  The effect of Lifshitz transition on thermodynamics and superconductivity in
hole-doped cuprates has been heavily debated but remains an open question. In
particular, an observed peak of electronic specific heat is proposed to
originate from fluctuations of a putative quantum critical point p* (e.g. the
termination of pseudogap at zero temperature), which is close to, but
distinguishable from the Lifshitz transition in La-based cuprates. Here, we
report an in situ angle-resolved photoemission spectroscopy study of
three-dimensional Fermi surfaces in La2-xSrxCuO4 thin films(x = 0.06 - 0.35).
With accurate kz dispersion quantification, the Lifshitz transition is
determined to happen within a finite range around x = 0.21. Normal state
electronic specific heat, calculated from spectroscopy-derived band parameters,
agrees with previous thermodynamic microcalorimetry measurements. The account
of the specific heat maximum by underlying band structures excludes the need
for additionally dominant contribution from the quantum fluctuations at p*. A
d-wave superconducting gap smoothly across the Lifshitz transition demonstrates
the insensitivity of superconductivity to the dramatic density of states
enhancement.
