Short-range correlations in a two-dimensional electron gas

Abstract

We construct a model for the value of the pair distribution function g↑↓(0) between antiparallel-spin electrons at contact in a two-dimensional electron gas with e2/r interactions, as a function of the coupling-strength parameter rs. The model involves an interpolation between the result of a low-rs expansion, including the second-order direct and exchange contributions to the energy in the paramagnetic state, and the result of a partial-wave phase-shift analysis near Wigner crystallization. The interpolation formula is in excellent agreement with many-body calculations based on the ladder approximation. We further show through an STLS self-consistent calculation that g↑↓(0) is essentially independent of the state of spin polarization of the electron gas.

Pair-distribution functions of the two-dimensional electron gas

“…39. As said at the beginning of this section, we determine the spin-resolved short-range coefficients for the ζ = 0 case, and then we assume an exchange-like ζ-dependence.…”

Correlation energy of a two-dimensional electron gas from static and dynamic exchange-correlation kernels

“…In determining the input for this form of the kernel we have again used the form of Rapisarda and Senatore 9 for ε c (r s ) and followed Atwal et al 16 in taking the values of g(0) from an interpolation formula proposed by Polini et al 18 . We have also checked simple variants of this scheme, taking g(0) from calculations in the ladder approximation 19 or dropping the frequency dependence of f AKA xc (q, iu).…”

Electron-electron interaction in a two-dimensional electron gas: Bound states at low densities

“…13,14 Moreover, this kind of channel could explain the recent finding of a bosonic contribution to the thermal conductivity of underdoped YBa 2 Cu 3 O x . 15 Recent success using the geminal representation for a correlated-pair state and different effective pair potentials [16][17][18][19][20] to calculate associated pair-correlation functions has motivated a further study on the possibility of pairing in 2D. As the onset of superconductivity is related to some form of increased order in the motion of the electrons, it is necessary, therefore, to take into account ways in which electrons interact with each other.…”

“…As the onset of superconductivity is related to some form of increased order in the motion of the electrons, it is necessary, therefore, to take into account ways in which electrons interact with each other. 21 Briefly, the motivating attempts [16][17][18][19][20] are based on properly weighted positive-energy scattering states ͑below the Fermi energy͒ needed to construct pair correlation functions. The success achieved suggests a similar attempt in the negativeenergy, bound-state region of the pair interaction.…”