Many-electron systems

Kirill E. Nagaev

The electron-electron scattering does not affect the electrical current in Galilean-invariant systems. We show that nevertheless electron-electron collisions may contribute to the electric resistivity of systems with parabolic spectrum provided that they have multiply connected Fermi surface and there is an additional mechanism of scattering. To this end, we calculate the resistivity of a two-dimensional electron gas with two filled transverse subbands in a presence of electron-electron and impurity scattering. Though the collisions between the electrons do not directly affect the current in such systems, they cause a redistribution of the electrons between the Fermi contours, which results in a noticeable change of resistivity for realistic mechanisms of impurity scattering.

L. C. M. Miranda, D. ter Haar

Toshikatsu Koga

The pth-order conditional electron density C(p)N(r1, ..., rp − 1|rp) of an N-electron system is shown to have a peculiar property that when the radius rp = |rp| of the pth electron approaches ∞, it reduces to the (p−1)th-order reduced density Γ(p − 1)N − 1(r1, ..., rp − 1) divided by p of the (N−1)-electron system arising from the removal of an electron from the original system, where both systems are considered to be in their ground states.

S. Raimes

Stefan Lundqvist

A. A. Slutskin, M. Pepper, H. A. Kovtun

We consider an electron system under conditions of strong Anderson localization, taking into account interelectron long-range Coulomb repulsion. We have established that with the electron density going to zero the Coulomb interaction brings the arrangement of the Anderson localized electrons closer and closer to an ideal (Wigner) crystal lattice, provided the temperature is sufficiently low and the dimension of the system is > 1. The ordering occurs despite the fact that a random spread of the energy levels of the localized one-electron states, exceeding the mean Coulomb energy per electron, renders it impossible the electrons to be self-localized due to their mutual Coulomb repulsion This differs principally the Coulomb ordered Anderson localized electron system (COALES) from Wigner crystal, Wigner glass, and any other ordered electron or hole system that results from the Coulomb self-localization of electrons/holes. The residual disorder inherent to COALES is found to bring about a multi-valley ground-state degeneration akin to that in spin glass. With the electron density increasing, COALES is revealed to turn into Wigner glass or a glassy state of a Fermi-glass type depending on the width of the random spread of the electron levels.