Comment on ``Friedel phases and phases of transmission amplitudes in quantum scattering systems''

Massimiliano Sassoli de Bianchi

Werner O. Amrein

Eric C. Andrade, E. Miranda, V. Dobrosavljević

We study how well-known effects of the long-ranged Friedel oscillations are affected by strong electronic correlations. We first show that their range and amplitude are significantly suppressed in strongly renormalized Fermi liquids. We then investigate the interplay of elastic and inelastic scattering in the presence of these oscillations. In the singular case of two-dimensional systems, we show how the anomalous ballistic scattering rate is confined to a very restricted temperature range even for moderate correlations. In general, our analytical results indicate that a prominent role of Friedel oscillations is relegated to weakly interacting systems.

H. Q. Xu

Abdelkader Mouadili, El Houssaine El Boudouti, Ali Soltani +4 more

We give an analytical and experimental demonstration of a classical analogue of the electromagnetic induced absorption (EIA) in a simple photonic device consisting of two stubs of lengths d1 and d2 grafted at the same site along a waveguide. By detuning the lengths of the two stubs (i.e. δ = d(2) - d(1)) we show that: (i) the amplitudes of the electromagnetic waves in the two stubs can be written following the two resonators model where each stub plays the role of a radiative resonator with low Q factor. The destructive interference between the waves in the two stubs may give rise to a sharp resonance peak with high Q factor in the transmission as well as in the absorption. (ii) The transmission coefficient around the resonance induced by the stubs can be written following a Fano-like form. In particular, we give an explicit expression of the position, width and Fano parameter of the resonances as a function of δ. (iii) By taking into account the loss in the waveguides, we show that at the transmission resonance, the transmission (reflection) increases (decreases) as a function of δ. Whereas the absorption goes through a maximum around 0.5 for a threshold value δth which depends on the attenuation in the system and then falls to zero. (iv) We give a comparison between the phase of the determinant of the scattering matrix, the so-called Friedel phase and the phase of the transmission amplitude. (v) The effect of the boundary conditions at the end of the resonators on the EIA resonance is also discussed. The analytical results are obtained by means of the Green's function method, whereas the experiments are carried out using coaxial cables in the radio-frequency regime. These results should have important consequences for designing integrated devices such as narrow-frequency optical or microwave filters and high-speed switches.

Banhi Chatterjee, Jan Skolimowski, Krzysztof Byczuk

We study the interference patterns in the Friedel oscillations (FO) due to the scattering off either two or multiple impurities and scattering off extended inhomogeneities both in the non-interacting and two-dimensional lattice systems of interacting fermions. Correlations are accounted for by using an approximate method based on the real-space dynamical mean-field theory. We find that the interference maxima and minima change systematically as we vary the relative distance between the two impurities. At the same time, the interaction increase does not shift the position of interference fringes but only reduces their intensities. A comparison with the single impurity studies clearly shows complex patterns in FO induced by the additional scattering potentials. In the case of an extended step potential the system becomes more homogeneous when the interaction increases. FO and interference patterns are not present in the Mott insulating phase in the single and the many impurity models. Our theoretical study provides promising initial insights and motivate a further realistic modeling to investigate the role of interstitial defects, embedded impurities, ad-atoms on the surfaces, and surface irregularities in materials with different degrees of electronic correlation. For a complete description we also present analytical and numerical results of FO for non-interacting particles moving in a two and three dimensional continuous spaces. In the diluted impurity limit we derive results for FO due to scattering off many impurities, which are generalization of the original Friedel formula.