Orbital magnetism of mesoscopic systems

Oh, Sangshik; Zyuzin, A. Yu.; Serota, R. A.

doi:10.1103/physrevb.44.8858

Cited by 65 publications

(73 citation statements)

References 22 publications

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“…The effect of disorder on persistent currents has been evaluated by diagrammatic perturbation theory [36]. A weak disorder potential does not alter the bulk Landau diamagnetism [41] and gives within perturbation theory enhancement factors proportional to k F l for finite samples [42]. Highly pure semiconductor heterojunctions combined with lithographic techniques allow the realization of samples small enough to be in the mesoscopic ballistic regime where l > a.…”

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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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confidence: 99%

Orbital magnetism in the ballistic regime: geometrical effects

1996

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“…The fluctuations of magnetic susceptibility turn out to be large and at low temperature can be of the order of χ L (k F l) 3/2 , where k F is the Fermi wavevector, l is the mean free path, and χ L is the Landau susceptibility. In the certain region of magnetic fields the paramagnetic contribution to the averaged response is field independent and larger than the absolute value of Landau response.In the recent years, the orbital magnetism of mesoscopic systems has attracted much attention [1][2][3]. In the limit of the classically weak magnetic field, when the cyclotron radius is larger than the electron mean free path, the structure of energy levels of mesoscopic sample is very sensitive to the impurity configuration.…”

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confidence: 99%

“…In the recent years, the orbital magnetism of mesoscopic systems has attracted much attention [1][2][3]. In the limit of the classically weak magnetic field, when the cyclotron radius is larger than the electron mean free path, the structure of energy levels of mesoscopic sample is very sensitive to the impurity configuration.…”

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confidence: 99%

“…Note that in the case of lattice, the number of electrons 1 We can consider the temperatures T ∼ △ when it does not contradict to the condition L T < L in a primitive cell is fixed. Calculating the correlation function δN 2 lat (Eqs.…”

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“…For complete discussion about the difference between canonical and grand-canonical situation see [1,3] and references therein. Note that in the case of lattice, the number of electrons 1 We can consider the temperatures T ∼ △ when it does not contradict to the condition L T < L in a primitive cell is fixed.…”

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Orbital magnetism of 2D chaotic lattices

Nesvizhskii

Zyuzin

1996

Jetp Lett.

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We study the orbital magnetism of 2D lattices with chaotic motion of electrons withing a primitive cell. Using the temperature diagrammatic technique we evaluate the averaged value and rms fluctuation of magnetic response in the diffusive regime withing the model of non-interacting electrons. The fluctuations of magnetic susceptibility turn out to be large and at low temperature can be of the order of χ L (k F l) 3/2 , where k F is the Fermi wavevector, l is the mean free path, and χ L is the Landau susceptibility. In the certain region of magnetic fields the paramagnetic contribution to the averaged response is field independent and larger than the absolute value of Landau response.In the recent years, the orbital magnetism of mesoscopic systems has attracted much attention [1][2][3]. In the limit of the classically weak magnetic field, when the cyclotron radius is larger than the electron mean free path, the structure of energy levels of mesoscopic sample is very sensitive to the impurity configuration. As a result, the fluctuations of magnetic response turn out to be larger than the disorder-averaged value, i.e., the magnetic response of mesoscopic metallic sample has a random sign as a function of impurity configuration.This makes the investigation of sample-specific fluctuations to be of great importance for the understanding of the orbital magnetism of mesoscopic systems.In the work of Oh et al.[1] the most attention was paid to the extreme quantum coherenceHere L is the linear size of sample, L φ is the phase coherent length, L H = ch/eH is the magnetic length, L T = hD/T is the thermal length, D is diffusion 1

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Mesoscopic systems with fixed number of electrons

Lehle

Schmid

1995

Annalen der Physik

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In this paper, we study the physics of mesoscopic systems with noninteracting, but fixed number of electrons. From a technical point of view, this means a discussion of the differences between the canonical and the grand canonical ensemble (fixed versus fluctuating number of particles). Such a discussion is not trivial since the grand canonical ensemble is the most convenient basis for the statistics of identical particles and one has to spend labour in order to retrieve the canonical ensemble. Specifically, we are considering ensembles of mesoscopic systems with disorder, either by atomic defects or by fluctuations in their geometric definitions and we discuss various forms of disorder averages. 05.30, 73.35, 72.10

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Orbital magnetism of mesoscopic systems

Cited by 65 publications

References 22 publications

Orbital magnetism in the ballistic regime: geometrical effects

Orbital magnetism in the ballistic regime: geometrical effects

Orbital magnetism of 2D chaotic lattices

Mesoscopic systems with fixed number of electrons

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