Reply to "Debate over dispersion direction in a Tomonaga–Luttinger-liquid system"

Blumenstein et al. reply

In their Correspondence, Nakatsuji et al. claim that the conduction path at the surface would be oriented perpendicular to the nanowire direction. They refer to three arguments: (1) the band dispersion in angle-resolved photoemission spectroscopy (ARPES) being allegedly stronger perpendicular to the chains; (2) the surface state being increasingly two-dimensional (2D) and anisotropic away from the Fermi energy; and (3) an eightfold superstructure existing on the nanowires. Although we welcome an independent view on this interesting system, we do not arrive at the same conclusions, based on our own results.

(1) The previous study by Nakatsuji et al.¹ is performed on a vicinal surface with a domain imbalance, which also shows large step bunches. Their ARPES signal is not sufficient to yield a band dispersion in both the first and the second Brillouin zone. Based on second derivative spectra from the third zone, Nakatsuji et al. conclude that the 1D electron path lies perpendicular to the chains. However, our scanning tunnelling microscopy investigations, including mapping of the density of states, clearly show a situation with seamlessly conducting 1D filaments oriented in the chain direction, not interrupted by insulating sections and without cross-links between wires^2,3.

(2) The nearly perfect 1D character of the Fermi surface was shown by us⁴. A lesser anisotropy towards higher binding energies of the surface state does not affect the 1D character of conduction electrons at the chemical potential. Moreover, this is not a relevant argument for the discussion of the orientation of the conduction path.

(3) The eightfold superstructure, which is completely described by us⁵, is also not applicable to the current discussion as the symmetry of the Fermi surface evidently does not show such periodicity⁴. Therefore the conduction electron system is clearly decoupled from this superstructure.

To conclude, all considerations brought forward in the Correspondence by Nakatsuji et al., leave our results² on the Tomonaga–Luttinger liquid in the Au/Ge(001) nanowires undisputed.