Periodic-orbits picture of fractal magnetoconductance fluctuations in quantum dots

Abstract

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 ω ⊥ 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 λ n with a curvature-dependent scaling factor λ= exp(−π/ ω ⊥ ) . 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.