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

To the Editor

One-dimensional (1D) metals show unique characteristics as a Tomonaga–Luttinger liquid (TLL). Blumenstein et al.¹ claimed recently that the density of states at Au-induced chains on a Ge(001) surface exhibits a power-law behaviour that is characteristic to a TLL on the basis of their measurements by scanning tunnelling spectroscopy and angle-resolved photoemission spectroscopy (ARPES). In this Correspondence, we present the following three pieces of evidence from ARPES^2,3 and scanning tunnelling microscopy⁴ against the presence of a 1D metal in the direction of the Au-induced chain.

(1) Our recent ARPES study for a single-domain surface³ demonstrated that the observed metallic surface band^1,2,5,6,7 disperses strongly in the direction perpendicular to the Au-induced chain.

(2) The ARPES results^2,3 indicated that the shape of the metallic band is 2D and anisotropic.

(3) An eightfold charge modulation along the Au-induced chain was observed by scanning tunnelling microscopy⁴ in the bias voltage range where the surface metallic band exists.

It is possible that the quasi-1D band shape close to the Fermi energy in the direction perpendicular to the chain gives the observed TLL-like behaviour¹ of the density of states in a limited energy range.