"Shubnikov-de Haas oscillations" .
"article" .
"antidot arrays" .
"stability" .
"action" .
.
"orbit" .
_:Ndd8b15a2c2bd4afdb905ba1ec5120dac _:N8a2e99becaa64af9b680acce6c2219ff .
"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 time\u0127/T\u03B3. 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 constant\u0127 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." .
"al" .
_:Nd57de1ec6cab46e1b57a9fd3e4b82a02 "97" .
"Weiss et al" .
"derivation" .
"Semiclassical theory of transport in antidot lattices" .
.
"1431-584X" .
_:Nd57de1ec6cab46e1b57a9fd3e4b82a02 .
"periodic orbits" .
.
"beating" .
"Zeeman splitting" .
"Hall" .
_:Ndd8b15a2c2bd4afdb905ba1ec5120dac .
"corresponding classical motion" .
"quantum corrections" .
_:Ndd8b15a2c2bd4afdb905ba1ec5120dac .
"length" .
"array" .
.
"Haas oscillations" .
"classical motion" .
_:N8a2e99becaa64af9b680acce6c2219ff .
_:Ne91538be242a4ed19ba504d6da873081 "dimensions_id" .
"theory" .
"study" .
"Atomic, Molecular, Nuclear, Particle and Plasma Physics" .
"1995-06" .
.
"amplitude" .
"true"^^ .
"Felix" .
.
.
.
"correction" .
"classical action" .
.
"1995-06-01" .
_:N369114f108ab480c9e12570b6640ccf5 .
"https://scigraph.springernature.com/explorer/license/" .
"Physical Sciences" .
.
"chaos" .
_:N5ccea21fa95f4620b2cfcd9160783623 .
_:Ne91538be242a4ed19ba504d6da873081 "pub.1050297696" .
_:N369114f108ab480c9e12570b6640ccf5 "2" .
"Max-Planck-Institut f\u00FCr Kernphysik, D-69117, Heidelberg, Germany" .
"velocity correlations" .
"Hackenbroich" .
"T\u03B3" .
.
"antidot lattices" .
_:N5ccea21fa95f4620b2cfcd9160783623 .
"consistent explanation" .
"lattice" .
_:Ne91538be242a4ed19ba504d6da873081 .
"Fermi energy" .
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"phase" .
"dynamics" .
"probe" .
"recent experiments" .
"https://doi.org/10.1007/bf01307466" .
"temperature" .
.
"157-170" .
"Zeitschrift f\u00FCr Physik B Condensed Matter" .
"addition" .
"transport" .
_:N369114f108ab480c9e12570b6640ccf5 .
"oscillations" .
"von Oppen" .
"Gregor" .
_:Nd57de1ec6cab46e1b57a9fd3e4b82a02 .
"formula" .
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"splitting" .
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"classical dynamics" .
_:N808dba8a2a224835a6ac3a80cf48c4fe .
"quantum oscillations" .
"correlation" .
"effect" .
"Max-Planck-Institut f\u00FCr Kernphysik, D-69117, Heidelberg, Germany" .
"0722-3277" .
.
"observations" .
"energy" .
_:N808dba8a2a224835a6ac3a80cf48c4fe .
"scattering length" .
_:Ne91538be242a4ed19ba504d6da873081 .
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_:N5ccea21fa95f4620b2cfcd9160783623 "10.1007/bf01307466" .
_:N5ccea21fa95f4620b2cfcd9160783623 "doi" .
"motion" .
"magnetoconductivity" .
_:N808dba8a2a224835a6ac3a80cf48c4fe "Springer Nature - SN SciGraph project" .
.
"detailed study" .
"quantum transport" .
.
"inelastic scattering length" .
"Springer Nature" .
_:N8a2e99becaa64af9b680acce6c2219ff