The Zintl compound TlInTe2 is an intriguing material because of its outstanding thermoelectric properties at ambient pressure. Interestingly, it has recently been found that TlInTe2 exhibits a V-shape dependence of the superconducting critical temperature (T c) under increasing pressure, which has been linked to the reversed behavior of the Raman active Ag phonon mode and anharmonic effects. In this study, we have performed first-principles calculations of the electron-phonon interactions and the superconducting properties of TlInTe2 in order to understand this unusual pressure-induced response. In contrast to experiment, we find a dome-shaped pressure-induced dependence of T c with a maximum value of 0.23 K at 18 GPa, significantly lower than the experimental results. Electron doping has the potential to adjust the T c to fall within the experimental range, but it necessitates considerably high levels of doping. Furthermore, our analysis of the phonon spectra and phonon lifetimes, including anharmonic effects, show that anharmonicity is unlikely to influence the superconducting properties of TlInTe2. It remains an open question whether there is indeed an unusual V-shape T c dependence with pressure or whether the phonon-mediated theory of superconductivity used here breaks down in this system.
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