Mesoscopic Fluctuations in the Ground State Energy of Disordered Quantum Dots

Sivan, Uri; Berkovits, Richard; Aloni, Yael; Prus, O.; Auerbach, Assa; Ben-Yoseph, Gdalyahu

doi:10.1103/physrevlett.77.1123

Cited by 169 publications

(362 citation statements)

References 11 publications

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“…Experimentally, the distribution is closer to a Gaussian, 5,6,7 and this was understood to be a residual interaction effect.…”

Section: Hartree-fock Approach To Disordered Systems: Addition Ofmentioning

confidence: 99%

“…While certain statistical properties of the conductance peak heights can be described within the CI plus RMT model, 3,4 other observables, most notably the distribution of the distance between successive conductance peaks (a distance known as the peak spacing), deviate significantly from the predictions of the CI plus RMT model. 5,6,7,8 These deviations have been understood, at least qualitatively, to follow from residual interaction effects beyond the charging energy. 5,9,10 Such residual interaction effects are at the center of the present investigation.…”

Section: Introductionmentioning

confidence: 99%

“…For a small number of electrons, exact numerical solutions are possible. 5,10 For a larger number of electrons, such models have been studied in the Hartree-Fock (HF) approximation 18,19,20 and in a density functional approach. 21,22,23 These models contributed significantly to our understanding of interaction effects in almost isolated dots, but they also contain non-generic features.…”

Section: Introductionmentioning

confidence: 99%

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Disordered mesoscopic systems with interactions: Induced two-body ensembles and the Hartree-Fock approach

2005

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We introduce a generic approach to study interaction effects in diffusive or chaotic quantum dots in the Coulomb blockade regime. The randomness of the single-particle wave functions induces randomness in the two-body interaction matrix elements. We classify the possible induced twobody ensembles, both in the presence and absence of spin degrees of freedom. The ensembles depend on the underlying space-time symmetries as well as on features of the two-body interaction. Confining ourselves to spinless electrons, we then use the Hartree-Fock (HF) approximation to calculate HF single-particle energies and HF wave functions for many realizations of the ensemble. We study the statistical properties of the resulting one-body HF ensemble for a fixed number of electrons. In particular, we determine the statistics of the interaction matrix elements in the HF basis, of the HF single-particle energies (including the HF gap between the last occupied and the first empty HF level), and of the HF single-particle wave functions. We also study the addition of electrons, and in particular the distribution of the distance between successive conductance peaks and of the conductance peak heights.

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“…Experimentally, the distribution is closer to a Gaussian, 5,6,7 and this was understood to be a residual interaction effect.…”

Section: Hartree-fock Approach To Disordered Systems: Addition Ofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Disordered mesoscopic systems with interactions: Induced two-body ensembles and the Hartree-Fock approach

2005

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“…For example, by measuring the spacings between the gate voltages for which a quantum dot connected to external leads exhibits conductance peaks, one can infer the inverse compressibility of the electron gas in the dot [1][2][3][4]. Devices of this type have recently been used to measure the manyparticle ground-state energy as a function of the number of electrons in a dot and large fluctuations (compared to the single electron level spacing) in this property were observed [3][4][5]. Large fluctuations have also been observed in earlier experiments in which the inverse compressibility of an insulating indium-oxide wire was measured [6].…”

Section: Introductionmentioning

confidence: 99%

Compressibility, capacitance, and ground-state energy fluctuations in a weakly interacting quantum dot

Berkovits

Altshuler²

1997

Phys. Rev. B

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We study the effect of electron-electron (e-e) interactions on compressibility, capacitance and inverse compressibility of electrons in a quantum dot or a small metallic grain. The calculation is performed in the random-phase approximation. As expected, the ensemble-averaged compressibility and capacitance decreases as a function of the interaction strength, while the mean inverse compressibility increases. Fluctuations of the compressibility are found to be strongly suppressed by the e-e interactions. Fluctuations of the capacitance and inverse compressibility also turn out to be much smaller than their averages. The analytical calculations are compared with the results of a numerical calculation for the inverse compressibility of a disordered tight-binding model. Excellent agreement for weak interaction values is found. Implications for the interpretation of current experimental data are discussed.

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“…However, s will also affect other properties which are more easily accessible in an experiment, like current-voltage characteristics: A nonzero ground state spin can serve to explain the absence of an even-odd structure in the addition spectra of Coulomb-blockaded quantum dots, 9,10,20,21 or the presence of kinks in the parametric dependence of Coulomb blockade peak positions, as was noted in Ref. 22.…”

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confidence: 99%

Mesoscopic fluctuations of the ground-state spin of a small metal particle

1999

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We study the statistical distribution of the ground state spin for an ensemble of small metallic grains, using a random-matrix toy model. Using the Hartree Fock approximation, we find that already for interaction strengths well below the Stoner criterion there is an appreciable probability that the ground state has a finite, nonzero spin. Possible relations to experiments are discussed. PACS numbers 71.24.+q, 75.10.Lp According to Hund's rule, 1 electrons in a partially filled shell in an atom form a many-body ground state with maximum possible spin. The maximum spin is preferred because it allows a maximally antisymmetric coordinate wavefunction in order to minimize the electrostatic repulsion between the electrons. In recent experiments, 2 Hund's rule was also observed in a cylindrically-shaped semiconductor quantum dot, or "artificial atom". The close similarity with real atoms is due to the degeneracy of single-particle levels, caused by the the high degree of symmetry of the device.In generic ultrasmall systems such as small metal grains, 3,4 semiconductor quantum dots, 5,6 or carbon nanotubes 7,8 there is no systematic degeneracy due to a spherical (or cylindrical) symmetric potential. However, even in the absence of degeneracies, a nonzero value of the ground state spin may occur, as long as the gain in electrostatic energy is larger than the loss in kinetic energy when an antisymmetric coordinate ground state wavefunction is formed. Such a ground state is most likely to be detected in ultrasmall metal and semiconductor devices, since in those systems, unlike in macroscopic samples, the spacing between single-particle energy levels and the typical interaction energies can be larger than the temperature. In fact, the possibility of such a "weakly ferromagnetic" ground state has been suggested as an explanation for some recent experiments, that could not be explained by simple noninteracting models. 4,7,9 In addition, a nonzero ground state spin from numerical simulations of a few particles in a chaotic dot, 10 and a theory of spin polarization in larger dots 11 were already mentioned in the literature. The stability of the zero spin ground state in a quantum dot was analyzed for weak interactions in Ref. 9.In this paper, we consider small metal grains in the mesoscopic regime, in which fluctuations of wavefunctions and energy levels, caused by, e. g., disorder or an irregular shape, control the behavior of kinetic and interaction energies at the vicinity of the Fermi energy. As a result, the ground state spin becomes subject to sampleto-sample fluctuations. Then, the relevant quantity to consider is the statistical distribution of the ground state spin for an ensemble of small metal grains or chaotic quantum dots, rather than the spin of a specific sample.Our starting point is a simple toy model that captures the essential mechanisms for mesoscopic fluctuations of the ground state spin. In second-quantized form, our model Hamiltonian H readswhere c † n,σ (c n,σ ) is the creation (annihilation) operator...

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Mesoscopic Fluctuations in the Ground State Energy of Disordered Quantum Dots

Cited by 169 publications

References 11 publications

Disordered mesoscopic systems with interactions: Induced two-body ensembles and the Hartree-Fock approach

Disordered mesoscopic systems with interactions: Induced two-body ensembles and the Hartree-Fock approach

Compressibility, capacitance, and ground-state energy fluctuations in a weakly interacting quantum dot

Mesoscopic fluctuations of the ground-state spin of a small metal particle

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