  We present a general semiclassical theory of the orbital magnetic response of
noninteracting electrons confined in two-dimensional potentials. We calculate
the magnetic susceptibility of singly-connected 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 finite-size corrections of a quasi-random 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 weak-field regime where classical trajectories remain essentially
unaffected, the intermediate field regime where we identify new oscillations
characteristic for ballistic mesoscopic structures, and the high-field regime
where the typical de Haas-van Alphen oscillations exhibit finite-size
corrections. We address the comparison with experimental data obtained in
high-mobility semiconductor microstructures discussing the differences between
individual and ensemble measurements, and the applicability of the present
model.
