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Transporteigenschaften von Graphen

Subject Area Theoretical Condensed Matter Physics
Term from 2008 to 2013
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 64202200
 
Final Report Year 2013

Final Report Abstract

In this project we have studied the transport properties of two-dimensional electronic systems with two bands and a particle-hole symmetry. A prominent example of this class of physical systems is graphene, other examples are surface states of topological insulators. In the first part we have analyzed electronic and optical properties near the Dirac nodes, the effect of disorder on the conductivity and the role of superstructures such as a localized spin texture or a periodic potential. A localized spin structure breaks the time-reversal invariance and enables us to tune the gap of the two Dirac nodes independently. As a result of this, we observe a quantum Hall effect without external magnetic field. A periodic potential, on the other hand, can create additional pairs of Dirac nodes. This provide a scheme to modify substantially the electronic transport and the optical properties. It turned out that the combination of intra- and interband scattering in two-band materials plays a crucial role for the transport properties. For instance, the Drude formula for conventional metals is not valid in this case. It was found in this project that the transport properties are controlled by a non-Abelian chiral symmetry. If this symmetry is spontaneously broken, the electrons follow a diffusive behavior due to a massless fermion mode. Moreover, the conductivity can be written in terms of a scaling law that represents a generalization of the Drude formula. An interesting effect is that the optical conductivity is constant over the entire band width, indicating a very robust behavior in opto-electronic applications of graphene. Another interesting effect for potential technological applications is the creation of plasmons. We have studied their spectral properties, including their anisotropic behavior on the honeycomb structure. Absorption of non-carbon atoms and doping can modify the properties of graphene substantially. Several options have been suggested and studied in this project. Besides the above mentioned periodic superstructures and spin textures, the modification of the twodimensional lattice can also affect the phonon spectrum. This may allow us to tune the phonon frequency over a wide range and can lead to instabilities due to the electron-phonon interaction. We have found that an Ising instability of the out-of-plane phonons is possible, which is accompanied by a gap-opening in the electronic spectrum. A Kosterlitz-Thouless instability of the in-plane phonons, on the other hand, creates a splitting of two degenerate phonon bands. Besides the transport properties we have studied other features in graphene, which are characteristic of the two-dimensional system with two bands and Dirac nodes. One is the formation of excitons in a graphene double layer. Another is the formation of polaritons in graphene which is inside a microcavity. In both cases we may observe Bose-Einstein condensation of tightly bound electron-hole pairs. Another interesting aspect was the observation that electrons in graphene can be coupled with a magnetic field to realize a Jaynes-Cummings model. This leads to a quantized exchange of energy between the electrons and the magnetic field. As a result, we have observed Rabi oscillations as well as collapse and revival of quantum states. This provides a potential for the creation of entangled states in solid-state materials.

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