Electrons can be described as classical particles in a billiard
...or as quantum mechanical waves in a quantum dot
Electron microscopic image of a quantum dot ratchet
Electron billiards are cavities in which electrons move on ballistic
trajectories unless they bounce off one of the boundaries. Electron
billiards allow experimental access to a fascinating regime: At
subkelvin temperatures, the electrons behave in certain aspects
similar to classical particles, while other properties of the electrons
must be explained using quantum mechanics. Billiards are therefore
also referred to as quantum dots.
In previous projects, we developed a detailed understanding of the classical trajectories of electrons in triangular and square billiards, and how these classical orbits relate to quantum interference effects. The classical orbits that turn out to be most important for the electronic properties are those that are most stable, or least chaotic. These same orbits can then semiclassically be related to the quantum transport properties - creating a link between classical chaos and quantum behaviour.
When bias voltages higher than a few µeV are used to probe
the electronic properties of quantum dots (billiards), the bias
voltage changes the scattering potential that the dot presents to
electrons, and conductance depends on voltage. In this nonlinear
regime, the symmetry of electronic conductance depends on the symmetry
of the dot.
We use semiconductor quantum dots with and without symmetry axes to establish symmetry rules for nonlinear, magnetoconductance, and to study the breakdown of the Onsager-Casimir relations under finite bias voltage and in finite magnetic fields. Previously, we used asymmetric quantum dots to realize quantum ratchets for the first time.
Quantum ratchets and symmetry of non-linear conductance
C.A. Marlow, R.P. Taylor, M.S. Fairbanks, I. Shorubalko,
and H. Linke: Experimental investigation of the breakdown
of the Onsager-Casimir relations.
To appear in Phys. Rev. Lett. (2006). Preprint:
A. Löfgren, C. A. Marlow, I. Shorubalko, R.P. Taylor, P.Omling,
L.Samuelson, H. Linke: Symmetry of two-terminal, non-linear
Phys. Rev. Lett. 92 , 046803 (2004)
H. Linke at al.: Quantum ratchets and quantum heat pumps.
Appl. Phys. A 75, 237 (2002)
H. Linke, W.D. Sheng, A. Svensson, A. Löfgren, L. Christensson,
H.Q. Xu, P.Omling, P.E. Lindelof: Asymmetric nonlinear
conductance of quantum dots with broken inversion symmetry.
Phys. Rev. B. 61, 15914 (2000)
H. Linke, T.E. Humphrey, A. Löfgren, A. Sushkov, R. Newbury,
R.P. Taylor, P.Omling: Experimental Tunneling Ratchets.
Science 286, 2314 (1999)
H. Linke, W.D. Sheng, A. Löfgren, H.Q. Xu, P.Omling, P.E.
Lindelof: A quantum dot ratchet: Experiment and theory.
Europhys. Lett. 44, 341 (1998)
Classical trajectories and quantum waves in billiards
H. Linke, L. Christensson, P.Omling, P.E. Lindelof: Stability
of classical electron orbits in triangular electron billiards.
Phys. Rev. B 56, 1440 (1997)
L. Christensson, H. Linke, P.Omling, P.E. Lindelof, I. Zozoulenko,
K.F. Berggren: Classical and quantum dynamics of electrons
in open equilateral triangular billiards.
Phys. Rev. B 57, 12309 (1998)
Popular reviews and news coverage
Quantum Clockwork (Michael Brooks in the New
Scientist, January 22, 2000)
Die Kanalisierung des Zufalls (Christian Speicher
in Neue Zürcher Zeitung, 2001)
Making Molecules into Motors (Dean Astumian in
Scientific American, July 2001)
Ratchets Reroute Electrons (P. Hänggi and
P. Reimann in Physics World, 2000)