Influence of the Surface Structure and Vibration Mode on the Resistivity of Cu Films

The influence of the surface structure and vibration mode on the resistivity of Cu films and the corresponding size effect are investigated. The temperature dependent conductivities of the films with different surface morphologies are calculated by the algorithm based upon the tight-binding linear muffin-tin orbital method and the Green's function technique. The thermal effect is introduced by setting the atomic displacements according to the Gaussian distribution with the mean-square amplitude estimated by the Debye model. The result shows that the surface atomic vibration contributes significantly to the resistivity of the systems. Comparing the conductivities for three different vibration modes, it is suggested that freezing the surface vibration is necessary for practical applications to reduce the resistivity induced by the surface electron-phonon scattering

Surface and Step Conductivities on Si(111) Surfaces

Four-point measurements using a multi-tip scanning tunneling microscope (STM) are carried out in order to determine surface and step conductivities on Si(111) surfaces. In a first step, distance-dependent four-point measurements in the linear configuration are used in combination with an analytical three-layer model for charge transport to disentangle the 2D surface conductivity from non-surface contributions. A termination of the Si(111) surface with either Bi or H results in the two limiting cases of a pure 2D or 3D conductance, respectively. In order to further disentangle the surface conductivity of the step-free surface from the contribution due to atomic steps, a square four-probe configuration is applied as function of the rotation angle. In total this combined approach leads to an atomic step conductivity of $\sigma_\mathrm{step} = (29 \pm 9)$ $\mathrm{\Omega}^{-1} \mathrm{m}^{-1}$ and to a step-free surface conductivity of $\sigma_\mathrm{surf} = (9 \pm 2) \cdot 10^{-6}\,\mathrm{\Omega}^{-1}/\square$ for the Si(111)-(7$\times$7) surface.Comment: Main paper: 5 pages, 4 figures, Supplemental material: 6 pages, 3 figures. The Supplemental Material contains details on the sample preparation and measurement procedure, additional experimental results for Si(111) samples with different doping levels, and the description of the three-layer conductance mode

How many surface modes does one see on the boundary of a Dirac material?

We present full expressions for the surface part of polarization tensor of a Dirac fermion confined in a half-space in $3+1$ dimensions. We compare this tensor to the polarization tensor of eventual surface mode (which is a $2+1$ dimensional Dirac fermion) and find essential differences in the conductivities in both Hall and normal sectors. Thus, the interaction with electromagnetic field near the boundary differs significantly in the full model and in the effective theory for the surface mode.Comment: 5 pages, 4 figures; slightly improved version, published in Physical Review Letter