This paper reports first-principles calculations on nanosheets of Ge–Sb–Te compounds, namely \(\hbox {Sb}_{2}\hbox {Te}_{3}\) , \({\hbox {GeSb}_{2}\hbox {Te}_{4}}\) and \({\hbox {Ge}_{2}\hbox {Sb}_{2}\hbox {Te}_{5}}\) under two crystalline atomic stakings S1 and S2. \(\hbox {Sb}_{2}\hbox {Te}_{3}\) , \({\hbox {GeSb}_{2}\hbox {Te}_{4}}\) and \({\hbox {Ge}_{2}\hbox {Sb}_{2}\hbox {Te}_{5}}\) -S1 are semiconductors with a narrow band gap ranging between 0.7 and 0.74 eV as evaluated with the HSEsol functional. The transport properties have been investigated by Boltzmann transport theory together with deformation potential theory. The strain effects on their electronic and thermoelectric properties as well as on their dynamical properties have been investigated. A valence band convergence is found in the equilibrium structures, which is an efficient approach to improve the thermoelectric performance of materials. \(\hbox {Sb}_{2}\hbox {Te}_{3}\) , \({\hbox {GeSb}_{2}\hbox {Te}_{4}}\) and \({\hbox {Ge}_{2}\hbox {Sb}_{2}\hbox {Te}_{5}}\) -S1 possess high TE performance in a wide range of temperature, and the highest values of zT are 2.94, 2.63 and 2.27, respectively.
