Tl2Mo6Se6 and K2Cr3As3 crystallise in hexagonal structures with chains of Mo3Se3 or Cr3As3 triangular clusters, sometimes referred to as double-walled nanotubes. The number of guest ions (Tl and K, respectively), the transition metal valence and the crystal space group are different in the two compounds. The electronic structure of both materials is highly one-dimensional with a single Mo dband Fermi surface in Tl2Mo6Se6 and a multiband Fermi surface in K2Cr3As3. Both materials display superconducting instabilities below 7 K. In this seminar we present data of the direct observation of the one-dimensional Fermi surfaces by angle-resolved photoemission spectroscopy (ARPES), taken at temperatures just above the superconducting transition Tc. A characteristic depletion of spectral weight near the chemical potential yields evidence of an excitation spectrum characteristic of a Tomonaga- Luttinger liquid (TLL). The data are analysed by fits to the spectral function proposed by Schönhammer and Meden 
I (ε ,T )∝Tα cosh(ε / 2) Γ 1+α 2 +i ε 2π ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 f (ε ,T ),
where T is the temperature, e = E/kT is the energy with respect to the chemical potential, rescaled by T, f is the Fermi-Dirac occupation function and a is a scaling coefficient. Temperature-dependent data are fully consistent with universal scaling with constant a, thus supporting the TLL picture. These results are placed in the context of other uniaxial quasi-one-dimensional materials ZrTe3 and NbSe3, which show unambiguous evidence for charge density wave (CDW) formation  and a dimensional cross-over .
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Fig. Structures of Tl2Mo6Se6 and K2Cr3As3