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Kim SC, Lee JW, Eric Yang SR. Resonant, non-resonant and anomalous states of Dirac electrons in a parabolic well in the presence of magnetic fields. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:495302. [PMID: 23137993 DOI: 10.1088/0953-8984/24/49/495302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We report on several new basic properties of a parabolic dot in the presence of a magnetic field. The ratio between the potential strength and the Landau level (LL) energy spacing serves as the coupling constant of this problem. In the weak coupling limit the energy spectrum in each Hilbert subspace of an angular momentum consists of discrete LLs of graphene. In the intermediate coupling regime non-resonant states form a closely spaced energy spectrum. We find, counter-intuitively, that resonant quasi-bound states of both positive and negative energies exist in the spectrum. The presence of resonant quasi-bound states of negative energies is a unique property of massless Dirac fermions. As the strong coupling limit is approached resonant and non-resonant states transform into anomalous states, whose probability densities develop a narrow peak inside the well and another broad peak under the potential barrier. These properties may investigated experimentally by measuring optical transition energies that can be described by a scaling function of the coupling constant.
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Affiliation(s)
- S C Kim
- Physics Department, Korea University, Seoul 136-713, Korea
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Yannouleas C, Landman U. Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2007; 70:2067-2148. [PMID: 34996294 DOI: 10.1088/0034-4885/70/12/r02] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2007] [Indexed: 06/14/2023]
Abstract
Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semiconductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a two-step method of symmetry breaking at the unrestricted Hartree-Fock level and of subsequent symmetry restoration via post Hartree-Fock projection techniques. Quantitative and qualitative aspects of the two-step method are treated and validated by exact diagonalization calculations.Strongly-correlated phenomena emerging from symmetry breaking include the following.Chemical bonding, dissociation and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot, with potential technological applications to solid-state quantum-computing devices.Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. Such electron molecules exhibit ro-vibrational excitation spectra, in analogy with natural molecules.At high magnetic fields, the REMs are described by parameter-free analytic wave functions, which are an alternative to the Laughlin and composite-fermion approaches, offering a new point of view of the fractional quantum Hall regime in quantum dots (with possible implications for the thermodynamic limit).Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs). For a small number of bosons, the RBMs are energetically favored compared with the Gross-Pitaevskii solutions describing vortex formation.We discuss the present status concerning experimental signatures of such strongly correlated states, in view of the promising outlook created by the latest experimental improvements that are achieving unprecedented control over the range and strength of interparticle interactions.
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Affiliation(s)
| | - Uzi Landman
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA
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Koskinen M, Reimann SM, Nikkarila JP, Manninen M. Spectral properties of rotating electrons in quantum dots and their relation to quantum Hall liquids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2007; 19:076211. [PMID: 22251598 DOI: 10.1088/0953-8984/19/7/076211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The exact diagonalization technique is used to study many-particle properties of interacting electrons with spin, confined in a two-dimensional harmonic potential. The single-particle basis is limited to the lowest Landau level. The results are analysed as a function of the total angular momentum of the system. Only at angular momenta corresponding to the filling factors 1, 1/3, 1/5, etc is the system fully polarized. The lowest energy states exhibit spin waves, domains, and localization, depending on the angular momentum. Vortices exist only at excited polarized states. The high angular momentum limit shows localization of electrons and separation of the charge and spin excitations.
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Affiliation(s)
- M Koskinen
- NanoScience Center, Department of Physics, University of Jyväskylä, FIN-40014, Finland
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Abolfath RM, Hawrylak P. Real space Hartree-Fock configuration interaction method for complex lateral quantum dot molecules. J Chem Phys 2006; 125:34707. [PMID: 16863373 DOI: 10.1063/1.2219447] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present unrestricted Hartree-Fock method coupled with configuration interaction (CI) method (URHF-CI) suitable for the calculation of ground and excited states of large number of electrons localized by complex gate potentials in quasi-two-dimensional quantum dot molecules. The method employs real space finite difference method, incorporating strong magnetic field, for calculating single particle states. The Hartree-Fock method is employed for the calculation of direct and exchange interaction contributions to the ground state energy. The effects of correlations are included in energies and directly in the many-particle wave functions via CI method using a limited set of excitations above the Fermi level. The URHF-CI method and its performance are illustrated on the example of ten electrons confined in a two-dimensional quantum dot molecule.
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Affiliation(s)
- Ramin M Abolfath
- Institute for Microstructural Sciences, National Research Council of Canada, Ottawa K1A 0R6, Canada.
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Rontani M, Cavazzoni C, Bellucci D, Goldoni G. Full configuration interaction approach to the few-electron problem in artificial atoms. J Chem Phys 2006; 124:124102. [PMID: 16599657 DOI: 10.1063/1.2179418] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a new high performance configuration interaction code optimally designed for the calculation of the lowest-energy eigenstates of a few electrons in semiconductor quantum dots (also called artificial atoms) in the strong interaction regime. The implementation relies on a single-particle representation, but it is independent of the choice of the single-particle basis and, therefore, of the details of the device and configuration of external fields. Assuming no truncation of the Fock space of Slater determinants generated from the chosen single-particle basis, the code may tackle regimes where Coulomb interaction very effectively mixes many determinants. Typical strongly correlated systems lead to very large diagonalization problems; in our implementation, the secular equation is reduced to its minimal rank by exploiting the symmetry of the effective-mass interacting Hamiltonian, including square total spin. The resulting Hamiltonian is diagonalized via parallel implementation of the Lanczos algorithm. The code gives access to both wave functions and energies of first excited states. Excellent code scalability in a parallel environment is demonstrated; accuracy is tested for the case of up to eight electrons confined in a two-dimensional harmonic trap as the density is progressively diluted up to the Wigner regime, where correlations become dominant. Comparison with previous quantum Monte Carlo simulations in the Wigner regime demonstrates power and flexibility of the method.
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Affiliation(s)
- Massimo Rontani
- CNR-INFM National Research Center on nanoStructures and bioSystems at Surfaces (S3), Via Campi 213/A, 41100 Modena MO, Italy.
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Korkusiński M, Hawrylak P, Ciorga M, Pioro-Ladrière M, Sachrajda AS. Pairing of spin excitations in lateral quantum dots. PHYSICAL REVIEW LETTERS 2004; 93:206806. [PMID: 15600956 DOI: 10.1103/physrevlett.93.206806] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2003] [Indexed: 05/24/2023]
Abstract
We demonstrate the existence of correlated electronic states as paired spin excitations of lateral quantum dots in the integer quantum Hall regime. Starting from the spin-singlet filling-factor nu=2 droplet, by increasing the magnetic field we force the electrons to flip spins and increase the spin polarization. We identify the second spin-flip process as one accompanied by correlated, spin depolarized phases, interpreted as pairs of spin excitons. The correlated states are identified experimentally in few-electron lateral quantum dots using high source-drain voltage spectroscopy.
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Affiliation(s)
- Marek Korkusiński
- Institute for Microstructural Sciences, National Research Council of Canada, Ottawa K1A0R6, Canada
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Sim HS, Kataoka M, Yi H, Hwang NY, Choi MS, Yang SRE. Coulomb blockade and kondo effect in a quantum Hall antidot. PHYSICAL REVIEW LETTERS 2003; 91:266801. [PMID: 14754077 DOI: 10.1103/physrevlett.91.266801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2003] [Indexed: 05/24/2023]
Abstract
We propose a general capacitive model for an antidot, which has two localized edge states with different spins in the quantum Hall regime. The capacitive coupling of localized excess charges, which are generated around the antidot due to magnetic flux quantization, and their effective spin fluctuation can result in Coulomb blockade, h/(2e) Aharonov-Bohm oscillations, and the Kondo effect. The resultant conductance is in qualitative agreement with recent experimental data.
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Affiliation(s)
- H-S Sim
- School of Physics, Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Dongdaemun-gu, Seoul 130-722, Korea
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Ciorga M, Wensauer A, Pioro-Ladriere M, Korkusinski M, Kyriakidis J, Sachrajda AS, Hawrylak P. Collapse of the spin-singlet phase in quantum dots. PHYSICAL REVIEW LETTERS 2002; 88:256804. [PMID: 12097113 DOI: 10.1103/physrevlett.88.256804] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2001] [Indexed: 05/23/2023]
Abstract
We present experimental and theoretical results on a new regime in quantum dots in which the filling factor two-singlet state is replaced by new spin polarized phases. We make use of spin blockade spectroscopy to identify the transition to this new regime as a function of the number of electrons. The key experimental observation is a reversal of the phase in the systematic oscillation of the amplitude of Coulomb blockade peaks as the number of electrons is increased above a critical number. It is found theoretically that correlations are crucial to the existence of the new phases.
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Affiliation(s)
- M Ciorga
- Institute for Microstructural Science, Research Council of Canada, Ottawa, Canada K1A OR6
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Rokhinson LP, Guo LJ, Chou SY, Tsui DC. Magnetically induced reconstruction of the ground state in a few-electron Si quantum dot. PHYSICAL REVIEW LETTERS 2001; 87:166802. [PMID: 11690224 DOI: 10.1103/physrevlett.87.166802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2001] [Indexed: 05/23/2023]
Abstract
We report unexpected fluctuations in the positions of Coulomb blockade peaks at high magnetic fields in a small Si quantum dot. The fluctuations have a distinctive sawtooth pattern: as a function of magnetic field, linear shifts of peak positions are compensated by abrupt jumps in the opposite direction. The linear shifts have large slopes, suggesting formation of the ground state with a nonzero angular momentum. The value of the momentum is found to be well defined, despite the absence of the rotational symmetry in the dot.
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Affiliation(s)
- L P Rokhinson
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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Oaknin JH, Martín-Moreno L, Tejedor C. Skyrmions and edge-spin excitations in quantum Hall droplets. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:16850-16859. [PMID: 9985814 DOI: 10.1103/physrevb.54.16850] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Hastings MB, Levitov LS. Bragg Resonances for Tunneling Between Edges of a 2D Quantum Hall System. PHYSICAL REVIEW LETTERS 1996; 77:4422-4425. [PMID: 10062534 DOI: 10.1103/physrevlett.77.4422] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Hu J, Dagotto E, MacDonald AH. Spontaneous coherence and collective modes in double-layer quantum-dot systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:8616-8622. [PMID: 9984539 DOI: 10.1103/physrevb.54.8616] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Karlhede A, Kivelson SA, Lejnell K, Sondhi SL. Textured Edges in Quantum Hall Systems. PHYSICAL REVIEW LETTERS 1996; 77:2061-2064. [PMID: 10061847 DOI: 10.1103/physrevlett.77.2061] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Zhitenev NB, Brodsky M, Ashoori RC, Melloch MR. New Class of Resonances at the Edge of the Two Dimensional Electron Gas. PHYSICAL REVIEW LETTERS 1996; 77:1833-1836. [PMID: 10063183 DOI: 10.1103/physrevlett.77.1833] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Bolton F. Fixed-phase quantum Monte Carlo method applied to interacting electrons in a quantum dot. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:4780-4793. [PMID: 9986440 DOI: 10.1103/physrevb.54.4780] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Maksym PA. Eckardt frame theory of interacting electrons in quantum dots. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:10871-10886. [PMID: 9982658 DOI: 10.1103/physrevb.53.10871] [Citation(s) in RCA: 96] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Chengguang B, Wenying R, Youyang L. Structures of low-lying states of a four-electron system in a quantum dot. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:10820-10829. [PMID: 9982650 DOI: 10.1103/physrevb.53.10820] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Tanaka Y, Akera H. Many-body effects in transport through a quantum dot. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:3901-3911. [PMID: 9983943 DOI: 10.1103/physrevb.53.3901] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Hallam LD, Weis J, Maksym PA. Screening of the electron-electron interaction by gate electrodes in semiconductor quantum dots. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:1452-1462. [PMID: 9983606 DOI: 10.1103/physrevb.53.1452] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Heinzel T, Johnson AT, Wharam DA, Kotthaus JP, Böhm G, Klein W, Tränkle G, Weimann G. Coulomb-blockade oscillations in a quantum dot strongly coupled to leads. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:16638-16645. [PMID: 9981067 DOI: 10.1103/physrevb.52.16638] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Ahn KH, Oh JH, Chang KJ. Correlation effects in a quantum dot at high magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:13757-13760. [PMID: 9980582 DOI: 10.1103/physrevb.52.13757] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kamilla RK, Jain JK. Composite-fermion description of correlated electrons in quantum dots: Low-Zeeman-energy limit. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:2798-2804. [PMID: 9981350 DOI: 10.1103/physrevb.52.2798] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Johnson NF, Quiroga L. Analytic results for N particles with 1/r2 interaction in two dimensions and an external magnetic field. PHYSICAL REVIEW LETTERS 1995; 74:4277-4280. [PMID: 10058460 DOI: 10.1103/physrevlett.74.4277] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Lieb EH, Solovej JP, Yngvason J. Ground states of large quantum dots in magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:10646-10665. [PMID: 9977761 DOI: 10.1103/physrevb.51.10646] [Citation(s) in RCA: 45] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Ugajin R. Far-infrared absorption in coupled quantum dots. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:11136-11139. [PMID: 9977825 DOI: 10.1103/physrevb.51.11136] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Klein O, Tang D, Abusch-Magder DM, Meirav U, Wen X, Kastner AM, Wind SJ. Exchange Effects in an Artificial Atom at High Magnetic Fields. PHYSICAL REVIEW LETTERS 1995; 74:785-788. [PMID: 10058847 DOI: 10.1103/physrevlett.74.785] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Palacios JJ, Hawrylak P. Correlated few-electron states in vertical double-quantum-dot systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:1769-1777. [PMID: 9978898 DOI: 10.1103/physrevb.51.1769] [Citation(s) in RCA: 56] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Ferconi M, Vignale G. Current-density-functional theory of quantum dots in a magnetic field. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:14722-14725. [PMID: 9975719 DOI: 10.1103/physrevb.50.14722] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Palacios JJ, Martín-Moreno L, Chiappe G, Louis E, Tejedor C. Capacitance spectroscopy in quantum dots: Addition spectra and decrease of tunneling rates. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:5760-5763. [PMID: 9976933 DOI: 10.1103/physrevb.50.5760] [Citation(s) in RCA: 58] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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