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Petrović, Alexander P.
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article
Phonon mode spectroscopy, electron-phonon coupling, and the metal-insulator transition in quasi-one-dimensional M<sub>2</sub>Mo<sub>6</sub>Se<sub>6</sub>
Abstract
We present electronic-structure calculations, electrical resistivity data, and the first specific-heat measurements in the normal and superconducting states of quasi-one-dimensional M<sub>2</sub> Mo<sub>6</sub> Se<sub>6</sub> (M=Tl,In,Rb). Rb<sub>2</sub> Mo<sub>6</sub> Se<sub>6</sub> 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, Tl<sub>2</sub> Mo<sub>6</sub> Se<sub>6</sub> and In<sub>2</sub> Mo<sub>6</sub> Se<sub>6</sub> remain metallic down to low temperature, with superconducting transitions at T<sub>c</sub> =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 D<sub>E<sub>F</sub></sub>=0.055 states eV<sup>-1</sup> atom<sup>-1</sup>, with BCS fits showing 2Δ/ k<sub>B</sub> T<sub>c</sub> 5 for Tl<sub>2</sub> Mo<sub>6</sub> Se<sub>6</sub> and 3.5 for In<sub>2</sub> Mo<sub>6</sub> Se<sub>6</sub>. 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 α<sup>tr</sup><sub>2</sub> F (ω). In Tl<sub>2</sub> Mo<sub>6</sub> Se <sub>6</sub> and In<sub>2</sub> Mo<sub>6</sub> Se<sub>6</sub>, F (ω) is dominated by an optical "guest ion" mode at ∼5 meV and a set of acoustic modes from ∼10 to 30 meV. Rb<sub>2</sub> Mo<sub>6</sub> Se <sub>6</sub> exhibits a similar spectrum; however, the optical phonon has a lower intensity and is shifted to ∼8 meV. Electrons in Tl<sub>2</sub> Mo<sub>6</sub> Se<sub>6</sub> couple strongly to both sets of modes, whereas In<sub>2</sub> Mo<sub>6</sub> Se<sub>6</sub> 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 Tl<sub>2</sub> Mo<sub>6</sub> Se<sub>6</sub>, given its extraordinarily large coupling strength and higher T<sub>c</sub> compared to In<sub>2</sub> Mo <sub>6</sub> Se<sub>6</sub>.