Elsevier

Surface Science

Volume 601, Issue 24, 15 December 2007, Pages 5788-5793
Surface Science

Hartree–Fock studies of quantum dots and the 0.7 anomaly

https://doi.org/10.1016/j.susc.2007.06.047Get rights and content

Abstract

We apply unrestricted Hartree–Fock to modelling two systems:

  • (1)

    We calculate the spin structure and addition spectra of small symmetric quantum dots (often called 2D “artificial atoms”), improving the accuracy considerably by including, for the first time, second-order correlation corrections. We compare the results to experiment and to previous numerical works, and find that our spin structure in some cases disagrees with that calculated within mean-field theories, such as Hartree–Fock without correlation corrections, or density-functional theory [C. Sloggett, O.P. Sushkov, Phys. Rev. B 71 (2005) 235326].

  • (2)

    We model the well-known 0.7 anomaly in the conductance of a quantum point contact. We calculate the conductance using direct calculation of scattering phases on a ring, within Hartree–Fock. We observe strong localisation of the Fermi electrons on the barrier, and suggest a mechanism for the observed temperature-dependent conductance anomaly.

Section snippets

Artificial atoms

Small (N < 20) symmetric quantum dots have been observed to act like atoms, in that they have a well-defined shell structure [2], [3] Such dots have been called “artificial atoms” and are of interest as they can be used to study some aspects of “atomic” physics in regimes inaccessible in real atoms: for instance, they allow direct measurement of transport properties and can be observed in magnetic fields that are very large relative to the orbital energies.

This shell structure was first observed

Model

The dot’s confining potential is roughly parabolic. This is a good approximation in the centre of the dot and hence for small numbers of electrons – one reason the shell structure breaks down at larger N.

We take the confining potential to beUext=12m∗(ωx2x2+ωy2y2),where m∗ is the effective mass of the electron, and for circular dots ωx = ωy.

A semiclassical estimate of the dot size allows us to define a characteristic rs for each dot as [1]:rs=3π413ω-23N-16.

Correlation corrections and symmetry

For a finite system such as a quantum

Model

To investigate the “pinching-off” of a quantum point contact we model a simple ring: a 1D chain with periodic boundary conditions. We place a barrier on the ring and, by varying the height of the barrier, can model the pinching off of the channel by a gate potential, so that the conductance varies from one unit of 2e2/h to zero. For the results shown in this paper, the external potential describing the barrier is given byU=U0exp((|x|-l)/d)+1,where we have taken l = 5aB and d = 1aB. This potential

Conclusions

We have used Hartree–Fock calculations for two distinct mesoscopic systems:

For the first time, we have calculated the correlation correction to the mean-field energy in small quantum dots. We find that the spin structure is notably different from that found in mean field theories alone such as HF or DFT, and that Hund’s rule often fails.

We have developed a new method of calculating conductance using scattering phases, which should be useful for other studies.

In a system exhibiting the 0.7

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