Semiclassical transport in nearly symmetric quantum dots. I. Symmetry breaking in the dot.
We apply the semiclassical theory of transport to quantum dots with exact and approximate spatial symmetries; left-right mirror symmetry, up-down mirror symmetry, inversion symmetry, or fourfold symmetry. In this work-the first of a pair of articles-we consider (a) perfectly symmetric dots and (b) nearly symmetric dots in which the symmetry is broken by the dot's internal dynamics. The second article addresses symmetry-breaking by displacement of the leads. Using semiclassics, we identify the origin of the symmetry-induced interference effects that contribute to weak localization corrections and universal conductance fluctuations. For perfect spatial symmetry, we recover results previously found using the random-matrix theory conjecture. We then go on to show how the results are affected by asymmetries in the dot, magnetic fields, and decoherence. In particular, the symmetry-asymmetry crossover is found to be described by a universal dependence on an asymmetry parameter gamma_{asym} . However, the form of this parameter is very different depending on how the dot is deformed away from spatial symmetry. Symmetry-induced interference effects are completely destroyed when the dot's boundary is globally deformed by less than an electron wavelength. In contrast, these effects are only reduced by a finite amount when a part of the dot's boundary smaller than a lead-width is deformed an arbitrarily large distance.
Whitney
Robert S
RS
Institut Laue-Langevin, 38042 Grenoble, France.
Schomerus
Henning
H
Kopp
Marten
M
D000465:Algorithms; D008280:Magnetics; D015233:Models, Statistical; D036103:Nanotechnology / Q000379:methods; D017711:Nonlinear Dynamics; D010363:Pattern Recognition, Automated; D010825:Physics / Q000379:methods; D045663:Quantum Dots; D015203:Reproducibility of Results