The properties of quasi-two-dimensional semiconductor quantum dots are reviewed. Experimental techniques for measuring the electronic shell structure and the effect of magnetic fields are briefly described. The electronic structure is analyzed in terms of simple single-particle models, density-functional theory, and "exact" diagonalization methods. The spontaneous magnetization due to Hund's rule, spin-density wave states, and electron localization are addressed. As a function of the magnetic field, the electronic structure goes through several phases with qualitatively different properties. The formation of the so-called maximum-density droplet and its edge reconstruction is discussed, and the regime of strong magnetic fields in finite dot is examined. In addition, quasi-one-dimensional rings, deformed dots, and dot molecules are considered. (Less)

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Electronic structure of quantum dots

It is now well established that the processing of bulk solids through the application of severe plastic deformation (SPD) leads to exceptional grain refinement to the submicrometer or nanometer level. Extensive research over the last decade has demonstrated that SPD processing also produces unusual phase transformations and leads to the introduction of a range of nanostructural features, including nonequilibrium grain boundaries, deformation twins, dislocation substructures, vacancy agglomerates, and solute segregation and clustering. These many structural changes provide new opportunities for fine tuning the characteristics of SPD metals to attain major improvements in their physical, mechanical, chemical, and functional properties. This review provides a summary of some of these recent developments. Special emphasis is placed on the use of SPD processing in achieving increased electrical conductivity, superconductivity, and thermoelectricity, an improved hydrogen storage capability, materials for use in biomedical applications, and the fabrication of high-strength metal-matrix nanocomposites.

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Producing Bulk Ultrafine-Grained Materials by Severe Plastic Deformation: Ten Years Later

Bulk nanoSPD materials are materials with nanostructural features, such as nanograins, nanoclusters, or nanotwins, produced by severe plastic deformation (SPD) techniques. Such nanostructured materials are fully dense and contamination free and in many cases they have superior mechanical and functional properties. Here, we provide a critical overview of such materials, with a focus on the fundamentals for the observed extraordinary properties. We discuss the unique nanostructures that lead to the superior properties, the underlying deformation mechanisms, the critical issues that remain to be investigated, future research directions, and the application potential of such materials.

https://www.tandfonline.com/doi/pdf/10.1080/21663831.2015.1060543

Fundamentals of superior properties in bulk NanoSPD materials

We report a transport experiment on the Fano effect in a quantum connecting wire with a side-coupled quantum dot (QD). The Fano resonance occurs between the QD and the ``T-shaped'' junction in the wire, and the transport detects antiresonance or a forward-scattered part of the wave function. While it is more difficult to tune the shape of the resonance in this geometry than in the previously reported Aharonov-Bohm-ring-type interferometer, the resonance purely consists of the coherent part of transport. Utilizing this advantage, we have quantitatively analyzed the temperature dependence of the Fano effect by including the thermal broadening and the decoherence. We have also proven that this geometry can be a useful interferometer for measuring the phase evolution of electrons at a QD.

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Fano resonance in a quantum wire with a side-coupled quantum dot

We review the theory of wave propagation in one dimension through a medium consisting of N identical “cells.” Surprisingly, exact closed-form results can be obtained for arbitrary N. Examples include the vibration of weighted strings, the acoustics of corrugated tubes, the optics of photonic crystals, and, of course, electron wave functions in the quantum theory of solids. As N increases, the band structure characteristic of waves in infinite periodic media emerges.

Waves in locally periodic media

Solving numerically the 3D nonlinear Ginzburg-Landau (GL) equations, we study equilibrium and nonequilibrium phase transitions between different superconducting states of mesoscopic disks which are thinner than the coherence length and the penetration depth. We have found a smooth transition from a multivortex superconducting state to a giant vortex state by increasing both the disk thickness and the magnetic field. A vortex phase diagram is obtained which shows, as a function of the magnetic field, a reentrant behavior between the multivortex and the giant vortex state.

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Vortex Phase Diagram for Mesoscopic Superconducting Disks

Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the one-dimensionality. The energy spectrum of the many-body states can be described by a rotation–vibration spectrum of a “Wigner molecule” of “localized” electrons, combined with the spin-state determined from an effective antiferromagnetic Heisenberg Hamiltonian. The persistent current as a function of the magnetic flux through the ring shows periodic oscillations arising from the “rigid rotation” of the electron ring. For polarized electrons the periodicity of the oscillations is always the flux quantum Φ 0 . For nonpolarized electrons the periodicity depends on the strength of the effective Heisenberg coupling and changes from Φ 0 first to Φ 0 /2 and eventually to Φ 0 / N when the ring gets narrower.

https://arxiv.org/pdf/cond-mat/0310064.pdf

Quantum rings for beginners: energy spectra and persistent currents

Solutions of Ginzburg-Landau equations coupled with three-dimensional Maxwell equations reveal an intriguing magnetic response of small superconducting particles, qualitatively different from the two-dimensional approximation but in agreement with recent experiments Depending on the radius and thickness, first or second order transitions are found for the normal to superconducting state For a sufficiently large radius of the disk, several transitions in the superconducting phase are obtained which correspond to different angular momentum giant vortex states The incorporation of the finite thickness in the calculation is crucial in order to obtain agreement with the position and the size of these jumps, and the line shape and magnitude of the magnetization curves

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Magnetization of mesoscopic superconducting disks

We have studied the quantum transmission properties of serial stub and loop structures. Throughout we have considered free-electron networks and the scattering arises solely due to the geometric nature of the problem. The band formation in these geometric structures is analyzed and compared with the conventional periodic-potential scatterers. Some essential differences are pointed out. We show that a single defect in an otherwise periodic structure modifies band properties nontrivially. By a proper choice of a single defect one can produce positive-energy bound states in continuum, in the sense of von Neumann and Wigner. We also discuss some magnetic properties of loop structures in the presence of Aharonov-Bohm flux.

Quantum waveguide transport in serial stub and loop structures.

We have considered a system of a metallic ring coupled to two electron reservoirs. We show that in the presence of a transport current, the persistent current can flow in a ring, even in the absence of a magnetic field. This is purely a quantum effect and is related to the current magnification in the loop. These persistent currents can be observed if one tunes the Fermi energy near the antiresonances of the total transmission coefficient or the two-port conductance.

P. Singha Deo

Papers

Vortex Phase Diagram for Mesoscopic Superconducting Disks

Quantum rings for beginners: energy spectra and persistent currents

Magnetization of mesoscopic superconducting disks

Quantum waveguide transport in serial stub and loop structures.

Persistent currents in the presence of a transport current