stability
Hall
velocity correlations
inelastic scattering length
explanation
length
oscillations
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scale
observations
1995-06-01
classical conductivity
detailed study
beating
Shubnikov-de Haas oscillations
157-170
https://doi.org/10.1007/bf01307466
Zeeman splitting
classical action
magnetoconductivity
chaos
recent experiments
theory
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Weiss et al
periodic orbit contributions
field
correlation
temperature
experiments
Motivated by a recent experiment by Weiss et al. [Phys. Rev. Lett. 70, 4118 (1993)], we present a detailed study of quantum transport in large antidot arrays whose classical dynamics is chaotic. We calculate the longitudinal and Hall conductivities semiclassically starting from the Kubo formula. The leading contribution reproduces the classical conductivity. In addition, we find oscillatory quantum corrections to the classical conductivity which are given in terms of the periodic orbits of the system. These periodic-orbit contributions provide a consistent explanation of the quantum oscillations in the magnetoconductivity observed by Weiss et al. We find that the phase of the oscillations with Fermi energy and magnetic field is given by the classical action of the periodic orbit. The amplitude is determined by the stability and the velocity correlations of the orbit. The amplitude also decreases exponentially with temperature on the scale of the inverse orbit traversal timeħ/Tγ. The Zeeman splitting leads to beating of the amplitude with magnetic field. We also present an analogous semiclassical derivation of Shubnikov-de Haas oscillations where the corresponding classical motion is integrable. We show that the quantum oscillations in antidot lattices and the Shubnikov-de Haas oscillations are closely related. Observation of both effects requires that the elastic and inelastic scattering lengths be larger than the lengths of the relevant periodic orbits. The amplitude of the quantum oscillations in antidot lattices is of a higher power in Planck's constantħ and hence smaller than that of Shubnikov-de Haas oscillations. In this sense, the quantum oscillations in the conductivity are a sensitive probe of chaos.
1995-06
correction
effect
Tγ
terms
Fermi energy
antidot lattices
action
sense
Kubo formula
semiclassical derivation
formula
conductivity
classical motion
splitting
power
et al
study
contribution
addition
Haas oscillations
classical dynamics
Semiclassical theory of transport in antidot lattices
magnetic field
semiclassical theory
articles
scattering length
orbit
amplitude
phase
energy
corresponding classical motion
antidot arrays
derivation
al
true
transport
lattice
high power
probe
quantum transport
quantum oscillations
article
consistent explanation
system
dynamics
periodic orbits
quantum corrections
2022-09-02T15:49
Max-Planck-Institut für Kernphysik, D-69117, Heidelberg, Germany
Max-Planck-Institut für Kernphysik, D-69117, Heidelberg, Germany
1431-584X
Springer Nature
0722-3277
Zeitschrift für Physik B Condensed Matter
Felix
von Oppen
Physical Sciences
Hackenbroich
Gregor
97
10.1007/bf01307466
doi
Atomic, Molecular, Nuclear, Particle and Plasma Physics
dimensions_id
pub.1050297696
2
Springer Nature - SN SciGraph project