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The European Physical Journal B

Spatial correlations of a two-dimensional electron gas

A. Isihara, Tadashi Toyoda

Published Dec 1, 1976• 11 citations
Publisher
DOI
10.1007/bf01316550

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We consider the static anomalous Cooper loop for the electron gas of arbitrary spatial dimensionality, D. This object enters the mean-field equation for the superconducting temperature, T_c. The closed expression in r- space is found at T=0 as an analytical function of D. Its counterpart in q-space has a logarithmic singularity at q=0 and no singularities at q=2k_F for any D. We extend our analysis for the case of finite T and note that in two dimensions the bound state of two electrons is possible even in the limit k_F -> 0. We comment on the possible implications of this fact for the theory of high-T_c cuprates.
We identify universal spatial fluctuations in systems with nontrivial spin dynamics. To this end we calculate by exact numerical diagonalization a variety of experimentally relevant correlations between spinor amplitudes, spin polarizations, and spin currents, both in the bulk and near the boundary of a confined two-dimensional clean electron gas in the presence of spin-orbit interaction. We support our claim of universality with the excellent agreement between the numerical results and system-independent spatial correlations of a random field defined on both the spatial and spin degrees of freedom. A rigorous identity relating our universal predictions with response functions provides a direct physical interpretation of our results in the framework of linear response theory.
We study spatial correlations in the ground state of a one-dimensional electron gas coupled to a dynamic quantum impurity. The system displays a nontrivial many-body effect known as the Fermi edge singularity: transitions between discrete internal states of the impurity have a power-law dependence on the internal energies of the impurity states. We present compact formulas for the static current-current correlator and the pair-correlation function. These reveal that spatial correlations induced by the impurity decay slowly (as the third inverse power of distance) and have a power-law energy dependence, characteristic of the Fermi edge singularity.