Origin of conductance fluctuations in large circular quantum dots

Berggren, Karl‐Fredrik; Ji, Zhen‐Li; Lundberg, Tomas

doi:10.1103/physrevb.54.11612

Cited by 18 publications

(18 citation statements)

References 5 publications

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“…The additional factor in the amplitudes stemming from the smoothing strongly suppresses the longer periodic orbits, 6 so that usually only a few of them (2 -10) contribute to the gross-shell structure. This makes the POT a very convenient tool for the calculation of this quantity.…”

Section: The Shell Structurementioning

confidence: 99%

Periodic orbit theory of a circular billiard in homogeneous magnetic fields

Blaschke

Brack

1997

Phys. Rev. A

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We present a semiclassical description of the level density of a two-dimensional circular quantum dot in a homogeneous magnetic field. We model the total potential (including electron-electron interaction) of the dot containing many electrons by a circular billiard, i.e., a hard-wall potential. Using the extended approach of the Gutzwiller theory developed by Creagh and Littlejohn, we derive an analytic semiclassical trace formula. For its numerical evaluation we use a generalization of the common Gaussian smoothing technique. In strong fields orbit bifurcations, boundary effects (grazing orbits) and diffractive effects (creeping orbits) come into play, and the comparison with the exact quantum-mechanical result shows major deviations. We show that the dominant corrections stem from grazing orbits, the other effects being much less important. We implement the boundary effects, replacing the Maslov index by a quantum-mechanical reflection phase, and obtain a good agreement between the semiclassical and the quantum result for all field strengths. With this description, we are able to explain the main features of the gross-shell structure in terms of just one or two classical periodic orbits.

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Section: The Shell Structurementioning

confidence: 99%

Periodic orbit theory of a circular billiard in homogeneous magnetic fields

Blaschke

Brack

1997

Phys. Rev. A

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“…This result, considered as a particle reservoir model, is compared with the characteristics of the classical reservoir model. This result demonstrates universal conductance fluctuation (UCF) by a concrete calculation from a certain point of view [9][10][11][12][13][14][15][16][17]. Furthermore, this result shows that for universal conduction, scattering on a rough boundary is sufficient and that scatterers are not necessary within a system.…”

Section: Introductionmentioning

confidence: 52%

Two-Dimensional Electron Systems in Magnetic Fields: The Current Equipartition Law

Ueta

2011

Advances in Condensed Matter Physics

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We consider two-dimensional randomly deformed circular quantum dots with two attached waveguides (an emitter and a collector) in magnetic fields as an electronic analogy of the blackbody radiation. Transport properties through them are numerically investigated. The fraction of the current carried by each propagating mode in the collector is computed for transmission currents when each propagating mode is incident. By taking the statistical average in shape, it is shown that a universal frequency distribution is obtained for a sufficiently deformed system even though magnetic fields are so strong that electron waves form edge states. Then, the transmission currents are randomly distributed over all propagating modes. On average, each propagating mode carries the same current as in the absence of a magnetic field. It is also confirmed that a finite size dot cannot be a model of a reservoir even if it is chaotic.

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“…Ψ (c) and ∂Ψ (c) ∂n are obtained using Eqs. (15), (16), (18), and (19). With suitable truncations, after integrating over each segment, we finally obtain a matrix equation A · x = B.…”

Section: Open Billiardmentioning

confidence: 99%

“…In Refs. [15] and [16], circular billiards with two leads were investigated with a homogeneous magnetic field applied. We will apply a point magnetic flux at the center of the circular billiard (AB billiard).…”

Section: Introductionmentioning

confidence: 99%

Aharonov-Bohm effect and resonances in the circular quantum billiard with two leads

Ree

Reichl

1999

Phys. Rev. B

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We calculate the conductance through a circular quantum billiard with two leads and a point magnetic flux at the center. The boundary element method is used to solve the Schrödinger equation of the scattering problem, and the Landauer formula is used to calculate the conductance from the transmission coefficients. We use two different shapes of leads, straight and conic, and find that the conductance is affected by lead geometry, the relative positions of the leads and the magnetic flux. The Aharonov-Bohm effect can be seen from shifts and splittings of fluctuations. When the flux is equal to h/2e and the angle between leads is 180°, the conductance tends to be suppressed to zero in the low-energy range due to the Aharonov-Bohm effect.

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Origin of conductance fluctuations in large circular quantum dots

Cited by 18 publications

References 5 publications

Periodic orbit theory of a circular billiard in homogeneous magnetic fields

Periodic orbit theory of a circular billiard in homogeneous magnetic fields

Two-Dimensional Electron Systems in Magnetic Fields: The Current Equipartition Law

Aharonov-Bohm effect and resonances in the circular quantum billiard with two leads

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