Semiclassical transport in nearly symmetric quantum dots I: symmetry-breaking in the dot

Details Semiclassical transport in nearly symmetric quantum dots I: symmetry-breaking in the dot Semiclassical transport in nearly symmetric quantum dots I: symmetry-breaking in the dot

2009-06-04

arxiv.org/abs/0906.0891v3

Phys. Rev. E 80, 056209 (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

(18pages - 9figs) This is the first of a pair of articles (v3 minor improvements to text)

Scientific paper

10.1103/PhysRevE.80.056209

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 four-fold 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.

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