Confined bulk states as a long-range sensor for impurities and a transfer channel for quantum information

We show that confinement of bulk electrons can be observed at low-dimensional surface structures and can serve as a long-range sensor for the magnetism and electronic properties of single impurities or as a quantum information transfer channel with large coherence lengths. Our ab initio calculations reveal oscillations of electron density in magnetic chains on metallic surfaces and help to unambiguously identify the electrons involved as bulk electrons. We furthermore discuss the possibility of utilizing bulk state confinement to transfer quantum information, encoded in an atom’s species or spin, across distances of several nanometers with high efficiency.

Figure 1

(a) Local density of $\mathit{sp}$ electronic states of each atom in the chain as a function of energy and the number of atoms in the chain. To produce the map, the LDOS has been evaluated at each atomic sphere along the chain and then linearly interpolated in between the atomic positions to produce a smooth map for clearer presentation. Arrows and letters mark the most pronounced oscillations. (b) 1D fast Fourier transform (FFT) of the LDOS map. Circles and arrows mark the peaks corresponding to the oscillations marked in (a) by arrows. (c) In-plane momentum-resolved electron density map for the Cu(111) surface. Arrows and letters mark the positions of peaks in (b).

Figure 2

The local density of $\mathit{sp}$ electrons at the central chain atom for a ferromagnetic Co chain (solid black curves), and for Co chains with the edge atom replaced by Cr, ferromagnetically (red long-dashed curve) or antiferromagnetically (blue short-dashed curve) coupled to the rest of the chain. The local density of $\mathit{sp}$ electrons at the edge chain atom for a Co chain with the opposite-edge atom replaced by Cr, ferromagnetically (red dash-dot-dotted curve) or antiferromagnetically (blue short-dash-dotted curve) coupled to the rest of the chain.