Collective Excitations of Electrons in High Magnetic Fields

G. Meissner, U. Brockstieger

F. J. Kok

Ken-ichi Shizuya

In a magnetic field two-dimensional (2D) electron systems host, with quenched kinetic energy, a variety of many-body correlation phenomena, such as interaction-driven new states and associated collective excitations over them. In a magnetic field, the two-body operators pertinent to the 2D Coulomb interaction obey a crossing relation, with which the Coulomb interaction is also cast into the form of manifest exchange interaction. It is shown that active use of this direct/exchange duality of the interaction allows one to develop, within the framework of the single-mode approximation, a new efficient algorithm for handling a wide class of collective excitations. The utility of our algorithm is demonstrated by studying some examples of inter- and intra-Landau-level collective excitations in graphene and in conventional electron systems.

Viktor Mikhaĭlovich Galit︠s︡kiĭ

Matthew Brownlie

This is a mathematical study of certain aspects of the interacting electron system in very high perpendicular magnetic field.\nWe analyse restrictions imposed upon the density correlation functions of this system and propose a set of sum rules which they must obey.\nWe study the possibility of building a bosonisation scheme for the projected density operators in the lowest Landau level. We suggest a second order bosonisation, along with an approximation scheme, which may be useful for carrying out calculations in the lowest Landau level.\nWe analyse the possible ground states of the system. We suggest a set of variational wavefunctions which can have lower energy than the Laughlin state for sufficiently soft interaction potentials.\nWe study the collective excitations of the system, paying particular attention to its symmetries. We suggest a set of variational excited states and discuss their applicability to finite as well as infinite systems.

P. Schlottmann, Rolf R. Gerhardts