Orbital magnetism in the ballistic regime: geometrical effects
Abstract
We present a general semiclassical theory of the orbital magnetic response of noninteracting electrons confined in twodimensional potentials. We calculate the magnetic susceptibility of singlyconnected and the persistent currents of multiply connected geometries. We concentrate on the geometric effects by studying confinement by perfect (disorder free) potentials stressing the importance of the underlying classical dynamics. We demonstrate that in a constrained geometry the standard Landau diamagnetic response is always present, but is dominated by finitesize corrections of a quasirandom sign which may be orders of magnitude larger. These corrections are very sensitive to the nature of the classical dynamics. Systems which are integrable at zero magnetic field exhibit larger magnetic response than those which are chaotic. This difference arises from the large oscillations of the density of states in integrable systems due to the existence of families of periodic orbits. The connection between quantum and classical behavior naturally arises from the use of semiclassical expansions. This key tool becomes particularly simple and insightful at finite temperature, where only short classical trajectories need to be kept in the expansion. In addition to the general theory for integrable systems, we analyze in detail a few typical examples of experimental relevance: circles, rings and square billiards. In the latter, extensive numerical calculations are used as a check for the success of the semiclassical analysis. We study the weakfield regime where classical trajectories remain essentially unaffected, the intermediate field regime where we identify new oscillations characteristic for ballistic mesoscopic structures, and the highfield regime where the typical de Haasvan Alphen oscillations exhibit finitesize corrections. We address the comparison with experimental data obtained in highmobility semiconductor microstructures discussing the differences between individual and ensemble measurements, and the applicability of the present model.
 Publication:

Physics Reports
 Pub Date:
 November 1996
 DOI:
 10.1016/03701573(96)000105
 arXiv:
 arXiv:condmat/9609201
 Bibcode:
 1996PhR...276....1R
 Keywords:

 Condensed Matter
 EPrint:
 88 pages, 15 Postscript figures, 3 further figures upon request, to appear in Physics Reports 1996