One and many-body effects on mirages in quantum corrals

ALEJANDRO M. LOBOS Y ARMANDO A. ALIGIA

PHYSICAL REVIEW B

AMER PHYSICAL SOC

Lugar: New York; Año: 2003 vol. 68 p. 35411 - 35411

1098-0121

Recent interesting experiments used scanning-tunneling microscopy to study systems involving Kondo impurities in quantum corrals assembled on Cu or noble-metal surfaces. The solution of the two-dimensional one-particle Schroedinger equation in a hard-wall corral without impurity is useful to predict the conditions under which the Kondo effect can be projected to a remote location (the quantum mirage). To model a soft circular corral, we solve this equation under the potential $W*delta (r-r_0)$, where $r$ is the distance to the center of the corral and $r_0$ its radius. We expand the Green´s function of electron surface states $G_{s0$} for $r<r_0$ as a discrete sum of contributions from single poles at energies $epsilon -i*delta_i$. The imaginary part $delta_i$ is the half width of the resonance produced by the soft confining potential, and turns out to be a simple increasing function of $epsilon_i$. In presence of an impurity, we solve the Anderson model at arbitrary temperatures using the resulting expression for $G_{s0}$  and perturbation theory up to second order in the Coulomb repulsion U. We calculate the resulting change in the  differential conductance $Delta dI/dV$ as a function of voltage and space, in circular and elliptical corrals, for different conditions, including those corresponding to recent experiments. The main features are reproduced. The role of the direct hybridization between impurity and bulk, the confinement potential, the size of the corral, and  temperature on the intensity of the mirage are analyzed. We also calculate spin-spin correlation function.