  Tuning superconductivity in topological materials by means of chemical
substitution, electrostatic gating, or pressure is thought to be an effective
route towards realizing topological superconductivity with their inherent
Majorana fermions, the manipulation of which may form the basis for future
topological quantum computing. It has recently been established that the
pseudo-binary chalcogenides (ACh)m(Pn2Ch3)n (A = Ge, Mn, Pb, etc.; Pn = Sb or
Bi; Ch = Te, Se) may host novel topological quantum states such as the quantum
anomalous Hall effect and topological axion states. Here we map out the phase
diagram of one member in this series, the topological insulator candidate
GeSb4Te7 up to pressures of ~35 GPa, through a combination of electrical
resistance measurements, Raman spectroscopy, as well as first-principles
calculations. Three distinct superconducting phases emerge under the pressure
above ~11, ~17, and ~31 GPa, which are accompanied by concomitant structural
transitions, evidenced from the changes in the Raman modes. The
first-principles calculations validate the existence of a topological
insulating state at ambient pressure and predict two possible structural
transitions at 10 and 17 GPa, in agreement with the experimental observations.
Overall, our results establish the GeSb4Te7 family of materials as a fertile
arena for further exploring various topological phenomena, including
topological phase transitions and putative topological superconductivity.
