Periodic-orbits picture of fractal magnetoconductance fluctuations in quantum dots

The recently observed fractal magnetoconductance fluctuations in general soft-wall quantum billiards are explained based on semiclassical periodic-orbit theory, in the frame of semiclassical Kubo formula for conductivity. The fractal-like fluctuations are shown to be due to self-similar periodic orbits born through pitchfork bifurcations of straight-line librating orbits oscillating towards harmonic saddles. The saddles with a transverse curvature omega(perpendicular to)(2) are naturally created right at the point contact between the attached leads and the cavity or at certain places inside the cavity as a consequence of soft-wall confinement. The fractal fluctuations are shown to obey the well-known Weierstrass-like spectrum lambda(n) with a curvature-dependent scaling factor lambda = exp(-pi/rootomega(perpendicular to)). They are self-affine, whose Hurst exponent are independent of the detailed shapes of the cavity, and determined only by the local geometrical feature of the leads. The experiment-oriented discussion is also given, revealing that the fluctuations of conductance as a function of Fermi energy does not give fractal-like fluctuations even though the magnetoconductance fluctuations are fractal-like. (C) 2002 Elsevier Science Ltd. All rights reserved.