SCATTERING THEORY AND MESOSCOPIC PHYSICS
Prof. Giorgio Cattapan
Electronic transport in ultra-small semiconductor structures has inspired a lot of experimental and theoretical work in the last several years. Research on these low-dimensional systems revealed many novel phenomena such as the quantized
conductance in point contacts, the anomalous magneto-resistance in lateral super-lattices and the Hall resistance quenching in narrow crosses, to name just a few.
Research on quantum mesoscopic devices entails promising and exciting applications in the fields of advanced electronics and quantum computing.
The main goal of our line of research consists in applying techniques borrowed from quantum scattering theory to analyze electron transport phenomena, and in particular transmission resonances in multi-mode quantum circuits as well as in arrays of quantum rings having non-trivial topology.
The first goal can be achieved locating the poles of the scattering matrix in the complex Riemann energy surface,
through the solution of differential equations, describing the coupling among propagating and evanescent modes. In so doing, we have recently exhibited the occurrence of bound states in the continuum in serial structures of quantum dots coupled to an external waveguide. We have also shown that the non-trivial dependence of the conductance upon the geometry of the quantum circuit allows for a simple
interpretation in terms of the motion of the S-matrix poles on the complex multi-sheeted energy plane. These techniques can be extended to the evaluation of the bound-state spectrum of closed quantum dots with arbitrary shape, thereby providing a viable alternative to the plane-wave decomposition method or to the boundary-integral method, commonly employed in the literature.
We are presently considering also spin transport phenomena in quantum rings threaded by a magnetic field, in presence of magnetic defects. As is well-known, these quantum circuits exhibit Aharonov-Bohm oscillations with varying magnetic flux, and may be amenable to applications in spintronics. The use of algebraic techniques familiar in scattering theory on graphs allows us to analyze electron transport phenomena in quantum rings decorated with several impurities and/or arranged in arrays with non-trivial structure.
RECENT RELEVANT REFERENCES
E. Maglione, L. S. Ferreira, and G. Cattapan: Asymptotic
properties of bound states in coupled quantum wave guides, J. Phys. A: Math. Gen., 39, 1207-1228 (2006).
G. Cattapan, P. Lotti, and A. Pascolini: S-matrix pole
trajectories in quantum wires with resonantly coupled cavities, Eur. Phys. J. B 53, 387-394 (2006).
G. Cattapan and P. Lotti: Fano resonances in stubbed quantum waveguides with impurities, Eur. Phys. J. B 60,
51-60 (2007).
G. Cattapan and P. Lotti: S-matrix poles close to thresholds in confined geometries, Eur. Phys. J. B 60,
181-186 (2007).
G. Cattapan and P. Lotti: Bound states in the continuum in
two-dimensional serial structures, Eur. Phys. J. B 66,
517-523 (2008).
G. Cattapan, P.Lotti, and A.Pascolini: A scattering--matrix
approach to the eigenenergies of quantum dots, Physica E 41, 1187-1192 (2009).