Abstract
In this chapter we employ oval shaped quantum billiards connected by quantum wires as the building blocks of a linear quantum dot array which allows for the control of magnetoconductance in the linear response regime. In particular, we aim at a maximal finite- over zero-field ratio of the magnetoconductance, achieved by optimizing the geometry of the billiards. The switching effect arises from a relative phase change of scattering states in the single oval quantum dot through the applied magnetic field, which lifts a suppression of the transmission characteristic for a certain range of geometry parameters. A sustainable switching ratio is reached for a very low field strength, which is drastically enhanced already in the double-dot array. The impact of disorder is addressed in the form of remote impurity scattering, which poses a temperature dependent lower bound for the switching ratio. Excerpts and figures from Morfonios et al. (Phys. Rev. B, 80(3):035301, 2009) reprinted with permission. Copyright (2009) by the American Physical Society.
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Notes
- 1.
In [15] the transmission through a two-terminal elliptical cavity is investigated in terms of the effect of finite leads, and for particular values of the semiaxes a clear suppression of transmission is indeed seen which becomes more irregular close to the circular limit.
- 2.
Note that, although the symmetry of the dot (and thereby parity of the eigenstates) and the lead positioning are essential in the description of the transmission features, the nomenclature of nodal pairs serves simply as a handy way of labeling the states for convenient reference. It becomes unambiguous at higher energies where the number of nodes varies along cross-sections in each direction; see, e. g., state ν = 102 in the upper row of Fig. 6.3.
- 3.
In this case, the practically vanishing influence of varying d on the even-n states is not due to a zero overlap with an even y-parity lead state, but due to the fact that odd y-parity billiard states decay exponentially in the lead stubs (and thus reach the ends with practically zero amplitude).
- 4.
Note that the resonant energies in the open system do not happen to coincide with the energies of the corresponding closed dot eigenstates for the stub length chosen in Fig. 6.6b, but for smaller stub lengths. This shows that the transmission spectrum cannot generally be deduced from a given closed dot eigenspectrum.
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Morfonios, C.V., Schmelcher, P. (2017). Magnetoconductance Switching by Phase Modulation in Arrays of Oval Quantum Billiards . In: Control of Magnetotransport in Quantum Billiards. Lecture Notes in Physics, vol 927. Springer, Cham. https://doi.org/10.1007/978-3-319-39833-4_6
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