Unified model of fractal conductance fluctuations for diffusive and ballistic semiconductor devices

Abstract

We present an experimental comparison of magnetoconductance fluctuations measured in the ballistic, quasiballistic, and diffusive scattering regimes of semiconductor devices. In contradiction to expectations, we show that the spectral content of the magnetoconductance fluctuations exhibits an identical fractal behavior for these scattering regimes and that this behavior is remarkably insensitive to device boundary properties. We propose a unified model of fractal conductance fluctuations in the ballistic, quasiballistic, and diffusive transport regimes, in which the generic fractal behavior is generated by a subtle interplay between boundary and material-induced chaotic scattering events.

Effects of Dissipation and Noise on Chaotic Transport in Superlattices

“…In semiconductor physics, chaotic electron transport has been explored using a variety of two-dimensional billiard structures [1][2][3][4][5][6][7][8][9][10], antidot arrays [1,2,[11][12][13] and resonant tunneling diodes containing a wide quantum well enclosed by two tunnel barriers [1,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Despite the diversity of the systems studied in these previous works, they all involve systems in which the transition to chaos occurs by the gradual and progressive destruction of stable orbits in response to an increasing perturbation.…”

Fractal dynamics in chaotic quantum transport

“…These self-similar (or self-affine) structures were also found in many branches of chemistry and physics; prominent examples are crystal growth and fractal surfaces, and transport in gold nanowires and electron "billiards" [3,[8][9][10][11][12][13][14][15]. In contrast with idealized mathematical fractals continuing to infinitely small scales, fractal scaling in nature has a lower and an upper limit.…”

Tunable transmission via quantum state evolution in oval quantum dots

“…2.d) are located at kW π = 1.3442 and 1.3452, respectively. The phase relation between the leads is zero for the (11, 1) and π for the (8,3) state. This mechanism of decoupling of eigenstates and destructive interference leading to a suppression of conductance is not a peculiarity of the oval, but is robust with respect to moderate changes of the geometry.…”

“…These properties are robust with respect to the presence of disorder in the quantum dot. Magnetoconductance of two-dimensional mesoscopic structures in semiconductors is an intense field of current research both with respect to its theoretical understanding as well as possible applications [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. The quantum Hall effect [14,15] and its various applications, are spectacular examples for high magnetic field strengths.…”

“…The quantum Hall effect [14,15] and its various applications, are spectacular examples for high magnetic field strengths. In the regime of weak magnetic fields phenomena like weak localization [4,5,6] and fractal conductance fluctuations [4,7,8,16] in quantum billiard systems and the Aharonov-Bohm effect in, e.g., quantum rings [9] represent important features. For higher energies scarring effects are observed [1], which can be described semiclassically [17,18] in many cases.…”