Closed-orbit dependence on the field direction in the anisotropic diamagnetic Kepler problem

Bruno-Alfonso, Alexys; Bleasdale, Colin; Souza, Gustavo Vanin Bernardino de; Lewis, R. A.

doi:10.1103/physreva.89.043425

Cited by 4 publications

(15 citation statements)

References 21 publications

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“…Recently, however, the diamagnetic Kepler problem was first detected in the semiconductor environment of silicon in a static magnetic field [22]. The oscillations in the spectrum were observed well above the ionization threshold corresponding to positive scaled energies of the order of 1 [23]. These measurements also provided an observation of this effect in an anisotropic medium which subsequently led to a comprehensive study on the effects of an anisotropic mass on the classical electron orbits and their periods [23].…”

Section: Introductionmentioning

confidence: 82%

“…Five years later, we have shown [23] that a scaled energy above the ionization threshold provides a good match between theory and experiment. This is due to the spectral oscillations occurring far beyond the ionization threshold.…”

Section: Intermediate Positive Energymentioning

confidence: 99%

“…The oscillations in the spectrum were observed well above the ionization threshold corresponding to positive scaled energies of the order of 1 [23]. These measurements also provided an observation of this effect in an anisotropic medium which subsequently led to a comprehensive study on the effects of an anisotropic mass on the classical electron orbits and their periods [23]. A numerical investigation into the experimental conditions needed to observe such an effect in a range of widely-utilized semiconductors was also completed [24].…”

Section: Introductionmentioning

confidence: 99%

“…The second considers the effects of small positive integer values of the scaled energy on both the angular spectrum of orbits, as well as the shapes and periods of the most important closed orbits. This is of particular interest when moving into the semiconductor environment where experimental work has shown oscillations in the spectrum well above the ionization energy [22][23][24]. For crossed fields, it is shown how the electric field breaks the rotational symmetry, splitting the shortest pure magnetic orbits into new ones which evolve quite differently as the field strength is increased.…”

Section: Introductionmentioning

confidence: 99%

“…We look here to investigate the effect positive energy values have on both the orbits and the system as a whole in the high-field regime of f = 1. Table II gives the values of the launching angle θ , orbit period, return distance, and the maximum distance for positive integer values of the classical scaled energy up to = 4 (the energy identified as being the best match to experimental data [23]). From Table II, the orbit periods do change substantially when varying the energy.…”

Section: Intermediate Positive Energymentioning

confidence: 99%

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Electric-field effects on the closed orbits of the diamagnetic Kepler problem

2016

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The nonrelativistic closed orbits of an electron interacting with a unit positive charge in the presence of homogeneous magnetic and electric fields are investigated. A simplified theoretical model is proposed utilizing appropriate initial conditions in semiparabolic coordinates for arbitrary magnetic-and electric-field alignments. The evolution of both the angular spectrum of orbits and the shape and duration of individual orbits, as the electric-field intensity and scaled energy are increased, is shown for the cases of both parallel and crossed fields. Orbit mixing in the high-field regime is investigated in the case of parallel fields, giving an indication of the system moving from the quasi-Landau chaotic regime to the electric-field-induced (Stark effect) regular regime. For crossed fields, it is shown that the Garton-Tomkins orbits lead to a pair of orbits that have opposite behaviors as a function of the electric-field intensity. The nonrelativistic closed orbits of an electron interacting with a unit positive charge in the presence of homogeneous magnetic and electric fields are investigated. A simplified theoretical model is proposed utilizing appropriate initial conditions in semiparabolic coordinates for arbitrary magnetic-and electric-field alignments. The evolution of both the angular spectrum of orbits and the shape and duration of individual orbits, as the electric-field intensity and scaled energy are increased, is shown for the cases of both parallel and crossed fields. Orbit mixing in the high-field regime is investigated in the case of parallel fields, giving an indication of the system moving from the quasi-Landau chaotic regime to the electric-field-induced (Stark effect) regular regime. For crossed fields, it is shown that the Garton-Tomkins orbits lead to a pair of orbits that have opposite behaviors as a function of the electric-field intensity.

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Section: Introductionmentioning

confidence: 82%

Section: Intermediate Positive Energymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Intermediate Positive Energymentioning

confidence: 99%

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Electric-field effects on the closed orbits of the diamagnetic Kepler problem

2016

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Semiconductor hydrogen analogue candidates for observation of quasi‐Landau oscillations associated with semi‐classical electron orbits

Bleasdale

Lewis

2015

Physica Status Solidi (b)

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Recently, oscillations above the ionization threshold were observed in high purity Si in a magnetic field. These oscillations were found to be related to the semi‐classical motion of excited electrons around impurity centers periodically returning to the nucleus. This effect had been previously observed for many elemental gases in magnetic fields, yet had never been observed in the semiconductor environment. In this work, we analyze other semiconductors to see if they provide a more favorable medium over Si for the observation of these orbits, and to establish the experimental conditions required to make such observations.

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