Quantum effects in Coulomb blockade

Aleǐner, I. L.; Brouwer, Piet W.; Glazman, L. I.

doi:10.1016/s0370-1573(01)00063-1

Cited by 491 publications

(791 citation statements)

References 134 publications

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“…(5) and taking the limit g → ∞, we obtain the universal Hamiltonian of the quantum dot, with v 0 =v αβ;αβ , J s =v αβ;βα , and J c =v αα;ββ the direct, exchange and the Cooper channel interaction strengths, respectively. 12, 13 We note, however, that Eq. (9) is valid beyond this limit.…”

Section: A Mean Valuesmentioning

confidence: 87%

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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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Section: A Mean Valuesmentioning

confidence: 87%

“…In the limit g → ∞, only a few interaction terms survive, leading to the so-called universal Hamiltonian. 12,13 For spinless electrons, the interaction part of the universal Hamiltonian is composed of just the charging energy term. This shows that the CI model is appropriate for spinless electrons and in the limit g → ∞.…”

Section: Introductionmentioning

confidence: 99%

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

2005

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“…This separation of scales allows us to first analyze the disordered wave functions in the noninteracting limit and then explore interactions projected onto the zero-mode subspace. We next carry out this program using random-matrix theory, which is expected to apply in the above regime [48,49].…”

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confidence: 99%

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

2017

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The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes. We propose a solid-state implementation based on a quantum dot coupled to an array of topological superconducting wires hosting Majorana zero modes. Interactions and disorder intrinsic to the dot mediate the desired random Majorana couplings, while an approximate symmetry suppresses additional unwanted terms. We use random-matrix theory and numerics to show that our setup emulates the SYK model (up to corrections that we quantify) and discuss experimental signatures. DOI: 10.1103/PhysRevB.96.121119 Introduction. Majorana fermions provide building blocks for many novel phenomena. As one notable example, Majorana-fermion zero modes [1,2] capture the essence of non-Abelian statistics and topological quantum computation [3,4], and correspondingly now form the centerpiece of a vibrant experimental effort [5][6][7][8][9][10][11][12][13][14][15][16]. More recently, randomly interacting Majorana fermions governed by the "Sachdev-YeKitaev (SYK) model" [17][18][19] were shown to exhibit sharp connections to chaos, quantum-information scrambling, and black holes-naturally igniting broad interdisciplinary activity (see, e.g., [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]). The goal of this Rapid Communication is to exploit hardware components of a Majorana-based topological quantum computer for a tabletop implementation of the SYK model, thus uniting these very different topics.The SYK Hamiltonian reads

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“…The second term consists of several parts, each proportional to some power of 1/g; soĤ (1) int is small and sample-specific. The form of the universal part of the interaction Hamiltonian can be established from the symmetry requirement [30]. Indeed, in view of the invariance of the distribution function of the Random Matrix Hamiltonian with respect to an arbitrary orthogonal (for GOE) or unitary (in the case of GUE) transformation, the termĤ (0) int should consist of operators invariant under such transformations.…”

Section: The Constant Interaction Model and Its Justificationmentioning

confidence: 99%

“…Here b 1 ∼ 1 is a numerical coefficient which depends on the details of the potential confining the electrons [30,38]. As one can see, the correction (15) causes some shifts of the single-particle energy levels described by Hamiltonian (14) …”

Section: Vol 4 2003 Mesoscopic Fluctuations and Kondo Effect S617mentioning

confidence: 99%

Mesoscopic Fluctuations of Co-Tunneling and Kondo Effect in Quantum Dots

Glazman

2003

Ann. Henri Poincaré

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Abstract. Conductance of a quantum dot in the Coulomb blockade regime is discussed. At moderately low temperatures, the thermally-assisted transport of electrons through the dot gives way to elastic co-tunneling [1]. The amplitude of the elastic co-tunneling is sensitive to the specific structure of electron wave functions in a given sample. The conductance exhibits strong mesoscopic fluctuations [2]. Statistical properties of these fluctuations are reviewed in this lecture. At lower temperatures, conductance through a dot is altered by the Kondo effect, if the number of electrons on the dot is odd. We describe the universal features of the Kondo conductance [3,4], and briefly discuss the manifestations of this effect in the limiting cases of weak and strong [5] dot-lead coupling.

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Quantum effects in Coulomb blockade

Cited by 491 publications

References 134 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

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

Mesoscopic Fluctuations of Co-Tunneling and Kondo Effect in Quantum Dots

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