Semiconductor Quantum Rings

Nanoscale semiconductor systems are technically very promising for the future components of electronic and optical devices. These small structures are also full of new, unusual and unexpected physical features that are actively explored both experimentally and theoretically. Many of the new nanoscale findings in semiconductors result from reduced dimensionality combined with enhanced effects of magnetic field and interparticle correlations. In addition to that, many of the new features can be controlled by tunable system parameters, both in theoretical models as well as experiments.

My research interest is mainly focused on semiconductor quantum rings. They are two dimensional quantum systems where electrons are restricted to a circular region on the boundary between two semiconducting materials. When a quantum ring is placed in a constant, external magnetic field, a current flows along the ring. This current is an equilibrium property of the ring and it does not decay unless the temperature is high or inelastic scattering is present. It is therefore called a persistent current. One intruiging fact about the ring is that its energy, and therefore persistent current, is periodic in the magnetic flux enclosed by the ring, a manifestation of the Aharonov-Bohm effect. Both theoretical calculations and experimental measurements have shown that the periodicity of the energy spectrum decreases with increasing strength of the electron electron interaction. This is sometimes referred to as the "fractional Aharonov-Bohm effect" (FABE).

Previously, I have performed groundstate and nonequilibrium calculations of quantum rings using the mean field Hartree-Fock method, which includes the Coulomb interaction partially by neglecting correlation between electrons. The quasi one dimensional electron gas is a challenging system, as the Coulomb interaction in the limit of one spatial dimension is quite pathologic and correlation between electrons is strong. Therefore, mean-field approximations are not an ideal tool for investigating such systems, since correlation effects determine many aspects of the system behaviour. To truly understand the many-body properties of these systems, more exact methods have to be employed. More recently we have been using the exact diagonalization method to study quantum rings. In this way we can capture all interaction effects, with the drawback that the number of electrons is restricted to a very low value. This is not a serious drawback, as we are mainly interested in the limit of low electron density, when the Coulomb interaction is strong and determines the properties of the system. The fractional Aharonov-Bohm effect in quantum rings is a good example of a phenomenon that is caused directly by electron correlation, and can not be adequately described by mean-field theories. We have done calculations with ED to investigate the fractional Aharonov-Bohm regime to find the underlying reasons for this effect.