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Theory of Mesoscopic Systems

Mesoscopic systems occupy the middle ground between our everyday world, in which objects obey the rules of classical physics, and the realm of elementary particles and atoms, which are governed by quantum mechanics. As the size of a macroscopic object is reduced, quantum mechanical effects become important and often lead to significant changes of its physical properties. Famous quantum effects in mesoscopic systems include conductance quantization, Coulomb blockade, the integer and fractional quantum Hall effects, and the Aharonov-Bohm effect.

Our group is interested in quantum mechanical effects in modern mesoscopic systems. The systems we are currently looking at are:

  • topological insulators and superconductors;
  • one-dimensional quantum systems;
  • nanomechanical systems in the quantum regime.

Topological insulators

Topological insulators form a new class of materials which were discovered only in the past decade. Inside the material they are insulators, but their surfaces or edges behave as metals. Their conducting surface states are a consequence of topological properties of the bulk band structure. As most of the mechanisms which contribute to the resistance of normal metals are not effective in the surface states, current may flow with very little dissipation. This is why topological insulators potentially have promising applications in future nanoelectronic devices. Our group investigates mainly topological insulators based on graphene-like materials, and their one-dimensional helical edge states.

One-dimensional quantum systems

One-dimensional quantum systems can be experimentally realized, for instance, by using quantum wires, carbon nanotubes or by confining atoms in optical traps. While many of their properties can be theoretically understood using Luttinger liquid theory – a field-theoretical description appropriate at low energies – certain observables, e.g., thermalization and transport properties at nonzero temperatures require extensions of this theory. Our group investigates such one-dimensional quantum systems at finite energies, in particular the interplay between electron-electron interactions and spin-orbit coupling.

Nanomechanical systems

Nanomechanical systems already have many applications as sensitive measurement devices. Moreover, recently it has become possible to cool mechanical resonators to their quantum mechanical ground state. This raises the question how one can achieve true quantum states, e.g., superpositions or entangled states, in these systems. Our group develops theoretical proposals for generating and observing quantum states in nanoelectromechanical systems.