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FeSe with the PbO structure is a key member of the family of new high-$T_c$iron pnictide and chalcogenide superconductors, as while it possesses the basiclayered structural motif of edge-sharing distorted FeSe$_4$ tetrahedra, itlacks interleaved ion spacers or charge-reservoir layers. We find thatapplication of hydrostatic pressure first rapidly increases $T_c$ which attainsa broad maximum of 37 K at $\sim$7 GPa (this is one of the highest $T_c$ everreported for a binary solid) before decreasing to 6 K upon further compressionto $\sim$14 GPa. Complementary synchrotron X-ray diffraction at 16 K was usedto measure the low-temperature isothermal compressibility of $\alpha$-FeSe,revealing an extremely soft solid with a bulk modulus, $K_0$ = 30.7(1.1) GPaand strong bonding anisotropy between inter- and intra-layer directions thattransforms to the more densely packed $\beta$-polymorph above $\sim$9 GPa. Thenon-monotonic $T_c$($P$) behavior of FeSe coincides with drastic anomalies inthe pressure evolution of the interlayer spacing, pointing to the key role ofthis structural feature in modulating the electronic properties.

Pressure evolution of low-temperature crystal structure and bonding of 37 K $T_c$ FeSe superconductor