Among the iron-based superconductors, the structurally simplest FeSe and FeSe-derived materials have attracted enormous research interest recently due to its unusual electronic properties and the great tunability of the superconducting transition temperature <italic>T</italic><sub>c</sub>. For the bulk FeSe single crystal, it shows a relatively low <italic>T</italic><sub>c</sub><x content-type=symbol>»</x>8 K within the unusual nonmagnetic nematic phase below <italic>T</italic><sub>s</sub><x content-type=symbol>»</x>90 K. It has been reported that the application of high pressure can induce a long-range antiferromagnetic order below <italic>T</italic><sub>m</sub><x content-type=symbol>»</x>20 K at <italic>P</italic><x content-type=symbol>»</x>1 GPa, and then achieve a high <italic>T</italic><sub>c</sub><x content-type=symbol>»</x>37 K at <italic>P</italic><x content-type=symbol>»</x>8 GPa. It remains unclear how the high-<italic>T</italic><sub>c</sub> superconductivity is achieved in FeSe under pressure. In this regard, a detailed temperature-pressure phase diagram mapping out the exact relationship between the high-<italic>T</italic><sub>c</sub> superconductivity and the normal-state nematic order and the pressure-induced antiferromagnetic order is indispensable for achieving a better understanding. By taking advantage of the cubic anvil cell apparatus that can maintain an excellent hydrostatic pressure condition up to 15 GPa, we recently undertook a comprehensive high-pressure magnetotransport study on high-quality FeSe single crystals and obtained important results. In this article, we give a brief review on the recent progresses about the high-pressure studies of FeSe. By tracking the characteristic resistivity anomalies at the nematic order, the pressure-induced antiferromagnetic order, and the superconducting transition, we constructed for FeSe a comprehensive temperature-pressure phase diagram, which depicts explicitly the detailed evolution of these competing electronic orders. We observed a dome-shaped antiferromagnetic phase boundary <italic>T</italic><sub>m</sub>(<italic>P</italic>), and revealed the competitive relationship between these electronic orders. The superconducting <italic>T</italic><sub>c</sub> experiences two successive step increases at the critical pressures when the nematic order and the antiferromagnetic order are respectively suppressed, and finally the highest <italic>T</italic><sub>c</sub><sup>max</sup>=38.5 K is realized near <italic>P</italic><sub>c</sub>≈6 GPa when the antiferromagnetic order just collapses. We further measured the Hall effect of FeSe to extract the electronic structure information under high pressure. Our Hall data show that the Fermi surface of FeSe in the normal state undergoes a reconstruction at <italic>P</italic><x content-type=symbol>»</x>2 GPa, when the nematic order is suppressed and the antiferromagnetic order just emerges. The dominant charge carriers for the transport properties in the normal state change from the electron to the hole type. In addition, in the high-<italic>T</italic><sub>c</sub> phase near the optimal<italic> </italic><italic>T</italic><sub>c</sub><sup>max</sup> at <italic>P</italic><sub>c</sub><x content-type=symbol>»</x>6 GPa, the Hall coefficient experiences a dramatic enhancement and the magnetoresistance exhibits anomalous scaling behaviors, signaling the presence of strongly enhanced inter-band spin fluctuations. These results suggest that the critical antiferromagnetic fluctuations play an important role for achieving the high-<italic>T</italic><sub>c</sub> superconductivity in FeSe. Aided by the first-principles calculations, we further confirmed that both electron-like and hole-like Fermi surfaces are present in FeSe under high pressures, in favor of the Fermi surface nesting scenario as in the FeAs-based high-<italic>T</italic><sub>c</sub><italic> </italic>superconductors. These above results on FeSe suggest great similarities with other FeAs-based superconductors, and thus constitute an important step toward a unified understanding of iron-based superconductivity.
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