Microscopic theory for quantum mirages in quantum corrals

Abstract

Scanning tunneling microscopy permits us to image the Kondo resonance of a single magnetic atom adsorbed on a metallic surface. When the magnetic impurity is placed at the focus of an elliptical quantum corral, a Kondo resonance has been recently observed both on top of the impurity and on top of the focus where no magnetic impurity is present. This projection of the Kondo resonance to a remote point on the surface is referred to as quantum mirage. We present a quantum mechanical theory for the quantum mirage inside an ideal quantum corral and predict that the mirage will occur in corrals with shapes other than elliptical.

Single-atom gating of quantum-state superpositions

“…While the exact origin of the Kondo resonance in our system is still debated 25,26 , microscopic calculations have indicated that the many-body complexity is manifested in the energy dependence of the density of states while its spatial dependence can be understood from a single-particle perspective 16,18 . Regardless of its origin, we have verified that Kondo scattering calculations 21 can reproduce many of the details of our images.…”

“…These perturbation theory results are implicit in microscopic Green's function results 16,18 in our engineered limit that the separation between relevant corral wavefunctions is much less than their linewidth. Physically, a single atom placed -7/13 -inside the corral causes the degenerate wavefunctions to reorganize themselves into new zeroth-order wavefunctions.…”

“…is much larger than the spacing between the wall atoms 1,3,10,[15][16][17][18] . As a first clue to the underlying physics, the original report of the quantum mirage 3 pointed out the similarity between the solitary eigenfunction closest to E F and the spatial fine structure around the -5/13 -projected Kondo image.…”

“…Surprisingly, however, when the Co atom was moved rightward to one of the strong maxima of the state 4, 4 , the image produced ( Fig. 2g) was manifestly different from either of the two eigenstates.We will show that our / dI dV Δ maps are images of superpositions: phase- Electrons in quantum corrals are well modelled by particle-in-a-box solutions to the Schrödinger equation because the surface state wavelength [30 Å in Cu(111) is much larger than the spacing between the wall atoms 1,3,10,[15][16][17][18] . As a first clue to the underlying physics, the original report of the quantum mirage 3 pointed out the similarity between the solitary eigenfunction closest to E F and the spatial fine structure around the (Fig.…”

Controlling the Kondo Effect inCoCunClusters Atom by Atom

“…The peculiar behavior of the Kondo resonance with cluster size is at variance with the monotonic dependence of T K on the average hybridization strength expected from bulk models of the Kondo effect. Theoretical approaches to the Kondo effect of magnetic impurities on surfaces consider the importance of bulk [20,21] and surface [22,23,24] states in the scattering of electron waves at the magnetic impurity site. Recent experiments with Co adatoms on Cu(100) [9], which does not host any surface state close to the Fermi level [25], or on Cu(111) but in the vicinity of atomic surface steps that affect the surface states [26] have indicated the importance of bulk rather than surface states for the Kondo effect.…”