  In this article, we study non-trivial topological phase and electron-hole
compensation in extremely large magnetoresistance (XMR) material YSb under
hydrostatic pressure using first-principles calculations. YSb is topologically
trivial at ambient pressure, but undergoes a reentrant topological phase
transition under hydrostatic pressure. The reentrant behavior of topological
quantum phase is then studied as a function of charge density ratio under
pressure. From the detailed investigation of Fermi surfaces, it is found that
electron to hole densities ratio increases with pressure, however a non-trivial
topological phase appears without perfect electron-hole compensation. The
results indicate that the non-trivial topological phase under hydrostatic
pressure may not have maximal influence on the magnetoresistance, and need
further investigations through experiments to determine the exact relationship
between topology and XMR effect.
