The Statistical theory of quantum dots

By Y. Alhassid. 2000

509 citations recorded by the source corpus.

A quantum dot is a sub-micron-scale conducting device containing up to several thousand electrons. Transport through a quantum dot at low temperatures is a quantum-coherent process. This review focuses on dots in which the electron's dynamics are chaotic or diffusive, giving rise to statistical properties that reflect the interplay between one-body chaos, quantum interference, and electron-electron interactions. The conductance through such dots displays mesoscopic fluctuations as a function of gate voltage, magnetic field, and shape deformation. The techniques used to describe these fluctuations include semiclassical methods, random-matrix theory, and the supersymmetric nonlinear \ensuremath{\sigma} model. In open dots, the approximation of noninteracting quasiparticles is justified, and electron-electron interactions contribute indirectly through their effect on the dephasing time at finite temperature. In almost-closed dots, where conductance occurs by tunneling, the charge on the dot is quantized, and electron-electron interactions play an important role. Transport is dominated by Coulomb blockade, leading to peaks in the conductance that at low temperatures provide information on the dot's ground-state properties. Several statistical signatures of electron-electron interactions have been identified, most notably in the dot's addition spectrum. The dot's spin, determined partly by exchange interactions, can also influence the fluctuation properties of the conductance. Other mesoscopic phenomena in quantum dots that are affected by the charging energy include the fluctuations of the cotunneling conductance and mesoscopic Coulomb blockade.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5b259bcf12282c22abafec4211d822f3b28a552e

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Magnetic dipole excitations in nuclei: Elementary modes of nucleonic motion (2010, background): “In these systems, electrons are laterally confined at the semiconductor boundary and form a two-dimensional (2D) quantum dot (see Alhassid (2000)).”
The uniform electron gas (2016, background): “The two-dimensional (2D) version of the UEG has also been the object of extensive research(14,15) because of its intimate connection to 2D or quasi-2D materials, such as quantum dots.(16,17) The one-dimensional (1D) UEG has recently attracted much attention due to its experimental realization in car”
Fano resonances in nanoscale structures (2009, background): “ibution from Coulomb interaction, the spectrum of many body states in a quantum dot can be obtained from the solution of the single particle problem. The single particle level spacing ∆sp = π~2/m∗L2 (Alhassid, 2000). The eﬀective mass of an electron in GaAs is rather low: m∗ = 0.067me (Alhassid, 200”
Granular electronic systems (2006, methodology): “In the latter case one may employ the random matrix theory (RMT) (Alhassid, 2000; Beenakker, 1997; Mehta, 1991) for an isolated single grain or, which is equivalent, the zero dimensional σ-model (Efetov, 1997).”
Electronic structure of quantum dots (2002, background): “(A review of the statistical theory of quantum dots, with a focus on chaotic or diffusive electron dynamics, was recently provided by Alhassid, 2000.)”
Light fields in complex media: Mesoscopic scattering meets wave control (2017, methodology): “In the specific context of disorder scattering it is mostly the work in mesoscopic physics (Akkermans and Montambaux, 2007; Imry, 2002; Sebbah, 2001; Stöckmann, 2006), quantum transport (Datta, 1997; Ferry and Goodnick, 1997; Mello and Kumar, 2004) and Random Matrix Theory (Alhassid, 2000; Beenakke”
Silicon quantum electronics (2012, background): “Much literature describes the electronic transport in all possible proportionalities of these energy scales with each other (Alhassid, 2000; Beenakker, 1991; Buttiker, 1988).”