Quantum corral wave function engineering

We present a theoretical method for the design and optimization of quantum corrals with specific electronic properties. Taking advantage that spins are subject to a RKKY interaction that is directly controlled by the scattering of the quantum corral, we design corral structures that reproduce spin Hamiltonians with coupling constants determined a priori. We solve exactly the two-dimensional electron gas scattering problem for each corral configuration within the effective mass approximation and s-wave scattering using a Green function method. Subsequently, the geometry of the quantum corral is optimized with an algorithm that combines simulated annealing and genetic approaches. We demonstrate that it is possible to automatically design quantum corrals with complicated target electronic properties, such as multiple mirages with predefined relative intensities at specific locations. In addition we design structures that are particularly sensitive to the phase shift of impurities at certain positions allowing the measurement of the value of this parameter on the copper surface.