Anisotropy in conductance of a quasi-one-dimensional metallic surface state measured by a square micro-four-point probe method.

We have devised a "square micro-four-point probe method" using an independently driven ultrahigh-vacuum four-tip scanning tunneling microscope, and succeeded for the first time to directly measure anisotropic electrical conductance of a single-atomic layer on a solid surface. A quasi-one-dimensional metal of a single-domain Si(111)4 x 1-In had a surface-state conductance along the metallic atom chains (sigma(axially)) to be 7.2(+/-0.6) x 10(-4) S/square at room temperature, which was larger than that in the perpendicular direction (sigma(radially)) by approximately 60 times. The sigma(axially) was consistently interpreted by a Boltzmann equation with the anisotropic surface-state band dispersion, while the sigma(radially) was dominated by a surface-space-charge-layer conductance.