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Modeling single-particle energy levels and resonance currents in a coherent electronic quantum dot mixer
5.S. Amaha, C. Payette, J. A. Gupta, T. Hatano, K. Ono, T. Kodera, Y. Tokura, D. G. Austing, and S. Tarucha, Phys. Status Solidi C 5, 174 (2008).
12.E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, Science 311, 636 (2006).
14.For a one-dimensional harmonic potential, an anharmonicity with at least equal to is required to couple eigenstates with quantum numbers and . To see this, note that in the energy representation of a linear harmonic oscillator, is a tridiagonal matrix so that is a symmetric band matrix of width . This result easily generalizes to two dimensions so that the minimum required values of and equal and , respectively. The -field mixes and and modifies this condition to the one stated in the text.
15.Our model implicitly assumes that the QD-to-QD tunneling is the rate limiting step compared to the tunneling rates from the emitter to QD and from QD to the collector. While the opposite may be true for tunneling under low bias where the nearly identical -like states in the two QDs can be brought into resonance, there are two aspects of the experimental data which favor our assumption. First, the tunneling processes of interest involve nearly orthogonal states with a small overlap induced by anharmonic perturbations. Secondly, the conditions of the measurement of the spectrum in Fig. 1 involve rather high bias voltages so that the contacts are more strongly coupled to the QDs than at equilibrium conditions. While our simple analysis does qualitatively reproduce the observed resonant current dependences, a more complete model is desired to shed more light on the microscopic tunneling processes.
16.We note that the additional perturbation terms in themselves shift features in the spectrum to higher -field, and thus tend to increase the effective confinement. Hence, the confinement strength used in the calculations, , is slightly less than the value of 4.6 meV quoted for the ideal elliptical parabolic spectrum which reproduces well the measured spectrum (except in the vicinity of the crossings) (Ref. 4).
17.In Ref. 4, we established by fitting the data with an independent model that the mixing at anticrossing II can be well explained by two dominant and approximately equal couplings between the - and -like states and the - and -like states, and one much weaker coupling between the - and -like states. This result influenced our choice for the strengths of the higher degree terms in .
18.M. Hilke (unpublished).
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