N-orbital model for a two-dimensional disordered system in a strong magnetic field

Abstract

2014 Dans un champ magnétique intense, orthogonal au plan d'un système désordonné bi-dimensionnel, un modèle à N orbitales par site est considéré. L'Hamiltonien est projeté dans le niveau de Landau fondamental. Dans la limite de N grand, le résultat correspond à un col, invariant par translation, d'une théorie des champs. Le développement en puissances de 1/N est effectué diagrammatiquement et la conductivité est calculée jusqu'à l'ordre 1/N2. Dans ce développement on n'observe aucun seuil de mobilité. Le résultat est conforme au modèle 03C3 non linéaire unitaire; il est indépendant du champ magnétique et de l'intensité du désordre si l'on exprime l'énergie en unités de la largeur de bande. Abstract. 2014 An N-orbital model is considered for a two-dimensional disordered system in a strong perpendicular magnetic field. The Hamiltonian is projected on the lowest Landau level. In a field theoretical formulation the large N limit result corresponds to the translationally invariant saddle point for this model. A diagrammatic expansion in powers of 1/N is performed around the large N limit. The conductivity is calculated up to order 1/N2. No mobility edge is found in this expansion. The result is consistent with the non-linear unitary 03C3-model and independent of magnetic field and disorder strength if the energy is measured in units of the bandwidth.

Magnetic field induced crossover in weakly localized regimes and scaling of the conductivity

“…For variable magnetic field strength only incomplete details on logarithmic quantum corrections of the 2D conductivity in the weakly localized regime were known so far. These are formally summarized by Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:0198400450240116100 where a = 0 is the zero-field case [5,6], while the « strong field » a = 1 solution has been obtained both by phase factor approximation with an n-orbital model [7] and by the opposite modelling of zeroth Landau level occupation only [8,9]. For weak fields the negative In H-magnetoresistance and the log T-temperature behaviour due to inelastic scattering [10,11] are most important, and these are big effects due to the sensitivity of the cooperon.…”

On the Conductivity of a Two-Dimensional System of Electrons Moving in a Strong Magnetic Field and a Random Potential

“…Physically, they describe how the distribution for A develops as one moves along the chain. Clearly, for t+ CO the distribution should be concentrated more and more in the region of A1 = 1, h2 = 1 (Q(m) = S), because the first term in (7) increases as one goes along the chain and forces &(m + 1) to become similar to Q(m), and then the symmetry-breaking term (q) in (7), present all along the chain, gives preference to &(m) = S. This mechanism is clearly seen in the first term in the brackets [ ] in (14). It is hard to solve (14) exactly.…”

“…For zero external frequency w, similar as in the work of ref. [7,8] no indication is seen for an extended state at E = t. Whether this behaviour at the point E = 4 is due to the neglection of the renormalization of the effective Lagrangian…”