Electronic states in two-dimensional interacting systems

Oracio Navarro, C. Wang

A. Karlhede

A solvable microscopic model of interacting electrons in a half-filled Landau level is presented. The Hamiltonian is a well-defined limit of the electron-electron interaction. The low energy sector consists of a set of independent, spatially interlaced, one-dimensional systems of non-interacting fermionic dipoles, each system with a Fermi sea ground state. The total number of dipoles in the set of Fermi seas forming the two-dimensional ground state equals the number of electrons in the system and the density of states at the Fermi level is that of a two-dimensional Fermi gas. The model is obtained by generalizing, or rather adopting, the existing exact solution on a thin, but not too thin, torus to the two-dimensional bulk case.

W. Hansen, D. Schmerek, Chr. Steinebach

Mohammed R. Sakr, Maryam Rahimi, S. V. Kravchenko

In noninteracting two-dimensional (2D) electron systems, the extended states ``float up'' in energy in the vanishing perpendicular magnetic field ${B}_{\ensuremath{\perp}},$ giving rise to an insulator. However, in strongly interacting 2D systems, the extended states remain at a finite energy as ${B}_{\ensuremath{\perp}}\ensuremath{\rightarrow}0,$ thus allowing conduction. Here we show that polarizing the electrons' spins in strongly interacting systems causes the extended states to once more ``float up'' in energy, as they do for noninteracting electrons. The difference between extended states that float up (an insulator) or remain at a constant energy (a metal) is thus unambiguously tied to the existence of the spins.

D. Baeriswyl, David K Campbell

Ryōen Shirasaki, Kaoru Iwano

One-dimensional strongly correlated electron system, which is accompanied by interaction with the lattice, has attracted a great deal of interest in both experimental and theoretical studies. At half-filling, this system is a Mott insulator when the electron–lattice interaction is weak. We performed a theoretical investigation of the stable ground state of the one-dimensional strongly correlated electron system with electron–lattice interaction in which one electron is doped from half-filling. We used an extended Peierls–Hubbard model. We report here that, contrary to “common sense” suppositions about the one-dimensional electron–lattice system, a polaron solution appears under conditions of comparatively strong electron–lattice interaction in the Mott phase and that the polaron delocalizes under conditions of weak electron–lattice interaction. These two states are separated by the strength of the electron–lattice interaction.