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Thermoelectric technology is an alternate way to efficiently utilize theenergy by converting waste heat into electricity. Thermoelectric requiresmaterial with low thermal conductivity to improves its thermoelectricperformance. In this work, by solving Boltzmann transport equation based onfirst principles calculations, we report an ultra-low room temperature thermalconductivity of 2.08 Wm$^{-1}$K$^{-1}$ and 2.9 Wm$^{-1}$K$^{-1}$ along c-axisand a-axis respectively for pure MgPb$_2$Te. To explain this ultra-low thermalconductivity, we analyzed the elastic constants, phonon group velocity,phonon-phonon scattering and contribution from transverse acoustic,longitudinal acoustic and optical phonon branches. We also report the thermalconductivity of MgPb$_2$Te nanostructures. At 50 nm, the room temperaturethermal conductivity of MgPb$_2$Te is 0.957 Wm$^{-1}$K$^{-1}$ and 1.459Wm$^{-1}$K$^{-1}$ along c-axis and a-axis respectively. Ultra-low thermalconductivity unraveled in this work shows MgPb$_2$Te would a promising materialfor thermoelectric applications.

Ultra-low lattice thermal conductivity of MgPb$_2$Te -- A first principles study