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Chalupa P, Schäfer T, Reitner M, Springer D, Andergassen S, Toschi A. Fingerprints of the Local Moment Formation and its Kondo Screening in the Generalized Susceptibilities of Many-Electron Problems. PHYSICAL REVIEW LETTERS 2021; 126:056403. [PMID: 33605751 DOI: 10.1103/physrevlett.126.056403] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2020] [Revised: 12/08/2020] [Accepted: 01/08/2021] [Indexed: 06/12/2023]
Abstract
We identify the precise hallmarks of the local magnetic moment formation and its Kondo screening in the frequency structure of the generalized charge susceptibility. The sharpness of our identification even pinpoints an alternative criterion to determine the Kondo temperature of strongly correlated systems on the two-particle level, which only requires calculations at the lowest Matsubara frequency. We showcase its strength by applying it to the single impurity and the periodic Anderson model as well as to the Hubbard model. Our results represent a significant progress for the general understanding of quantum field theory at the two-particle level and allow for tracing the limits of the physics captured by perturbative approaches for correlated systems.
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Affiliation(s)
- P Chalupa
- Institute of Solid State Physics, TU Wien, A-1040 Vienna, Austria
| | - T Schäfer
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
- CPHT, CNRS, École Polytechnique, Institut Polytechnique de Paris, Route de Saclay, 91128 Palaiseau, France
| | - M Reitner
- Institute of Solid State Physics, TU Wien, A-1040 Vienna, Austria
| | - D Springer
- Institute of Solid State Physics, TU Wien, A-1040 Vienna, Austria
- Institute of Advanced Research in Artificial Intelligence, IARAI, A-1030 Vienna, Austria
| | - S Andergassen
- Institut für Theoretische Physik and Center for Quantum Science, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - A Toschi
- Institute of Solid State Physics, TU Wien, A-1040 Vienna, Austria
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2
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Transmission phase read-out of a large quantum dot in a nanowire interferometer. Nat Commun 2020; 11:3666. [PMID: 32699261 PMCID: PMC7376064 DOI: 10.1038/s41467-020-17461-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2020] [Accepted: 06/26/2020] [Indexed: 11/08/2022] Open
Abstract
Detecting the transmission phase of a quantum dot via interferometry can reveal the symmetry of the orbitals and details of electron transport. Crucially, interferometry will enable the read-out of topological qubits based on one-dimensional nanowires. However, measuring the transmission phase of a quantum dot in a nanowire has not yet been established. Here, we exploit recent breakthroughs in the growth of one-dimensional networks and demonstrate interferometric read-out in a nanowire-based architecture. In our two-path interferometer, we define a quantum dot in one branch and use the other path as a reference arm. We observe Fano resonances stemming from the interference between electrons that travel through the reference arm and undergo resonant tunnelling in the quantum dot. Between consecutive Fano peaks, the transmission phase exhibits phase lapses that are affected by the presence of multiple trajectories in the interferometer. These results provide critical insights for the design of future topological qubits.
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Edlbauer H, Takada S, Roussely G, Yamamoto M, Tarucha S, Ludwig A, Wieck AD, Meunier T, Bäuerle C. Non-universal transmission phase behaviour of a large quantum dot. Nat Commun 2017; 8:1710. [PMID: 29167429 PMCID: PMC5700201 DOI: 10.1038/s41467-017-01685-z] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2017] [Accepted: 10/10/2017] [Indexed: 11/09/2022] Open
Abstract
The electron wave function experiences a phase modification at coherent transmission through a quantum dot. This transmission phase undergoes a characteristic shift of π when scanning through a Coulomb blockade resonance. Between successive resonances either a transmission phase lapse of π or a phase plateau is theoretically expected to occur depending on the parity of quantum dot states. Despite considerable experimental effort, this transmission phase behaviour has remained elusive for a large quantum dot. Here we report on transmission phase measurements across such a large quantum dot hosting hundreds of electrons. Scanning the transmission phase along 14 successive resonances with an original two-path interferometer, we observe both phase lapses and plateaus. We demonstrate that quantum dot deformation alters the sequence of phase lapses and plateaus via parity modifications of the involved quantum dot states. Our findings set a milestone towards an comprehensive understanding of the transmission phase of quantum dots.
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Affiliation(s)
- Hermann Edlbauer
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
| | - Shintaro Takada
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
- National Institute of Advanced Industrial Science and Technology (AIST), National Metrology Institute of Japan (NMIJ), 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8563, Japan
| | - Grégoire Roussely
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
| | - Michihisa Yamamoto
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan
- RIKEN Center for Emergent Matter Science (CEMS), 2-1 Hirosawa, Wako-shi, Saitama, 31-0198, Japan
| | - Seigo Tarucha
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan
- RIKEN Center for Emergent Matter Science (CEMS), 2-1 Hirosawa, Wako-shi, Saitama, 31-0198, Japan
| | - Arne Ludwig
- Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Universitätsstraße 150, 44780, Bochum, Germany
| | - Andreas D Wieck
- Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Universitätsstraße 150, 44780, Bochum, Germany
| | - Tristan Meunier
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France
| | - Christopher Bäuerle
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France.
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Kreisbeck C, Kramer T, Molina RA. Time-dependent wave packet simulations of transport through Aharanov-Bohm rings with an embedded quantum dot. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:155301. [PMID: 28195564 DOI: 10.1088/1361-648x/aa605d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We have performed time-dependent wave packet simulations of realistic Aharonov-Bohm (AB) devices with a quantum dot embedded in one of the arms of the interferometer. The AB ring can function as a measurement device for the intrinsic transmission phase through the quantum dot, however, care has to be taken in analyzing the influence of scattering processes in the junctions of the interferometer arms. We consider a harmonic quantum dot and show how the Darwin-Fock spectrum emerges as a unique pattern in the interference fringes of the AB oscillations.
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Affiliation(s)
- C Kreisbeck
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, United States of America
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Brun B, Martins F, Faniel S, Hackens B, Cavanna A, Ulysse C, Ouerghi A, Gennser U, Mailly D, Simon P, Huant S, Bayot V, Sanquer M, Sellier H. Electron Phase Shift at the Zero-Bias Anomaly of Quantum Point Contacts. PHYSICAL REVIEW LETTERS 2016; 116:136801. [PMID: 27081995 DOI: 10.1103/physrevlett.116.136801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2015] [Indexed: 06/05/2023]
Abstract
The Kondo effect is the many-body screening of a local spin by a cloud of electrons at very low temperature. It has been proposed as an explanation of the zero-bias anomaly in quantum point contacts where interactions drive a spontaneous charge localization. However, the Kondo origin of this anomaly remains under debate, and additional experimental evidence is necessary. Here we report on the first phase-sensitive measurement of the zero-bias anomaly in quantum point contacts using a scanning gate microscope to create an electronic interferometer. We observe an abrupt shift of the interference fringes by half a period in the bias range of the zero-bias anomaly, a behavior which cannot be reproduced by single-particle models. We instead relate it to the phase shift experienced by electrons scattering off a Kondo system. Our experiment therefore provides new evidence of this many-body effect in quantum point contacts.
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Affiliation(s)
- B Brun
- Université Grenoble Alpes, F-38000 Grenoble, France
- CNRS, Institut NEEL, F-38042 Grenoble, France
| | - F Martins
- IMCN/NAPS, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
| | - S Faniel
- IMCN/NAPS, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
| | - B Hackens
- IMCN/NAPS, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
| | - A Cavanna
- CNRS, Laboratoire de Photonique et de Nanostructures, UPR20, F-91460 Marcoussis, France
| | - C Ulysse
- CNRS, Laboratoire de Photonique et de Nanostructures, UPR20, F-91460 Marcoussis, France
| | - A Ouerghi
- CNRS, Laboratoire de Photonique et de Nanostructures, UPR20, F-91460 Marcoussis, France
| | - U Gennser
- CNRS, Laboratoire de Photonique et de Nanostructures, UPR20, F-91460 Marcoussis, France
| | - D Mailly
- CNRS, Laboratoire de Photonique et de Nanostructures, UPR20, F-91460 Marcoussis, France
| | - P Simon
- Laboratoire de Physique des Solides, Université Paris-Sud, F-91405 Orsay, France
| | - S Huant
- Université Grenoble Alpes, F-38000 Grenoble, France
- CNRS, Institut NEEL, F-38042 Grenoble, France
| | - V Bayot
- Université Grenoble Alpes, F-38000 Grenoble, France
- IMCN/NAPS, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
| | - M Sanquer
- Université Grenoble Alpes, F-38000 Grenoble, France
- CEA, INAC-SPSMS, F-38054 Grenoble, France
| | - H Sellier
- Université Grenoble Alpes, F-38000 Grenoble, France
- CNRS, Institut NEEL, F-38042 Grenoble, France
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Dinaii Y, Gefen Y, Rosenow B. Transmission phase lapses through a quantum dot in a strong magnetic field. PHYSICAL REVIEW LETTERS 2014; 112:246801. [PMID: 24996099 DOI: 10.1103/physrevlett.112.246801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2013] [Indexed: 06/03/2023]
Abstract
The phase of the transmission amplitude through a mesoscopic system contains information about the system's quantum mechanical state and excitations thereof. In the absence of an external magnetic field, abrupt phase lapses occur between transmission resonances of quantum dots and can be related to the signs of tunneling matrix elements. They are smeared at finite temperatures. By contrast, we show here that in the presence of a strong magnetic field, phase lapses represent a genuine interaction effect and may occur also on resonance. We identify a relevant physical regime where these phase lapses are robust against finite temperature broadening.
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Affiliation(s)
- Yehuda Dinaii
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Yuval Gefen
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Bernd Rosenow
- Institut für Theoretische Physik, Universität Leipzig, D-04103 Leipzig, Germany
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Jalabert RA, Weick G, Weidenmüller HA, Weinmann D. Transmission phase of a quantum dot and statistical fluctuations of partial-width amplitudes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:052911. [PMID: 25353865 DOI: 10.1103/physreve.89.052911] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2013] [Indexed: 06/04/2023]
Abstract
Experimentally, the phase of the amplitude for electron transmission through a quantum dot (transmission phase) shows the same pattern between consecutive resonances. Such universal behavior, found for long sequences of resonances, is caused by correlations of the signs of the partial-width amplitudes of the resonances. We investigate the stability of these correlations in terms of a statistical model. For a classically chaotic dot, the resonance eigenfunctions are assumed to be Gaussian distributed. Under this hypothesis, statistical fluctuations are found to reduce the tendency towards universal phase evolution. Long sequences of resonances with universal behavior only persist in the semiclassical limit of very large electron numbers in the dot and for specific energy intervals. Numerical calculations qualitatively agree with the statistical model but quantitatively are closer to universality.
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Affiliation(s)
- Rodolfo A Jalabert
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504, F-67034 Strasbourg, France
| | - Guillaume Weick
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504, F-67034 Strasbourg, France
| | | | - Dietmar Weinmann
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504, F-67034 Strasbourg, France
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Ţolea M, Moldoveanu V, Dinu IV, Tanatar B. Electronic transmittance phase extracted from mesoscopic interferometers. NANOSCALE RESEARCH LETTERS 2012; 7:568. [PMID: 23061877 PMCID: PMC3583753 DOI: 10.1186/1556-276x-7-568] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/16/2012] [Accepted: 09/25/2012] [Indexed: 06/01/2023]
Abstract
: The usual experimental set-up for measuring the wave function phase shift of electrons tunneling through a quantum dot (QD) embedded in a ring (i.e., the transmittance phase) is the so-called 'open' interferometer as first proposed by Schuster et al. in 1997, in which the electrons back-scattered at source and the drain contacts are absorbed by additional leads in order to exclude multiple interference. While in this case one can conveniently use a simple two-path interference formula to extract the QD transmittance phase, the open interferometer has also a number of draw-backs, such as a reduced signal and some uncertainty regarding the effects of the extra leads. Here we present a meaningful theoretical study of the QD transmittance phase in 'closed' interferometers (i.e., connected only to source and drain leads). By putting together data from existing literature and giving some new proofs, we show both analytically and by numerical simulations that the existence of phase lapses between consecutive resonances of the 'bare' QD is related to the signs of the corresponding Fano parameters - of the QD + ring system. More precisely, if the Fano parameters have the same sign, the transmittance phase of the QD exhibits a Π lapse. Therefore, closed mesoscopic interferometers can be used to address the 'universal phase lapse' problem. Moreover, the data from already existing Fano interference experiments from Kobayashi et al. in 2003 can be used to infer the phase lapses.
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Affiliation(s)
- M Ţolea
- , National Institute of Materials Physics, P. O. Box MG-7, Bucharest-Magurele 77125, Romania
| | - V Moldoveanu
- , National Institute of Materials Physics, P. O. Box MG-7, Bucharest-Magurele 77125, Romania
| | - IV Dinu
- , National Institute of Materials Physics, P. O. Box MG-7, Bucharest-Magurele 77125, Romania
| | - B Tanatar
- Department of Physics, Bilkent University, Bilkent, Ankara 06800, Turkey
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Ţolea M, Ostahie B, Niţă M, Ţolea F, Aldea A. Phase extraction in disordered isospectral shapes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:036604. [PMID: 22587199 DOI: 10.1103/physreve.85.036604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2011] [Indexed: 05/31/2023]
Abstract
The phase of the electronic wave function is not directly measurable but, quite remarkably, it becomes accessible in pairs of isospectral shapes, as recently proposed in the experiment by Moon et al. [Science 319, 782 (2008)]. The method is based on a special property, called transplantation, which relates the eigenfunctions of the isospectral pairs, and allows us to extract the phase distributions, if the amplitude distributions are known. We numerically simulate such a phase extraction procedure in the presence of disorder, which is introduced both as Anderson disorder and as roughness at edges. With disorder, the transplantation can no longer lead to a perfect fit of the wave functions, however we show that a phase can still be extracted-defined as the phase that minimizes the misfit. Interestingly, this extracted phase coincides with (or differs negligibly from) the phase of the disorder-free system, up to a certain disorder amplitude, and a misfit of the wave functions as high as ~5%, proving a robustness of the phase extraction method against disorder. However, if the disorder is increased further, the extracted phase shows a puzzle structure, no longer correlated with the phase of the disorder-free system. A discrete model is used, which is the natural approach for disorder analysis. We provide a proof that discretization preserves isospectrality and the transplantation can be adapted to the discrete systems.
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Affiliation(s)
- Mugurel Ţolea
- National Institute of Materials Physics, POB MG-7, 77125 Bucharest-Magurele, Romania
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Molina RA, Jalabert RA, Weinmann D, Jacquod P. Scattering phase of quantum dots: emergence of universal behavior. PHYSICAL REVIEW LETTERS 2012; 108:076803. [PMID: 22401237 DOI: 10.1103/physrevlett.108.076803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2011] [Indexed: 05/31/2023]
Abstract
We investigate scattering through chaotic ballistic quantum dots in the Coulomb-blockade regime. Focusing on the scattering phase, we show that large universal sequences emerge in the short wavelength limit, where phase lapses of π systematically occur between two consecutive resonances. Our results are corroborated by numerics and are in qualitative agreement with existing experiments.
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Andergassen S, Meden V, Schoeller H, Splettstoesser J, Wegewijs MR. Charge transport through single molecules, quantum dots and quantum wires. NANOTECHNOLOGY 2010; 21:272001. [PMID: 20571187 DOI: 10.1088/0957-4484/21/27/272001] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We review recent progress in the theoretical description of correlation and quantum fluctuation phenomena in charge transport through single molecules, quantum dots and quantum wires. Various physical phenomena are addressed, relating to cotunneling, pair-tunneling, adiabatic quantum pumping, charge and spin fluctuations, and inhomogeneous Luttinger liquids. We review theoretical many-body methods to treat correlation effects, quantum fluctuations, non-equilibrium physics, and the time evolution into the stationary state of complex nanoelectronic systems.
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Affiliation(s)
- S Andergassen
- Institut für Theoretische Physik A, RWTH Aachen, 52056 Aachen, Germany
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12
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Goldstein M, Berkovits R, Gefen Y. Population switching and charge sensing in quantum dots: a case for a quantum phase transition. PHYSICAL REVIEW LETTERS 2010; 104:226805. [PMID: 20867195 DOI: 10.1103/physrevlett.104.226805] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2009] [Indexed: 05/29/2023]
Abstract
A broad and a narrow level of a quantum dot connected to two external leads may swap their respective occupancies as a function of an external gate voltage. By mapping this problem onto a multiflavored Coulomb gas we show that such population switching is not abrupt. However, trying to measure it by adding a third electrostatically coupled lead may render this switching an abrupt first order quantum phase transition. This is related to the interplay of the Mahan mechanism versus the Anderson orthogonality catastrophe, in similitude to the Fermi edge singularity. A concrete setup for experimental observation of this effect is also suggested.
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Affiliation(s)
- Moshe Goldstein
- The Minerva Center, Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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Baksmaty LO, Yannouleas C, Landman U. Nonuniversal transmission phase lapses through a quantum dot: an exact diagonalization of the many-body transport problem. PHYSICAL REVIEW LETTERS 2008; 101:136803. [PMID: 18851479 DOI: 10.1103/physrevlett.101.136803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2007] [Indexed: 05/26/2023]
Abstract
Systematic trends of nonuniversal behavior of electron-transmission phases through a quantum dot, with no phase lapse for the transition N = 1-->N = 2 and a lapse of pi for the N = 2-->N = 3 transition, are predicted, in agreement with experiments, from many-body transport calculations involving exact diagonalization of the dot Hamiltonian. The results favor shape anisotropy of the dot and strong e-e repulsion with consequent electron localization, showing dependence on spin configurations and the participation of excited doorway transmission channels.
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Affiliation(s)
- Leslie O Baksmaty
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA
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