Phonon mode spectroscopy, electron-phonon coupling, and the metal-insulator transition in quasi-one-dimensional M2Mo6Se6

We present electronic-structure calculations, electrical resistivity data, and the first specific-heat measurements in the normal and superconducting states of quasi-one-dimensional M2Mo6Se6 (M=Tl,In,Rb). Rb2Mo6Se6 undergoes a metal-insulator transition at ∼170 K: electronic-structure calculations indicate that this is likely to be driven by the formation of a dynamical charge-density wave. However, Tl2Mo6Se6 and In2Mo6Se6 remain metallic down to low temperature, with superconducting transitions at Tc=4.2 K and 2.85 K, respectively. The absence of any metal-insulator transition in these materials is due to a larger in-plane bandwidth, leading to increased interchain hopping which suppresses the density wave instability. Electronic heat-capacity data for the superconducting compounds reveal an exceptionally low density of states DEF=0.055 states eV−1 atom−1, with BCS fits showing 2Δ/kBTc≥5 for Tl2Mo6Se6 and 3.5 for In2Mo6Se6. Modeling the lattice specific heat with a set of Einstein modes, we obtain the approximate phonon density of states F(ω). Deconvolving the resistivity for the two superconductors then yields their electron-phonon transport coupling function αtr2F(ω). In Tl2Mo6Se6 and In2Mo6Se6, F(ω) is dominated by an optical "guest ion" mode at ∼5 meV and a set of acoustic modes from ∼10 to 30 meV. Rb2Mo6Se6 exhibits a similar spectrum; however, the optical phonon has a lower intensity and is shifted to ∼8 meV. Electrons in Tl2Mo6Se6 couple strongly to both sets of modes, whereas In2Mo6Se6 only displays significant coupling in the 10-18 meV range. Although pairing is clearly not mediated by the guest ion phonon, we believe it has a beneficial effect on superconductivity in Tl2Mo6Se6, given its extraordinarily large coupling strength and higher Tc compared to In2Mo6Se6.