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Atomic nanowires on semiconductor surfaces induced by the adsorption of metallic atoms have attracted a lot of attention as possible hosts of the elusive, one-dimensional Tomonaga-Luttinger liquid. The Au/Ge(100) system in particular is the subject of controversy as to whether the Au-induced nanowires do indeed host exotic, 1D metallic states. In light of this debate, we report here a thorough study of the electronic properties of high quality nanowires formed at the Au/Ge(100) surface. The high resolution ARPES data show the low-lying Auinduced electronic states to possess a dispersion relation that depends on two orthogonal directions in k-space. Comparison of the E(kx,ky) surface measured using high-resolution ARPES to tight-binding calculations yields hopping parameters in the two different directions that differ by a factor of two. Additionally, by pinpointing the Au-induced surface states in the first, second and third surface Brillouin zones, and analysing their periodicity in k || , the nanowire propagation direction seen clearly in STM can be imported into the ARPES data. We find that the larger of the two hopping parameters corresponds, in fact, to the direction perpendicular to the nanowires (tperp). This, the topology of the E=EF contour in k || , and the fact that t || /tperp∼0.5 proves that the Au-induced electron pockets possess a two-dimensional, closed Fermi surface, and this firmly places the Au/Ge(100) nanowire system outside potential hosts of a Tomonaga-Luttinger liquid. We combine these ARPES data with scanning tunneling spectroscopic measurements of the spatially-resolved electronic structure and find that the spatially straight -wire-like -conduction channels observed up to energies of order one electron volt below the Fermi level do not originate from the Au-induced states seen in the ARPES data. The former are rather more likely to be associated with bulk Ge states that are localized to the subsurface region. Despite our proof of the 2D nature of the Au-induced nanowire and sub-surface Ge-related states, an anomalous suppression of the density of states at the Fermi level is observed in both the STS and ARPES data, and this phenomenon is discussed in the light of the effects of disorder.

Pumping a finite energy density into a quantum system typically leads to 'melted' states characterized by exponentially-decaying correlations, as is the case for finite-temperature equilibrium situations. An important exception to this rule are states which, while being at high energy, maintain a low entropy. Such states can interestingly still display features of quantum criticality, especially in one dimension. Here, we consider high-energy states in anisotropic Heisenberg quantum spin chains obtained by splitting the ground state's magnon Fermi sea into separate pieces. Using methods based on integrability, we provide a detailed study of static and dynamical spin-spin correlations. These carry distinctive signatures of the Fermi sea splittings, which would be observable in eventual experimental realizations. Going further, we employ a multi-component Tomonaga-Luttinger model in order to predict the asymptotics of static correlations. For this effective field theory, we fix all universal exponents from energetics, and all non-universal correlation prefactors using finite-size scaling of matrix elements. The correlations obtained directly from integrability and those emerging from the Luttinger field theory description are shown to be in extremely good correspondence, as expected, for the large distance asymptotics, but surprisingly also for the short distance behavior. Finally, we discuss the description of dynamical correlations from a mobile impurity model, and clarify the relation of the effective field theory parameters to the Bethe Ansatz solution. SciPost Physics SubmissionA Simplification for symmetric seas 23 B Moses states and generalized TBA 24 C Perturbative expressions for effective-field-theory parameters 24References 25

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