  Superconductivity (SC) in so-called "unconventional superconductors" is
nearly always found in the vicinity of another ordered state, such as
antiferromagnetism, charge density wave (CDW), or stripe order. This suggests a
fundamental connection between SC and fluctuations in some other order
parameter. To better understand this connection, we used high-pressure x-ray
scattering to directly study the CDW order in the layered dichalcogenide TiSe2,
which was previously shown to exhibit SC when the CDW is suppressed by pressure
[1] or intercalation of Cu atoms [2]. We succeeded in suppressing the CDW fully
to zero temperature, establishing for the first time the existence of a quantum
critical point (QCP) at Pc = 5.1 +/- 0.2 GPa, which is more than 1 GPa beyond
the end of the SC region. Unexpectedly, at P = 3 GPa we observed a reentrant,
weakly first order, incommensurate phase, indicating the presence of a Lifshitz
tricritical point somewhere above the superconducting dome. Our study suggests
that SC in TiSe2 may not be connected to the QCP itself, but to the formation
of CDW domain walls.
