Excitation Spectra of Circular, Few-Electron Quantum Dots

Ashoori R. C., Nature 379, 413 (1996).

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10.1103/PhysRevLett.77.3613

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10.1103/PhysRevLett.78.1544

Figure 2 actually reproduces in large detail in four different samples implying that the structure in the density of states in the leads is not originating from a random impurity potential but probably from the lateral confinement potential of the pillar.

The sign of V sd is such that electrons first tunnel through the thicker barrier. In this situation only the excited states above the ground-state electrochemical potential are observed. For equal tunnel barriers tunneling out of the dot from excited states below the ground-state electrochemical potential can also be measured; see (2). Note that for a thick enough entrance barrier we can assume relaxation to the ground state between tunneling out and tunneling into the dot of the next electron.

See for example J. J. Palacios L. Martin-Moreno G. Chiappe E. Louis C. Tejedor Phys. Rev. B 50 5760 (1994); for more references see the review by

Johnson N. F., J. Phys. Condens. Matter 7, 965 (1995) .

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; C. G. Darwin Proc. Cambridge Philos. Soc. 27 86 (1930).

We believe that the smaller slopes in the experimental data of Fig. 5 for B > ∼7 T are due to a changing confinement potential because screening from the leads is modified by the formation of Landau levels in the leads. This is also reflected in the changing stripe width at high B.

Thurner G., Herold H., Ruder H., Schlicht G., Wunner G., Phys. Lett. 89A, 133 (1982).

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For details of the calculation see

Eto M., Jpn. J. Appl. Phys. 36, 3924 (1997);

. In the numerically exact calculations every electron is assumed to occupy one of the lowest 15 single-particle states at B = 0. The strength of the Coulomb interaction is fixed such that e 2 / ε ℏ︀/m*ωo = ℏ︀ω o (ε is the permittivity). (Interactions between electrons in the dot and in the leads are neglected.) The calculated results indicate that the many-body states consist of one main configuration [two main configurations for N = 3 and ( S M ) = (½ 2)] and several small contributions from other configurations. The depicted configurations in Fig. 3 overlap by ∼70% or more with the many-body ground states (the spin-polarized states overlap by more than 95%).

For a theoretical analyses of the N = 2 excitation spectrum see for example

Pfannkuche D., Gerhardts R. R., Maksym P. A., Gudmundsson V., Physica B 189, 6 (1993).

Also for N ∼ 100 quantum dots the excitation spectra of N and N + 1 can be strongly correlated as observed recently by D. R. Stewart et al. [

10.1126/science.278.5344.1784

We thank R. J. van der Hage J. Janssen Y. Kervennic J. E. Mooij S. K. Nair L. L. Sohn Y. Tokura and T. Uesugi for help and discussions. Supported by the Dutch Foundation for Fundamental Research on Matter. L.P.K. was supported by the Royal Netherlands Academy of Arts and Sciences.