Abstract
Numerical simulations have been carried out of the magneto-transport and corresponding wave functions of two quantum dot structures, namely the stadium and the Sinai billiard. In our simulations, the Schrödinger equation is mapped onto a tight-binding lattice by replacing derivatives by finite differences, and the conductance is calculated via the Landauer formula following the application of an iterative technique to translate across the structure. In both structures, many of the resonance features in the transport show scarring, that is, the amplitude of the corresponding wave functions is highly concentrated along underlying periodic classical orbits. Our analysis indicates that certain periodicities evident in the magneto-transport can be associated with particular orbits.
Highlights
Semiconductor billiards have recently attracted considerable interest as a novel probe of transport and quantum chaos
Despite the fact that the closed, classical analogs of the structures we have studied are know to be chaotic, we have found that regular periodic orbits strongly influence the magneto-transport of both the stadium and Sinai billiard structures
Evidence for these orbits is seen in scarred wave functions, which can recur periodically in magnetic field
Summary
Semiconductor billiards have recently attracted considerable interest as a novel probe of transport and quantum chaos. While it has been suggested that multiple billiard scattering from cavity walls will induce chaotic behavior [1], recent studies of rectangular billiards have established the basic regular nature of the orbits [2]. K. FERRY this effect, we have modeled the dots by solving the quantum mechanical problem on a discrete lattice using a numerically stabilized variant of the transfer matrix approach [6]. FERRY this effect, we have modeled the dots by solving the quantum mechanical problem on a discrete lattice using a numerically stabilized variant of the transfer matrix approach [6] The details of this method are summarized . We consider the Sinai billiard, which consists of a nominal square ballistic quantum dot with a circular anti-dot in the center and is another structure whose classical analog is chaotic.
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