid crossover between theoretically-derived small-$q$ and large-$q$ expansions of $G_\pm$. These expansions are completely determined by $r_\mathrm{s}$, the UEG correlation energy per electron, and the UEG on-top pair distribution function. We demonstrate their utility by computing uniform electron gas correlation energies over a range of densities. These models, which hold over an extremely wide range of densities, are recommended for use in practical time-dependent density functional theory calculations of simple metallic systems. A revised model of the spin susceptibility enhancement is developed that fits QMC data, and does not show a ferromagnetic instability at low density.

cond-mat.str-el↗

arXiv2021

Insights into the Electron-Electron Interaction from Quantum Monte Carlo Calculations

The effective electron-electron interaction in the electron gas depends on both the density and spin local field factors. Variational Diagrammatic Quantum Monte Carlo calculations of the spin local field factor are reported and used to quantitatively present the full spin-dependent, electron-electron interaction. Together with the charge local field factor from previous Diffusion Quantum Monte Carlo calculations, we obtain the complete form of the effective electron-electron interaction in the uniform three-dimensional electron gas. Very simple quadratic formulas are presented for the local field factors that quantitatively produce all of the response functions of the electron gas at metallic densities. Exchange and correlation become increasingly important at low densities. At the compressibility divergence at rs = 5.25, both the direct (screened Coulomb) term and the charge-dependent exchange term in the electron-electron interaction at q=0 are separately divergent. However, due to large cancellations, their difference is finite, well behaved, and much smaller than either term separately. As a result, the spin contribution to the electron-electron interaction becomes an important factor. The static electron-electron interaction is repulsive as a function of density but is less repulsive for electrons with parallel spins. The effect of allowing a deformable, rather than rigid, positive background is shown to be as quantitatively important as exchange and correlation. As a simple concrete example, the electron-electron interaction is calculated using the measured bulk modulus of the alkali metals with a linear phonon dispersion. The net electron-electron interaction in lithium is attractive for wave vectors $0-2k_F$, which suggests superconductivity, and is mostly repulsive for the other alkali metals.

cond-mat.quant-gas↗