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AG Scheer
Mesoscopic Systems

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In the Scheer group, we explore mesoscopic phenomena in metals as well as in organic molecules. For the investigation of both materials, the use of the mechanically controllable breakjunction technique plays a crucial role. For more information about our ongoing projects, please refer to the according site:

Nanooptics Group - Influence of incident light on electronic transport

Low Temperature Group - Investigation of mesoscopic phenomena in metals

Molecular Electronics Group - Driving electrical current through organic molecules

Nanomechanics Group - Oscillations of thin membranes

Hybrid Nanosystems Group - Spin- and charge transport phenomena in nano-scale devices

MCB Technique - Details about the mechanically controllable breakjunction (MCB) technique, which is applied in both the Low Temperature and the Molecular Electronics Group.

A Short Introduction to Mesoscopic Physics

Mesoscopic physics deals with the investigation of structures in the size range between microscopic (e.g. single atoms) and macroscopic (e.g. infinite solid) objects. The physical properties of mesoscopic systems reveal effects caused by the quantum nature of electrons. On the one hand, this is the quantization of the electric charge by the elementary charge , and on the other hand the wave nature of the electrons.

Optical microscope picture of a Coulomb island
Optical microscope picture of a Coulomb island with an additional gating electrode

Coulomb Blockade and Single-Electron Transistors

The phenomena caused by the charge quantization are summarized under the terms "charging effects", "single-electron effects" or "Coulomb blockade". The circuits based on these phenomena usually contain one or several small metallic islands that are weakly coupled to the environment via tunnel barriers and capacitors. The small size of the islands goes along with a small capacitance versus the environment. Thus, a large electrostatic energy is required for adding an electron to it, according to  = 2/2. This opens the possibility to control the number of electrons on the islands. The particular interest in these devices, nicknamed "single-electron transistor (SET)", "single-electron pump (SEP)", "single-electron turnstile device (SETD)" or similar, lies in the fact that information can in principle be stored by the movement of a single electron. This requires very small currents and thus yields small losses. An introduction into the field can be found in [Grabert and Devoret (eds.): , Plenum, New York (1992): Proceedings of NATO Institute at Les Houches].

Electron Wavefunctions and Electronic Pathways

The wave nature of electrons becomes observable if the quantum mechanical coherence is maintained throughout the sample, i.e. the electrons keep their phase memory. This gives rise to sizeable interference effects between different electronic paths. When the electrons are in phase, constructive interference occurs; while the interference is destructive if the phases of the electron wavefunctions are shifted with respect to each other. In principle, these interferences are present all the time, but in macroscopic systems they are averaged out due the huge number of possible electronic paths and phase shifts. In metallic nanostructures, the number of possible paths is limited, and interference becomes observable by changes of the electrical resistance if the coherence conditions are fulfilled, i.e. at low temperature.

Electron Interference: the Aharonov-Bohm Effect

The conceptually most simple realization of electron interference in solids is the Aharonov-Bohm effect (ABE), the analogy to the famous double-slit experiment for light waves. The ABE was first demonstrated experimentally in 1984 by Sean Webb and coworkers from IBM at the Thomas Watson Research Center in Yorktown Heights (New York). In the following years, many groups started working on this topic. While the early experiments focused on the proof and understanding of the interference effects themselves, the ABE has now become a tool to study more sophisticated properties of electrons in solids, e.g. interaction effects.

The Conductance Quantum G0

A second consequence of the wave properties of the electrons is the fact that they cannot be transferred resistive-less through small apertures. This effect becomes obvious in the phenomenon of conductance quantization. In analogy to the glass fiber as a waveguide for light waves, which only transmits particular modes of the wave field, a constriction in a conducting system serves as a mode filter for the electronic wave field. An important parameter is the relation between the wave length of the electrons, i. e. the Fermi wave length, and the lateral dimensions of the constriction, nicknamed "quantum point contact (QPC)". The Fermi wave length depends on the electron density (the higher the density, the lower the wave length). Therefore, conductance quantization has first been observed experimentally in two-dimensional electron gases in semiconductor heterostructures with comparatively low electronic densities, yielding wave lengths in the order of 10 to 100 nanometers. In such a structure, van Wees et al. from the Technical University Delft (The Netherlands) and Wharam et al. (University Cambridge, United Kingdom) had found that the conductance occurs in multiples of the conductance quantum G0 = 2e2/h.

The electronic density of elementary metals like copper, aluminum and gold is such that the Fermi wave length corresponds approximately to the lattice constants. This means that the individual electronic modes can only be observed in QPCs of atomic size. Contacts of this size range can be obtained with different techniques, including the use of scanning-tunneling microscopes (STM) and mechanically controlled break-junctions (MCB). In our group, we use lithographically fabricated MCBs.