On size corrections to the diamagnetic susceptibility of a free electron gas

Denton, Richard V.

doi:10.1007/bf01394652

Cited by 24 publications

(15 citation statements)

References 10 publications

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“…There is an extensive literature on finite-size orbital magnetic effects in conductors, [5][6][7][8] and Sivan and Imry 9 have discussed the de Haas-van Alphen oscillations in small (and simply connected) quantum dots. Several investigators have also studied the related problem of magnetization in semi-conductor quantum dots; see Refs.…”

Section: Introductionmentioning

confidence: 99%

Magnetic-moment oscillations in a quantum Hall ring

Georgiev

Geller

2004

Phys. Rev. B

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We predict nonmesoscopic oscillations in the orbital magnetic moment of a thin semiconductor ring in the quantum Hall effect regime. These oscillations, which occur as a function of magnetic field because of a competition between paramagnetic and diamagnetic currents in the ring, are a direct probe of the equilibrium current distribution in the nonuniform quantum Hall fluid. The amplitude of the oscillating moment in a thin ring with major radius R and minor radius (half-width) a is approximately aRe c / c, where c is the cyclotron frequency.

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Section: Introductionmentioning

confidence: 99%

Magnetic-moment oscillations in a quantum Hall ring

Georgiev

Geller

2004

Phys. Rev. B

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“…The importance of geometrical effects for the finite-size corrections in the above defined macroscopic limit had already been noticed in terms of the sensitivity of the magnetic susceptibility on the structure of the confining potential [10][11][12]. The chosen potentials were obviously non generic but used due to their calculational simplicity, and therefore it was not possible to anticipate the order-of-magnitude effect that classical dynamics might have on the susceptibility outside the macroscopic limit.…”

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confidence: 99%

Orbital magnetism in the ballistic regime: geometrical effects

1996

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We present a general semiclassical theory of the orbital magnetic response of noninteracting electrons confined in two-dimensional potentials. We calculate the magnetic susceptibility of singly-connected and the persistent currents of multiply-connected geometries. We concentrate on the geometric effects by studying confinement by perfect (disorder free) potentials stressing the importance of the underlying classical dynamics. We demonstrate that in a constrained geometry the standard Landau diamagnetic response is always present, but is dominated by finite-size corrections of a quasi-random sign which may be orders of magnitude larger. These corrections are very sensitive to the nature of the classical dynamics. Systems which are integrable at zero magnetic field exhibit larger magnetic response than those which are chaotic. This difference arises from the large oscillations of the density of states in integrable systems due to the existence of families of periodic orbits. The connection between quantum and classical behavior naturally arises from the use of semiclassical expansions. This key tool becomes particularly simple and insightful at finite temperature, where only short classical trajectories need to be kept in the expansion. In addition to the general theory for integrable systems, we analyze in detail a few typical examples of experimental relevance: circles, rings and square billiards. In the latter, extensive numerical calculations are used as a check for the success of the semiclassical analysis. We study the weak-field regime where classical trajectories remain essentially unaffected, the intermediate field regime where we identify new oscillations characteristic for ballistic mesoscopic structures, and the high-field regime where the typical de Haas-van Alphen oscillations exhibit finite-size corrections. We address the comparison with experimental data obtained in high-mobility semiconductor microstructures discussing the differences between individual and ensemble measurements, and the applicability of the present model. 03.65.Sq,05.45.+b,05.30.Fk,73.20.Dx

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“…In the presence of external electromagnetic fields, these model might play a role in semiconductor physics. Diamagnetic properties of small metallic particles are mapped to these models [43]. An empirical polarizable force field, based on the classical Drude oscillator model, is another area of application [44].…”

Section: Discussionmentioning

confidence: 99%

Entanglement Induced by Noncommutativity: Anisotropic Harmonic Oscillator in Noncommutative space

Abhishek¹,

Sinha²,

Ghosh³

2020

Preprint

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Quantum entanglement, induced by spatial noncommutativity, is investigated for an anisotropic harmonic oscillator. Exact solutions for the system are obtained after the model is re-expressed in terms of canonical variables, by performing a particular Bopp's shift to the noncommuting degrees of freedom. Employing Simon's separability criterion, we find that the states of the system are entangled provided a unique function of the (mass and frequency) parameters obeys an inequality. Entanglement of Formation for this system is also computed and its relation to the degree of anisotropy is discussed. It is worth mentioning that, even in a noncommutative space, entanglement is generated only if the harmonic oscillator is anisotropic. Interestingly, the Entanglement of Formation saturates for higher values of the deformation parameter θ, that quantifies spatial noncommutativity.

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On size corrections to the diamagnetic susceptibility of a free electron gas

Cited by 24 publications

References 10 publications

Magnetic-moment oscillations in a quantum Hall ring

Magnetic-moment oscillations in a quantum Hall ring

Orbital magnetism in the ballistic regime: geometrical effects

Entanglement Induced by Noncommutativity: Anisotropic Harmonic Oscillator in Noncommutative space

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